A FLEXIBLE SIMULATION MODEL
OF
AIRPORT AIRSIDE OPERATIONS
by
JOHN PHILIP NORDIN
B.S., Michigan State University
(1976)
of Technology
S.M., Massachusetts Institute
(1978)
SUBMITTED IN PARTIAL
FULFILLMENT
OF THE
OF THE REQUIREMENTS
DEGREE OF
DOCTOR OF PHILOSOPHY
CIVIL
IN
ENGINZERING
at the
MASSACHUSETTS INSTIiTUTE
August
©
John
OF TECHNOLOGY
1980
Philip Nordin 1980
The author hereby grants to M.I.T. permission to reproduce
and to distribute copies of this thesis document
or in part.
in whole
Signature of Author
I3
'
Certified
I
Department
of Civil Engineering
August
29, 1980
by _
0)
Amiedeo R. Odoni
'IAis Supervisor
Departmental
Graduate Committee
J.
Accepted by
. _
AMMIts
IIIUTE
MASSACHUSETTST
OFTECHNa[lrman,
OCT 9
1980
v
NOTICE: THISM
AL AY BE
PROTECTEDYCOPYRIt
LAW
(TITLE17 US CO)
2
Abstract
A Flexible Simulation Model of Airport Airside Operations
by
John Philip Nordin
Submitted to the Department of Civil Engineering on
August 22, 1980 in partial fulfillment of the
requirements for the degree of Doctor of Philosophy
The expanding problem of
airport congestion emphasizes
the need for general purpose models of airport performance.
Previous-efforts to develop simulations that could analyze a
have not been entirely
wide range of airport geometries
not treat
models could
The
resulting
satisfactory.
This work
analysis.
in airport
significant problems
develops, from a new foundation, a flexible simulation model
A number of contributions are made
of airport operations.
A new method for
to modeling of airport performance.
is developed which avoids
describing the demand for service
A procedure for
a significant bias of existing methods.
of the effect
analysis
permits
operations
modeling landing
of exit location on overall airport congestion. Methods for
separating aircraft are developed which can describe the
of the airport with greater accuracy than
actual behavior
previous models
operating
and methods for
policies in
response to
modeling
weather and
changes
in
congestion
also are developed. Numerous additional optional provisions
and the overall design of the model offer flexibility to the
These
efficiency.
improve computational
analyst and
expanded capabilities permit the wide use of the model not
only in analyzing existing conditions but also in studies of
Tests of the model against
of airports.
optimal design
to be
show this model
models
airport
several other
satisfactory. This study of airport operations and modeling
techniques
has also
resulted in
the
identification of
numberof important topics for future research.
Thesis Supervisor:
Amedeo R Odoni
Titl e:
Professor in Aere & Astro
a
3
ACKNOWLEDGEMENTS
I wish to thank Professor Amedeo Odoni, Department of
Aeronautics and Astronautics, I.I.T., for his advice and
direction as my advisor over the last three years. His
painstaking and prompt reading of each draft of this work was
greatlyappreciated.Professor
Robert Simpson, Department of
Aeronautics and Astronautics, M.I.T. gave valuable advice
basedon his extensive
knowledge of airport
operations.
Professor Nigel Wilson, Department of Civil Engineering,
M.I.T., asked many difficult questions, which hopefully have
now been answered. Professors Odoni, Simpson and Wilson
are also to be thanked for serving on my Ph.D. committee.
Professor William Dunsmuir, Department of Mathematics,
M.I.T., was generous with his time and helped with a number
of statistical questions. Professor L.E. Grosh, Department
of Industrial Engineering, Kansas State University, provided
guidance to the simulation literature and loaned me a number
of items out of his personal library which were unavailable
at M.I.T. Mr. William Hoffman, Flight Transportation
Associates,
Cambridge,
Massachusetts, helped in defining the
case study in Chapter IV.
Mr. Art Anger, Information Processing Center (IPC),
M.I.T., provided uniquely accurate and unfailingly friendly
advice on programming questions. Mr. Joseph Connors, Director of Purchasing, IPC, helped me obtain several important
items.
Mr. Joe Hevey
and all the employees
of User Accounts,
IPC, have given me excellent and friendly service these past
four years. Ms. Victoria Murphy, Graduate Program Administrator, Department of Civil Engineering was extremely indulgent with deadlines and provided good advice about the thesis
requirements.
Mr. Harold Clark, Department of Materials Science, M.I.T.
applied his amazing command of English grammer to greatly
improve the readability of this work. Ms. Marjorie Shane,
Department of Chemistry, M.I.T., assisted with figure preparation, insured continuity and generally cleaned up what the
texteditorcouldnt handle.
came her natural
My wife, Barbara Grosh, over-
antipathy to typing and performed excellently
as "data entry operator". as well as acting as general editor
and stylistic critic. I incurred a large debt to her which I
expect to repay in several years when she finishes her Ph.D.
thesis. A great deal of thanks goes to Dr. Linda Anthony,
Bell Laboratories, Murray Hill, New Jersey, for all of her
"thesis stories" and for proving that it was possible to complete a Ph.D. thesis.
And finally, I wish to acknowledge whoever it is that manufactures fortune cookies for causing me to receive the following fortune during the final weeks of my thesis: "Work hard
and you will achieve your goals."
4
TABLE
OF CONTENTS
Page
Abstract
...............................................
Acknowledgements
...................................
3
Table of Contents ...............................
4
List of Figures ...............................
7
List of Tables .......................................
10
Chapter I.
12
Introduction..............................
A. The Problem of Modeling Airport
Operations
...............
.....................
12
B. Approachesto Modeling Airport
Operations
. .....................
.............. 14
C.
D.
Contributions
to Modeling
Airport Operations .............................
16
Overview of Chapters II
Through V ...................................
20
Chapter II.
Model Structure
........................
A.
Major Issues ..................................
B.
Airfield
Geometry
Operations ...........
1.
Introduction
23
23
and Ground
..........................
.........
2. Description of airfield
3.
C.
Geometry
..............................
Ground operations
Demand for Service ...........................
1. Introduction
............................
attributes....................
28
32
42
42
44
3.
Aircraft
4.
Modeling the level of demand ............
61
5.
Comparison of the methods
of-demand generation.....................
73
47
Runway Operations .............................
1.
Introduction.........................
2.
Aircraft
83
83
performance on landing
3. Aircraft performance
E.
27
....
........................
2. Present schedule algorithms ...............
D.
27
.....
85
on takeoff...........
111
4. Separation of aircraft movements ..........
Dependent Runway Opeartions...
113
138
1'.
Introduction.
138
2.
Intersecting runways ......................
140
5
F.
G.
3.
4.
Parallel runways ..........................
Projected intersecting runways............
5.
Assignment
runways...................................
156
6.
7.
Special problems .........................
Comparison of separation
163
Control of the Airport ........................
1.
Introduction.............................
177
177
B.
to
methodologies
..........................
2.
Weather ...................................
3.
Congestion
4.
Other
.
factors.............................
Statistical
D.
Chapter
...
186
190
Issues in Modeling
191
1.
Introduction..............................
2.
Survey of statistical issues
relevant to simulation
....................
191
3.
Selection of simulation outputs...........
209
191
ModelValidation.........................
The Problem of Validation ....................
Test Case: La Guardia ......................
1. Comparison to FAA capacity
analysis...................................
C.
170
178
....................
Airport Operation..........................
s
Chapter III.
A.
of aircraft
149
154
215
215
221
221
2. Comparison with ASM and MITASIM ...........
229
Test
244
Case:
Bromma Airport...................
1.
Case description.........................
244
2.
Discussion of results .....................
251
Conclusions ...................................
IV.
Example of Model Application
256
..............
257
A.
Introduction..................................
257
B.
The Airport.................................
258
C.
Description of Operating Policies .............
262
D.
Characteristics
267
1.
2.
3.
E.
F.
of Demand
..............
Aircraft classes.........................
Aircraft performance ....................
Aircraft mix ..............................
Air Traffic Control Rules ....................
Input Requirements
.........................
1. Summary of input requirements .............
2. Comparison of input requirements ..........
267
268
268
270
275
275
276
6
G.
Capacity Analysis............
1. VFR results.............
2.
H.
IFR results..............
Delay Analysis...............
1. Case description ........
2.
Discussion
................. 280
.................
.................
280
290
292
.
... .. ........... 292
of results....
.................
297
I. Model Properties .............
.................
301
1. Sensitivity Analysis..... ................. 301
2. Computational Efficiency.
.................
303
J. Conclusions...............
Chapter V.
.................
Summary and Conclusions... .................
A.
Review ....................... .................
B.
Further Work.................
.................
1. Needed research.........
305
307
307
311
311
2.
Potential uses for FLAPS. ................. 314
3.
Extensions
to FLAPS......
Bibliography
.....................
.................
319
..321
Biographical Note ...................................... 325
.
7
LIST OF FIGURES
Page
Figure No.
II-1.
New York La Guardia:
Airport Map............
29
II-2.
New York La Guardia:
ASM Modeling Geometry ........................
30
II-3.
Selection of Aircraft Attributes .............
60
II-4.
Rate Function
II-5.
Rate Function and Integrated Rate
................................
62
Function .....................................
66
II-6.
Summary of Nomenclature ......................
68
II-7.
Numerical Example ............................
72
II-8.
Comparison of Schedule Generation
Methods: Parameters .........................
80
............................
84
II-9.
Runway Operations
II-10.
Landing Aircraft Profile.....................
90
II-11.
Interrelationships of Aircraft
Floating Phase Parameters ....................
95
Effect of Va on Floating Phase
Parameters ...................................
97
II-12.
II-13.
Arrival/Arrival Separations:
Closing Case ................................
121
II-14.
Arrival/Arrival Separations:
Opening Case................................. 123
II-15.
Separations for Mixed Operations
on a Single Runway...........................
II-16.
Dulles International Airport,
Washington,
II-17.
130
D.C
...
........................ 141
Intersecting Runway Departure
Operations ...................................
144
II-18.
Mixed Operations on Intersecting
Runways ...................................... 145
II-19.
Airports with Projected Intersecting
Runways...................................... 155
8
List of Figures, continued
Page
Figure No.
11-20.
Displaced Runway Thresholds..................
164
II-21.
Hold Short Arrivals.........................
167
II-22.
Distribution of Average Delay................
204
11-23.
Distribution of Number of
III-1.
Landings....................................
La Guardia:
205
FLAPS Geometry
...............................
Representation
222
111-2.
La Guardia Configurations ....................
224
111-3.
Sensitivity
III-4.
Sensitivity Run 2A:
Run 1A:
Base Case...............
234
Group 2
Separations
.................................
235
111-5.
Sensitivity
Run 3A:
III-6.
Sensitivity
Case 7A:
III-7.
Sensitivity Case 8A:
111-8.
Bromma:
Demand Profile .....................
248
III-9.
Bromma:
Demand Functions ...................
250
III-10.
Bromma Airport:
400 op./day.................
253
III-l.
Bromma Airport:
600 op./day.................
254
II-12.
Bromma Airport:
800 op./day ................
255
IV-1.
Boston Logan Airport.........................
259
IV-2.
Logan Airport:
FLAPS Geometry
. .........................
Reprewentation
264
IV-3.
Logan Configurations.........................
266
IV-4.
Logan VFR Capacity Input Fil
IV-5.
Interpolation-Extrapolation Method
for "Percentage Arrival" Capacity
.......
Separations
Group 4
...........................236
Q = 24..................
237
Q=
238
...................
Le................
Estimation
...................................
277
288
9
List of Figures, continued
Figure No.
Page
IV-6.
Logan Delay Configurations..................
294
IV-7.
Logan Delay Cases:
Demand Function ..............................
295
Logan Delay Cases:
Summary of Parameter Changes.................
296
Logan Delay Cases:
Landing Delay...............................
298
Logan Delay Cases:
Takeoff Delavy.........9.....................
299
IV-8.
IV-9.
IV-10.
10
LIST OF TABLES
Page
Table II-1.
Table 11-2.
Probabilistically Generated
Schedules ................................
76
Base Method Schedules....................
77
Table11-3. Comparison of Schedule Generation
Method:
Results .......................
.................
81
Table 11-4.
Float Phase Parameters
Table II-5.
Landing Model Validation:
Common Parameters ........................
106
Landing Model Validation:
Case Description ......
107
1.................
Table 11-6.
Table 11-7.
Table 11-8.
Table 11-9.
Table II-10.
92
Landing Model Validation:
Results
............
......................
109
Terms used in Derivation of
Separations ............................
122
Arrival/Arrival Separations:
Typical Values ........................
126
Departure/Departure
Separations:
Typical Values.......................
129
Table II-11.
Terms used for MixedOperation
Separations.............................
131
Table 11-12.
Mixed Operations:
Summary of
Rules......................................
~Rules
Table 11-13.
Dependent Runway Nomenclature............
Table 11-14.
Normality Test:
Table III-1.
La Guardia Validation:
Capacity Parameters.......2............
Summary Results ..
~~..
137
*
139
2.....
202
225
Table III-2.
La Guardia Validation:.
Capacity
Results.................
2...
226
Table 111-3.
Sensitivity Runs: Parameters .............
232
Table
Sensitivity
III-4.
Runs:
Summary Statistics......................
239
11
List of Tables, continued
Table III-5. Average Departure Queue Length
Statistics .............................
242
Table III-6.
Practical Separation Minima at
Bromma Airport .......................... 245
Table III-7.
FLAPS Equivalent Separations ............. 247
Table III-8.
Bromma: Summary Comparison
of Results ............................... 251
Table IV-1.
Logan Airport: Geometry Elements ......... 261
Table IV-2.
Logan Airport: Runway Modules ............
Table IV-3.
Assumed Aircraft Performance
Parameters
Table IV-4.
Table IV-5.
.............................
263
269
Logan Airport: Aircraft Mix
and Runway Assignment ....................
271
Logan Airport: Separation
Parameters ............................
272
Table IV-6.
Air Traffic Control Dependencies......... 274
Table IV-7.
Logan VFR Results
Table IV-8.
IFR Capacity Estimates.................
.......................
282
291
12
I
INTRODJC TI
ON
A
THE PRO-ELE4 0F i40DELIG
In
the
several
late
major
attention.
AIRPORT
1960's
air
OPERATIONS
severe
carrier
congestion
airports
attracted
at
national
This problem eventually receded due, in part, to
wide-body jets reducing the number
the
problems
economic
slowdown
of the
of flights needed and to
mid-i970's.
Following the
demandsurge of 1978, however, reports are being heard with
increasing
of
freq~uency and from a
a rising
incidence
of conges ion and delay (LEF 80).
example, delays of 50 minutes
Angeles from
growing number of locations
the first half
1978 (SWE 79 p.1-1 ).
or more increased
of 1977
States airport
prevalence of
delays is cited
The
from December 1973
significantly the
over
to
system from 1973
growth (SWE 79 p.1-1 ).
by 8
to the first
Delays of 30 minutes
from3 to 6 per thousand operations
300
1979
For
at Los
half of
or more increased
the entire
(ATS
United
1980).
as one restraint
The
on airline
increase of airline fuel costs
to December 1979 (ATW 80)
cost of forcing
aircraft to
raises
fly holding
patterns while waiting to land.
The significance
makes
apparent
performance
as
the
a
of the problem of
necessity
function
of
for
modeling
demand
capabilities of airport facilities.
airport congestion
for
airport
service
and
Delay and congestion,
13
of course, are
caus3ed by 7m any different
and it will
factors,
require action on several fronts to control them.
any significant
to
be assessed
ciange
as
in the
to its
before implementation.
airport
on airport
impact
Because of
will have
performance
the complex
nature of
resources nece3sary to implement
airports and the amount of
it would seem obvious that
all but the most modest change,
careful mathematical
environment
However,
modeling of
the consequences of each
proposed change would be necessary.
The
modeling
of
performance
airport
poses
interesting challenge to transportation analysts.
like other complex transportation facilities,
behave
in
simple
or
intuitively
an
Airports,
do not always
obvious
fluctuating
loads. The factthat each airport
ways
under
is different
same generic components and is
despite bein, made up of the
subject to different loads, complicates the analysis.
Flows
of aircraft intersect which makes it difficult to accurately
analyze portions of the
airport independently.
the capacity of one flog of
Increasing
aircraft may have the effect of
restricting other flows that must be fitted between aircraft
of the first flow.
Analysis can not be confined
state
results but
airport.
must model
to predictions of steady-
the dynamic
aspects of
Demand for service is strongly time-varying.
characteristics of aircraft using the
significantly over the course of a lay.
the
The
airport may also vary
14
Another level
the fact
change
of analytical problems is
that the
during a
runways in
day.
use,
aircraft can
rules under
and
which airports
Priorities
response to
operate can
of various
inimum separations
vary in
introduced by
operations,
permitted between
weather,
congestion
or
equipment failures.
While the airport
with attention
must be modeled
airport.
and
information is
results but about performance
time period and at
each major facility
of the
The need is for analytical tools that predict the
performance
average
its entirety
to its dynamic environment,
needed not only about overall
during each
in
of
an
number of
number of
airport (average
aircraft waiting
operations)
flow rates,
types of
change in performance
under a
delay,
to
as
due to altering
delay,
takeoff and
variety of
aircraft)
peak
land,
loads (aircraft
well as
estimate the
the number
or type of
facilities or the rules for the use of facilities.
B
APPROACHES TO MODELING AIRPORT OPERATIONS
A number of
of predicting
approaches have been taken
the performance of
to the problem
the airside
of airports.
These approaches have included analytical capacity and delay
formulas,
special
purpose
simulations
tailored
particular airport and general purpose simulations.
an airfield simulation, "general purpose",
to
one
We term
or "flexible" if
15
operating
range of airport geometries,
it can model a wide
rules and service patterns.
a general purpose simulation
Of the three approaches,
The tradeoffs between
has the widest potential usefulness.
established (TEI
analytical models are well
simulation and
66 p.724, SHA 75 pp.10-13, FTIS 7
advantages of
a simulation
p.4-5).
One of the major
models is
over analytical
the
capability of a simulation to model the transient conditions
are an inherent part of
and changes in operating rules that
A simulation can
the questions to be analyzed at airports.
also accurately
model special situations
approximated by
analytical approaches.
a series
compared to
analysis
simulation.
for
of special
provide the same
together might
purpose
imply
also
would
simulation
answers
A
general purpose
cost
significant
savings
purpose simulations
widespreai
to
performance
airport
in
desire
questions
related
model would
that
the general
capability as
The
a general purpose
insures that
only be
that can
have extensive
application.
Efforts to develop a model flexible enough to analyze a
wide range of airport geometries and operating policies have
been only partially sucessful.
Only one model developed by
Peat, Marwick, Mitchell and Company for the FAA was intended
to be truly general purpose (HOC 77, PMM 77, BAL 76).
This
model
simulation
is
commonly
o;del or ASM.
referred
to
Unfort.unately,
as
the
this
airfield
mnolei,
an
16
evolutionary
lescendant
ten years ago,
of a model first
was designed to examine only a limited
It requires nuc'
of operating policies.
to be performed externally
fundamental design,
and cost
specific
developed more than
the model.
analysis
Because
of its
using the ASi4 model imposes large time
re-uliremaets
features
to
iportant
range
on the user
of the
(OR 78
pp.34-
AS4 model that
60
).
he
support
this
conclusion are discussed in detail in chapter II below.
C
CONTRIBUTIONS
0? THIS3 WORK TO
This work develops
analyzing
performance
a flexible
ODELING AIRPORT OPERATIONS
tool
related issues
directed towards meeting
for
genera]
use in
at airports.
the needs of airport
It is
analysis and
overcoming the serious limitations of existing models.
The model
follows the
movement of
aircraft from
the
start of final approach throug-hlanding and ground movements
then to the
point
of clearing
the runway
on takeoff.
For
convenience it is referred to in this document as FLAPS, for
FLexible AirPort Simulation.
to strive
for
significant
The objective of this work was
advances in the
modeling of
airport operations in order to achieve a comprehensive model
that is both theoretically correct
and economical enough to
reduce the cost of such analysis to feasible levels.
The model that was developed, implemented and validated
here extends ,the modeling of airport operations
to include
17
following aspects of the
1 ) The effect
over the
switch
ynamics of airport
of
course
irection
a
ay.
of operation
on any given runway.
represent
an entire
during
of
a single
run
course
capabilities
additions
to
minimize delay.
to
to
balance
conflictin,
be an input for
use in the
Aircraft
held constant
analysis be
the
over
resultin
general purpose
rules to
are often given runway assignments
lengths.
over the
queues
flows of aircraft.
landing
II.D.)
The
aircraft movements
long
limited
exit type and
of dynamically chilaningoperating
traffic controllers
eliminate
of
performance of
model and
queue
Previoai
II.F).
the
(See section
The impact
because
exit location,
runway
to
ay's operation
models req-uiredthat this
externally
performance
in
exits on
Previous
performed
model.
of changes
of new
aircraft.
3)
in this area (see section
The impact
being able
This includes
to
the
operation:
of changes of the rnways used for oerations3
models were not able
2)
model the
time in a general purpose simulation
for the first
relative
are
often
course of a
and take
advantage
priorities
altered by
day in
of
of
air
order to
gaps in
the
Previous models require such rules to be
the duration
of a run.
18
4)
The effect of wind spee-
and direction
nd rainfall
aircraft performance.
Jeather has a major impact
the rules
of
aircraft
above,
model
5)
of operation
airports
and the
but it has not been explicitly
the analysis
had to be performed
on both
performance
modeled.
on
of
As in (2)
to the
externally
and input.
The interaction of
logic.
aircraft performance and separation
did
Previous models
involving aircraft
not
accurately handle
on two different
cases
runways where
the air
traffic control separation is based
on aircraft clearing an
intersection
runway.
or exiting
from
the
(See
section
II.E.)
6)
Expanded
schedules.
techniques
Included
technique of using
for
in
generation
FLAPS
are
a base schedule and
way of generating schedules.
both
or
aircraft
the
standard
a new probabilistic
As explained in section iI.C,
the two techniques have different underlying assumptions.
The base schedule method is suitable for short term analysis
whereas
the
probabilistic
term prediction.
method
is more
suited for
The inclusion of the second method expands
the type of problems that can be analysed.
facilitates
long
analysis
of the effect of changes
aircraft using the airport over the
capability permits
This new method
in the type of
course of a day.
the analysis of operating
This
policies such
19
as
restrictions
on
general
av.ation
of
a simple
method
aircraft
at
peak
periods.
7)
Proposition
operations of
actual
aircraft.
taxiing
movements.
delay
This
of
metnod
modeling
an
without detailed
ground
approximate the
modeling
of
such
Previous models used an extremely complex method
of modeling taxiing operations.
8)
Collection and
outputs
to
computation of a full
support
hypotheses.
statistical
set of necessary
testing
This includes disaggregate
of
various
as well as summary
statistics and time series outputs.
The
inclusion
in
dynamics indicated
precision of the
significant
a
eneral
purpose
above results in
overall estimates of performance
expansion
in
(1) to (3)
that can be
studies,
used,
but
to
of
an enhancement
the types of policies
analyzed compared to previous models.
of points
model
the
of the
and in a
that can be
The aggregate effect
above is that a model is now available
not only for overall
assess various
capacity and delay
dynamic
strategies
for
managing congestion at the airport.
The
model
simulation.
not result in
has
The
been
mplemented
as
an
event
increased capabilities of this
an increase in the resources
based
model did
requires to use
20
the model compared to previous
New techniques for
geometry elements
specifying airfield
section II.B)
models.
that result in a
were developed
reduction
of about
(see
75
in
resources requirel to prepare and use the simulation.
D
OVERVIE-W O
CAPERS
Chapter II
II THROUG
contains
V
a detailed
various problems in the analysis
discussion
of airport
of the
operations.
Becausethe set of issues that arise in modelingairports is
large,
chapter I
is organized on a topic-by-topic basis.
Thus there is no separate review of previous work.
this
material,
discussed
model.
primarily
in parallel
After the
topic are reviewed,
with
the
the
existing
ASM
the portion
model,
presentation of
problems associated
Rather,
with a
the
is
new
particular
of FLAPS dealing with that
topic is described.
A satisfactory degree of confidence
FLAPSwas achieved by several
approaches.
the assumptions used in FLAPS is
introduced.
was tested
give good
observed
The validity
of
defended as they are
The important landing performance sub-section
independently
results.
FLAPS were
in the validity of
on two sets
Estimates of
compared to estimates
data.
These
of data and
capacity and
found to
delay from
from other models
tests are reported
in chapter
and to
III.
A
variety of tests with data from two airports show that FLAPS
can model airport performance acceptabl-y.
21
To illustrate
chapter
analyze
thre scope of the caopbilities
IV presents
airport
selection
performsance.
and
Capacity and
derivation
Several
capabilities
In the
course
of input
runs
are
is
given.
for several
made
to
runway
demonstrate
of
conducting
a number
the
study necessary
for
of topics for further work
These are discussed in chapter V.
Studies
to collect a comprehensive
Very few studies of any type on takeoff movements
have been found.
still in
of FLAPS to
parameter3
are made
of landing operations are needed
data set.
use
of the model.
developing this model,
were identified.
the
A omnDletedescription of the
delay estimates
configurations.
various
an example of
of FLAPS,
Collection of accurate delay statistics i3s
its infancy.
much research on
hampered by the
Work is
airport performance is not
conveniently available
form but circulates
fact
that
published in a
as memorandums,
unpublished papers and the like.
There
be
are a number
directly
used.
of areas of study in which FLAPS csan
Capacity
estimates
periodically by
most airport
authorities,
study
comtemplated
change.
of
any
possibilities using FLAPS can
experiments
location,
on how
and
performance,
control
strategies
changes in
assessing, the
usel by
as
needed
is detailed
Several
be suggested.
research
These include
landing performance,
separation standaris affect
and
are
exit
overall airport
optimality of
the various
zontrollers to manage congestion
22
and delay at
the airport.
Several models of
terminal
airspace and of groiundside operations have been developed.
These could be operated in tandem ith ?LAPS to assess the
interaction of operations in each area.
There
described
The
are
a number of -logical extensions
in chapter V,
extension with
to FLAPS, also
tha-t could enhance its usefulness.
the highest
implementation of the method
suggested in section II.B.
priority
is probably
the
of modeling ground operations,
23
II
MODEL
3STRUCTURE
This chapter
escribes in detailthe majorconceptual
components of airzraft
methods
of
evaluated.
and
modeling
operations
each
at airports. Current
componen-t are
haere a1decaatemethods exi3t, they are
incorporated
into
PFAPS.
of the individual features of PFLP3 i
describing
that
the
major
e-eloped.
methods
Validation
escribed.
components
and
escribed
WnJhere no adequate
currently exist, a new methodology is
by
discussed
of
,de begin
aircraft
operations at airports are and how they relate to each other
and to the analysis problem.
A
AJOR ISSUES3
Modeling airport
subjects.
scope
This
of modeling
operations requires analy3is
section presents a
issues
adresse
brief overview
in
of many
of the
epth in the following
sections of chapter II.
First
of all,
variety of airports,
airport facilities
this,
that
but at
can
if the model is
to be ablie to analyze a
a method of specifying the positions of
is needed.
significant cost.
accomplish the
same
Present methodsaccomplish
A new
task
method is proposed
at much
lower
cos't.
Aircraft to be modelel can flow over a large number of paths
between runways and gates.
Modeling this process is
esired
24
to
assess taxiway
taxiway
lesign
constraint3 for
problems.
techniques prohibit
are
difficult
to
Present
analysis or
manual
path switching to avoid
use.
automatic generation
delay
The
enlmerat ion
congestion and
difficultiees associated
of pat'ns are
iscus3el
for
with
and a compromi3e
procedure is proposed (but not implemented) that limits the
effort
required
to model taxiing
and provides an approximate
means to analyze taxiway system problems.
These topics are
discussed in section II.B.
The characteristics
airport
greatly
experienced
of the various aircraft
influence
during
the
cap-acity
operation.
Any
and
estimate
using the
d el ay
the
of
present
conditions and especially any forecast of future demanis for
service involve uncertainties as to number,
of the
aircraft
that will
type and timing
use the airport.
discusses how present methods of translating
Section
these estimates
into a schedule of operations in the
systematically underestimate the uncertainty,
consequence of underestimating
given
situation.
II.C
simulation
with the
the expected delay in the
A new demand generation
technique
is
developed to avoid thisproblem.
It is recognized that the operation of runwaysis the
major determinant of the capacity of the airport.
Sections
II.D and II.E address this topic.
Modeling of runways
involves the analysis of both the factors
performance of
aircraft
and the
separation of aircraft movements.
rules
influencing the
governing the
25
Significant
stu ly
determine
that
sl;cftion
3it
landing aircraft.
by a
bezn d'a
1one to ilentify
lesire to facilitate
Ho-wever, thus far,
delay
riot
nave
run~-.'y
occtpan7y time for
.n1.
This stady
ha
early
been partially Activate
exit ani to
intnlei
;noels
nodelel
f.ctos.
I
performanca
method of
molel ing landing =erforn-ance is
in a
a
an input
irect assessment
number of
factors
to
these
f
as tne
the
olels.
A
ievelope' wti-ch
of
of the irmpacton lTlAy
uch
elay.
Inrstea(I,
predictel
allovs
reduce
for lirect estimation
tiaes3
.is
the fctors
location
.n
chan,;es
type of
exits.
The rate at
which air,-raft -an use t
limitel
by
Modeling
separation rules is
ways in
which aircraft
the
impo ae
separations
omplex:
carl interact
vary in response to weather.
runway is
be t een
Tue to
th
an because
Significant
(aircraft
the
Analysis
on ifferent
single
runway
separations
Further,
on the analyst
certain cases lifficult
t e rules
aircraft
on
as far as
Current methods of speoifying these
allow only approxima-te solution
between separations
variety of
ranwtay separations
runways) has3 not progressed
case.
interesting cases.
methods rely
of depenlent
,iraft
work ha3 been ione
on analysis of single runway separations (both
the same runway).
lso
and aircraft
it will
be seen that current
to assess3
any interaction
performance.
to analyze.
logic to modelthis interaction
to several
This makes
We develop separation
irectly.
26
Section
in a lynamic environment.
Airports operate
II.F will discuss the interactions betseen the airport and
its
environment.
eather
complexset of changes in
and congestion
operating policies,
control
ith
the
rules
for
a
demandfor
Because airports saldom
service, and aircraft performance.
operate
can produce
same runway configuration andi air traffic
an entire day,
the impact of such changes.
almost no ability to do this.
it is
important to model
Existing models, however, have
We will develop an extensive
capability for FLAPS to model changes in operating policies.
Many statistical
Unfortunately,
issues underlie
they are not
outputs
will be
The proper construction
generators and the analysis
discussed.
model.
often sufficiently appreciated
by applications oriented analysts.
of random number
a simulation
W3
ill discuss
of simulation
the selection
and design of the various statistics computed by FLAPS.
27
B
AIRFIELD
1
Introduction
EODAIE'RY
D ,-
'>,-'.i;,
This section deals with the closely related
how the
issues of
eometry of the airport and the routes aircraft, take
in moving over the airoort
need to
are represente4
in the model.
-arAnattributes
model' t .e location
facilitiesto provide a frame -o r
for
e-
of airport
odelin-
aircraf t
movements between. runways and aprons.
In this
section we
currentlyuse to
taxiing
oerations.o
examine and
model both airor-t
,e wil l
tie
methods
eometry 'and aircraft
see that
unsatisfactory both in terms of
on aalysis
evaluate
these
ethods
are
the restrictions they place
and in the tine and cost requirements
they place
on the user.
We then review a method of modelinc
proposed in an earlier work by
is a
and
satisfactory means
has
been
difficulty of
in
specifying taxiing
described below,
eometry
this author ('.OR78).
of reprasentin:
implemented
airfield
FLAPS.
airfield geometry
It
routes but,
does not represent
This
a complete
reduces
the
for reasons
solution
to
the problem.
Finally,
we propose a modification of this method that
provides
reater
time and
ost
flexibility.
tae method
Due to constraints
was not implementel
on both
in FLAPS.
28
Wefirst
discuss geometryrepresentation, then describe
taxiway modeling.
2 Description of Airfield Geometry
The ASMmodel represents
modules where a module consists
element.
the airfield
as a set of
of any one aircraft
Typical elements are runways,
taxiway segments and runway crossing
capacity
intersections,
links. * Each taxiway
segment has a length and a taxiing speed associated with it.
Figure II-1 shows
a
map of La Guardia
and figure
II-2
presents the airport geometry as described by ASM.
This representation if airfield geometry is accurate but
demanding.
Taxiway links are so short
enough to be of interest
describe and prepare
that
any airport large
in this study is very difficult
as an input to the model.
to
For the model
of OHare (BAL 76 p. 94-103), perhaps the most complex site,
545 links were defined,
taxiing
speed.
each associated
The model of La Guardia
with a length and
(PIM!77 p. 90-3)
required 230 taxiway links.
Describing
the
airport
methodology also
leads to
model.
maintains
The model
geometry
very high
next event.
Links
costs in
an events
aircraft which must be scanned after
range from 200
through this
list
running the
of up
to 200
every event to find the
to
400 feet
in length
with an average of 300 feet and taxiing speeds range from 10
*taxiway segments that cross a runway.
29
V
D
(
7
6
•
7Z;s
00_.%¢
(- 1'W
Dk-.
7.l
WAUB
FIGURE II-1.
Xj
O
N
i ?-
New York La Guardia:
Airport
Map.
30
!.
.4
FIGURE 11-2.
New York La Guardia:
ASMModeling Geometry.,
31
mph with
to 30
20 being the
tend to
surprisingly,
speeds so
that travel
seconds.
A taxiing
list scan
events
Short
average.
with slower
be associated
a
time across
aircraft
thus
link
re1ires
of approximately
links,
taxiing
runs around
10
upda-ting and an
times per
6
not
simulated
minute.
A
mnaking, considerably
procedure
on the realization
and links.
that the airfield
with nodes
The links are the aiorport facilities
and the
set of
apron,
(with
where facilities
modules
defined.
Y
to
join or intersect. A
represent
and taxiway)
intersection
X and
on
is a network
nodes are the places
minimum
d;emands
The procedure was based
eveloped in NOR 7.
resources was
less
to
coordinates)
the
links
of keypoints
-and a set
represent
(runwLay,
the noses
'was
The keypoints provile the information nece3s-aryto
locate the modules
of the facility
This
to which it corresponds.
procedure is
preparation
the attributes
and each module provides
implemented
of two files:
in
FLAPS through
The keypoint
1)
file and 2)
the
the
module file.
The
numbers
keypoint
and
file
X
the
consists
and Y
coordinates
relative -to a user defined origin.
every point
on the
aircraft cross,
and runagy
a
list
of
of
keypoint
each
keypoint
A keypoint is located at
airfield where two
for example:
taxiway intersections
of
or more
streams of
runway endpoints and exits,
intersections.
See the
32
examples for New York La
Logan (figure IV-1 and IV-2)
geometry.
Table
II-!)
Guardia (figure
for
and Boston
maps of airport and model
IV-1 shows the
keypoint
file
for Boston
Logan.
The module
file consists
used in the module.
parameters
of a list
specifying
what
keypoints
define
what keypoints
parameters defining
exit velocities and
approach
to be
Associated with each runway is a set of
(runway end points),
final
of runways
for
the
runway
are located
its
limits
at exits and
the length
(see
section
of the
II.D
for
descriptions of these parameters).
The model processes the airport geometry information to
derive additional information
For example,
about each
the compass orientation
distance of each exit and intersection
runway are derived
type of
module.
of the runway and the
from the ends of the
from the runway information
rather than
being separate inputs.
3
Ground Operations
3.a
Existing approaches
Aircraft ground
movements between
runways and
aprons
are provided for in the ASMImodel by a set of user-specified
aircraft
paths.
One
path
is
required
between
every
combination of runway exits and
each gate and between every
combination of runway endpoints
(where takeoffs begin)
and
33
each gate.
A path consists of an ordered list of the links,
intersections, and runway crossing elements that an aircraft
will traverse
while taxiing.
Only
one path
between each
origin-destination pair is permitted and can not be modified
during
a run.
This procedure
work (NOR 7)
was evaluated
which identified
First the
method,
in an earlier
two major weaknesses.
while
permitting modeling
of many
situations, imposes a significant burden in time and cost on
the user.
paths
Again
using the O'Hare example,
with an average length
required to
permit
permit landings
takeoffs
of 20 links (BAL 76 p. 154) are
on 6
exits of
2 runways
at one end of a third runway.
paths allowing landings at 37 exits
ends of
1293 aircraft
7 runways would consist
and
and
A full set of
takeoffs
of about 5500
from both
paths.
La
Guardia Airport requires 372 paths with an average length of
14 links
(PMX 77 p.
125).
for simulation it can,
Once an airport
of course,
adding a single
Testing
set up
be used as often as one
wishes with no additional preparation.
in airport geometry could
has been
However alterations
pose significant problems.
taxiway would alter several
alternative taxiing
routes would
Even
hundred paths.
be
a very
time
consuming task.
The second
model is
that it
congestion.
airport' s
_
_III__I
YI-I--Y·I·I
and more fundamental
does not permit
the ASMI
criticism of
path switching
to avoid
A controller, when routing aircraft through the
taxiway
1IIII·-·-I
system
Il--I^II__IY
·1--1
during
a
period
-11111·11111_1-
-1_1___.
of
heavy
34
congestion, would be likely to divert aircraft to new routes
Confining aircraft to a single
that are less congested.
pre-specified
movements and
Having
path
will likely
exaggerate estimates
this criticism,
made
devising a
flexible,
simple
aircraft
concentrate
congestion.
of taxiway
it must
out that
be pointed
alternative turns
out to
be
difficult.
of possible alternatives
3.b Discussion
In this section we discuss
automated methods of aircraft
the possibility of devising
flexibility by permitting multiple routes.
solution
can
satisfactory (both
be achieved
We conclude that
economical and
and that a
the
and enhancing
objective of reducing the input requirements
no perfectly
with
path generation
efficient)
options and
range of
levels of modeling detail might be the best choice in this
case.
unalterable
with one user-defined,
If the AS; model,
aircraft path between runway exit
and gate,
represents one
extreme, then perhaps the other extreme would be to
simulation select the best path
method a
criterion for deciding
of
this
criterion
established.
for
each
To use this
which prospective
function or procedure for
best and a
link
the
to follow
for each aircraft
every time an aircraft reaches an intersection.
have
path is
calculating the value
would
The usual situation is to have
need
to
be
minimum travel
35
time be the criterion
link
travel
time
as a
characteristics.
Dijkstra (DIJ
and to define
function
59 )
links
could
be used
with the
criterion chosen.
travel time,
of link
giving
volume and
link
The well-knomn shortest path algorithm of
between the aircraft's current
traverses
a supply function
If our
the Dijksra
to determine
which path
location and its destination
lowest
sum
of values
criterion,
algorithm
for
for
example,
the
were
would find the minimum
travel time path.
There
are,
unfortunately,
shortcomings to such a scheme.
from
conventional
traffic
a
number
of
serious
The airport network differs
networks
in
that
ost
taxiway
delay to aircraft is likely to occur in trying to cross busy
intersections or
opposite
in waiting for
direction
to
clear
an aircraft moving
a
link
rather
in the
than from
interference
with other aircraft on the same link.
To deal
with this problem, the expected delay offered by rossing an
intersection will have to be explicitly modeled,
perhaps as
a function of the utilization rate of the intersection.
An additional problem is that
a-time links
routes
rather than either
in any
single
aircraft .are to be
method
must
conflicts.
NOR78.
1__
_
1
--·-·--)·1111·-··-I^
be
two-way routes
direction.
assigned to
developed
to
taxiways are one-way-at-
This means
or one-way
that,
conflicting routes,
some
prevent
such
or
resolve
This problem was not adequately dealt
The su,-estedi method di
1----1_
if
1__11 11111111111-
with in
orevent certain types of
36
conflicts,
for
example,
intersections.
or prevent
taxiing
other conflicts,
have
for several
best
network.
each
link
relatively
path
such as
paths
may include
a network
more tan
at
any
to determine
of vehicles
of
characteristics
and
Neither
remain st able.
an airfield network.
This means that
will
using
are on
time one vehicle
rates
Flow
are
on a path being considered
t-raffic maychange significantly
time one aircraft
opposite
one time and the number stays
The number of aircraft
for additional
when
the present state of the
the network,thenlink
condition applies to
in
needed
hundreds
the choiceof best path will
very low.
proceeding
constant over the length
takes to cross
taxiway
those occuring
is that the data
In highway traffic,
of
at
links.
A second problem
the
collisions
However, the method was not able to resolve
aircraft
directions
side-on
require to
during the
moveover the network.
a recent average
of travel
time as a
best path criterion may be misleading.
The conclusions
drawn from the
above is that any automated
be
very difficult
believed
situations,
to
to be the
difficulties described
dynamic routing procedure would
implement.
If ground
major component of
delay
this would provide a motivation
accurate
model of ground operations.
agreed,
however,
important problem
that
at all.
ground
delay
delay
were
in most
to seek such an
It
is
is usually
generally
not
an
Ground delay may sometimes be
___ ___·___
37
significant in particular
very rarely is
taxiing
easily
ground delay a major problem
system.
idiosyncratic
shifted
locations of an airport
The
and future
that it
operation
of
aircra
' ft
flos
is not
clear
as "Yes
- with no problems",
is
so
and routings
so
significance
an
rnat
to ask questions such as
handle a demand increase of 304?"
over an entire
airports
"exact" estimate of ground delay would have.
much more likely
but only
The analyst is
"Can the taxiway
and look for answers such
"Yes -
ith some trouble spots
that may require redesigning" or "No- it causes airport-wide
problems."
So while ground delay is not often a significant
part of total delay,
it is
very important that the analyst
be able to
prove this for any
Therefore,
we cannot simply abandon
operations.
We do, however,
technique.
The
solution.
We
given airport configuration.
the modeling of ground
need a more flexible modeling
following
technique
will explain
is
the method
proposed
by showing
as
a
how it
would be used in the analysis of an airport.
3.c
Proposed solution
The
described
following discussion
in part
3a.
assumes
The method
is
the geometry
basically
input
iterative.
In the first pass through the process the analyst prepares a
set of aircraft paths,
one for each origin-destination pair
over which aircraft will travel.
list
1I__·_I_·I
II____Y__ -LLIUI
of
-1
keypoints,
1II
-LIU-YYC·Y·-
in
1
order,
11--1
__ C-
Each path consists of the
on the
1
III
route taken
CII-I-IIPI·_I-----Y--l·--ll·l··-ll
by the
--I·-·I
_1 I
I^-_-
38
'When the model is run, the length of each path is
aircraft.
calculated
by summing
keypoints on the path.
each pair
between
the distance
of
As each aircraft moves onto a path a
and
taxiing speed is determined (from user-supplied inputs)
Each aircraft is
the taxiing time over the path calculated.
made
then
from
interference
move without
to
any
other
aircraft, even aircraft moving in opposite directions.
procedure will result
This
being recorded by
in no ground delay
the simulation.
An
additional
indication
of
recorded with
how
much
in
taxiway
the
is noted.
have
been
Each
time and direction
At the end of the run the average
number of times that two aircraft
specified interval of
would
intersections.
crosses a keypoint the
an
provides
model
delay
a complete modeling of
time an aircraft
of the crossing
provision
cross a keypoint within a
time is displayed for
each keypoint.
A separate (presumably larger) interval is used for aircraft
moving in opposite directions across the keypoint to pick up
head-on
encounters.
This
output enables
the analyst
to
assess the magnitude and location of the congestion problem.
For example, if the results indicated that two aircraft came
within 20 seconds of each other
three times during the course of
at keypoint X an average of
the day,
then it is clear
that even if the most sophisticated intersection module were
to be
used to
model this
intersection there
would be
no
discernible impact on overall airport performance. If this
__^_ ____
________I
39
is the situation
satisfied
around
that
delays and
at all keypoints,
turn to
operations
of the
analysis without
if the average number
Conversely,
is very large at a significant
of close encounters
then
encounter serious
do not
other aspects
proceeding any further.
keypoints,
then the analyst will be
the
analyst knows
number
that serious
of
problems
exist and that some action will be necessary in order to
flow on the ground.
expedite the aircraft
Intermediate
caseswillrequire a revised approach.
a
number of
then the
intersections are
analyst
may
either
try
paths to reduce the problem at
to
place
intersection
intersections
module
and run
would be
showing severe
to redesign
at
the model
designed
the
a keypoint
again.
to permit
An
If
the
would hold
outputs
intersections
of
with
results may be taken
this
of only
if
one
necessary
to
the intersection.
reveal
serious congestion
congested
An intersection
aircraft
case
ay elect
intersect Lon
passage
aircraft from "colliding" at
prevent two
the aircraft
most
aircraft at a time across an intersection.
module at
congestion,
these locations or
modules
if
no
problems
remaining
then
the
The same can be said if
as accurate.
some congestion exists but overall delay figures are largely
unchanged
from the
first iteration.
If,
the
however,
original case had many intersections with severe delay or if
the addition
of a few
taxiway capacity
*
-l
intersection modules has
to be reduced
--
--
-
so that the
'LI··IIII·-YIII--11111-1_
---
caused the
congestion has
·1
1_1_11_____1_1.
____
__._.
40
propagated to other
odules
intersection
additional
has
designed or
lmaybe
A new set of paths
several options.
the analyst
then
intersections,
see if
may be installed to
significant adlitional delay will result.
As
ore and
problemscan occur. First the simple
conflicting
will
are
more intersection modules
or
not prevent
"low level"
control
resolve
heal-on
of
modules
individual intersection
movements via
two
added,
between
conflicts
Secondly the danler arises that round delay ay
aircraft.
be increased over the real world situation because the model
has only one path between
the analysis,
then the
advantage of the model's
controller
this limits
implement a path switching
developing a "high
level"
If
and destination.
each origin
to take
user may wish
odule to design and
mechanism.
This
control
strategy
would involve
that
could
oversee the entire state of the airport's
round operations.
Any path switching mechanism could be as
simple
as desired and may be tailored to the specific
a general procedure.
The point is that,
No such mechanism
is
or complex
or be
airport
proposed
here.
while it is very difficult to anticipate
all of the options that may be needed to model operations at
any
airport,
a
procedure
can
be provided
for
allowing
airport specific changes within the overall model.
An additional
benefit
of the time of crossing
that it enables checkin;g~ of the very important
The
intersection
of two runways
record
is
runway logic.
is a keypoint.
Thus the
41
average
cnuber
of near-1>Oll is,
runway intersection
a nodel
that the
desi red.
a>, i.el.
development tool
run ay
o... be recorlel
This would be valuable
an as
.andseparation
-proof in
lo iic is
for each
both -tas
production
performin-
runs
as
42
C
DEMAND FOR SERVICE
1
Introduction
The
previous section
characteristics
model.
of the
of
this
airport,
chapter described
the
supply
side of
the
the
This section considers the aspects of the model that
are related to the generation
of demand for service.
involves modeling how many aircraft
times of
the day,
involves
the
aircraft.
i.e.,
of
class)
uses the
airport.
schedule
of the
attributes
of
the manner in
section of
operations
It also
the model
that will
take
schedule are those
which it
produces a
place at
airport during a given replication of the model.
in the
the
any aspect of an aircraft
that could affect
This
of demand.
the
By attributes we mean
(such as
,usethe airport at what
the level
specification
This
attributes of aircraft
the
Contained
that are
exogenous to the airport.
Three
modeling
construction
of
attributes has
what
significant
attributes are in
and what attributes
conditions at
are
aircraft schedules.
characteristics or
airport,
issues
the
'What aircraft
fact external
to the
are determined dynamically by
the airport?
2)
been chosen for
Once
3)
the correct
inclusion in
relationships (correlations
exist among the attributes?
1)
in
or logical
set of
the schedule,
dependencies)
'Whatmethod should be used
43
to generate
the
number
and times of entry
that
of aircraft
are to be modeled?
We
will
reads
used
algorithm
schedule
significant
section 5
of a number
needed
improvements are
three of the modeling
the
model
and
Evaluation of the
procedure.
schedule"
it permits analysis
that while
the
schedule for each replication.
this procedure (in
assumptions of
evaluate
This procedure
to
externally
shuffles the aircraft in the
We term this a "base
briefly
and
in the AS4 model.
prepared
schedule
a
describe
first
with
shows
of situations,
respect to -all
to correctly simulate
in order
issues
below)
all the situations of interest.
We
will
then discuss
in
times
interdeparture
distribution,
probability
appropriate
replication
thus
replications.
present schedule
FLAPS for
drawn
from
interarriv.-l
a
probability
distribution with
a
Other aircraft attributes are drawn from
time varying rate.
other
are
an exponential
usually
three
procedure for
method,
In this
schedule."
the
This new procedure is termed
generating aircraft schedules.
and
each of
nd propose a nw
modeling issues raised above
a "probabilistic
detail
uses
This
a
distributions.
schedule
method expands
generation
technique
forecasting future
independent
of
Each
other
the capability
of the
to permit the
.use of
airport performance.
FLAPS
provides for the generation of schedules using either a base
schedule procedure or a probabilistic
chedule procedure.
44
2
2.a
Present Schedule Algorithms
Description
The schedule
generation method used
consists simply of
main simulation.
in the
preparing a schedule as an
The schedule contains one
ASM model
input to the
record
for each
aircraft to be modeled, including
1)
Airline
2)
Flight number
3)
Gate
4)
Flight type code
(originating, terminating,
through, turnaround, touch
go*)
5)
Aircraft class
6)
Arrival time at threshold of landing runway
7)
Departure time from the gate
8)
Approach
9)
Landing runway
10)
Takeoff runway
11)
Departure fix
name
(UA, EA, AA etc.)
(category of aircraft, i.e.,
heavy, medium, light)
fix
In each replication of
to control
In each
perturbed
the insertion of
replication
by
distribution"
*
the
the model the
aircraft into
the arrival
addition
(which may
schedule is used
of
and
a
include
the simulation.
departure times are
random
negative
"lateness
values)
Intended for modeling GAtraining maneuvers. It
to
is not intended to model missed approaches induced by
separation violations
45
simulate
the
day-to-dy
varia.icns
and departure of the aircraft.
the set of
time of
are specified in
the schedule because there
delay
is no internal
for altering attributes during
For example,
to minimize
Because the
not change from
The attributes are used as tey
mechanism in the model logic
the simulation.
the arrival
The number of aircraft and
attributes for each aircraft do
replication to replication.
varied
in
runway assignments cannot be
or
to avoid
original input schedule is
future schedules, this method
weather
problems.
used as a
base for
ill-be referred-to as a 'base
schedule" method.
2.b
Evaluation
In
this
section
we
will
briefly
present
observations about the ASM schedule procedure.
3 and
4 below we will
examine
in more detail
some
In sections
the modeling
implications of this method.
The
most obvious
point
schedule procedure
is the
analyst
in order
must know
example,
aircraft
etc.)
followed
not
only
must be known
but
the exact
by class
the
to make
amount of
of
the
classes
also required:
by class 2.
among various attributes is needed
3:15 used runway 3).
a schedule.
5`t of class 1, 20% of class
sequence is
3 followed
the AS'A base
information that
to prepare
istribution
(e.g.
about
Collation
the
For
of
2,
class 1
The relationship
(the class 2 aircraft
of OJA entries
ill
at
provide
46
the
analyst with
existing
For
airports
analysis
existing
o
much
of this
and
only for past or
new
airports
airports the
departure
fix,
but only
w ll
AS4 model.
and runway
studies
have to
In any
ass
for
present situations.
or forecasting
analyst
information outsile the
fix,
information
create
case,
of
this
arrival
gnment will have to be
supplied by thn analyst.
The second point that should be-ade is that regardless
of the
source of schedule information,
technique imposes certain' restrictions
that can be correctly
aircraft
in
modeled.
each replication
accurate analysis
the base schedule
on the situations
The use of the same set of
elinminates the
of situations
possibility
of
where only an aporoximate
estimate of some schedule parameter is available.
"Thus,tthis
approach implies, in effect, that information about aircraft
is deterministic,
not stochastic.
in each replication
in analyzing
Usin
same aircra
t
perations at
t
somfefuture
date implies more exact knowledge about the future than it
seems reasonable
to assume.
probabilistic schedule
in depth in section
A
third
generation
that
included
have
developed
method this point will
the
be discussed
5 below.
difficulty
with
AS-.
the
model's
schedule
procedure is in the choice of aircraft attributes
are included
example,
Once we
runway
in the
schedule.
assignments
in the schedule
are
and cannot
As mentioned,
among
the
be altered.
for
attributes
if we wish
47
to model thaiynr.aics o-f1-ircot
will have to be
reated.
In su:nary,
the
tha3. tne an'liysis
effect ,
stuy
forel
outsie
uncertainty in
a:fect
.chequles
uncer ainty
nor te
ef'fet
is,
in
One cannot easily
in the
prediction
of
of v-arying the amount of
the schedule.
Since it
is reasonable
kind of sinuiation -will
expect that this
ASM1
method is
rformaace
thae mnain model.
of
flows,
obln. a ith the
-asic
3o ioW
the effect
aircraft
opr-r ition,
, this capability
be used
to
primarily
for forecasting congestion problems, this schedule procedure
is a serious
two ections
we d'evelop an al-ternative
methodology that
explicitly
In the follow.in
schedule generation
mcre responsivP to
is
ques-tionsan analyst
is
of the AS, model.
deficiency
will
be likely
orientel toward
to ask.
modeling
the types
of
The new method
the
uncertainity
inherent in the forecasting process.
3
Aircraft Attributes
In
this section
-we take up
the
first two
modeling
issues posed in the introduction.
3.a
Implications for analysis
Briefly
stated
information about
arrival
the
schedule
the aircraft
t the airort.
It
should
which is
contain
known before
that
its
should not inclule information
48
which is in fact
such as
durin. the simulation,
etermineA
runway assignment or specific path over the airport surface.
one.
This distinction is an important
attribute,
which in
the course of
If a given aircraft
the real airport is
determined during
operations and can be altered
developments (i.e.
in reaction to
the landing runway used by an aircraft),
were to be specified in the model as an input,
fixed before
the simulation run, then the potential arises for misleading
It may very well be that for a base or test case,
results.
data
given attribute
about the
This information will enable the model
input to the model.
to
produce accurate
input
data
However,
were
the base
results for
collected
when the
model is
for
that
used to
particular
analyze a
a
which no
data exist
attribute,
one of two situations
may occur.
case for
the base case data on the
the
case since
situation,
continue to use
and used as
can be obtained
case.
different
on the
given
The user may
new case.
This
will create misleading results as the real airport would not
exhibit the same
situation
as
pattern of the given attribute
it did in
the base case.
user may estimate the attribute
Alternatively
the
from the user's expectation
of what it should be for the new case.
may turn out
in the new
to be very accurate or may
Such estimated data
be quite different
from what the airport would actually be like.
The point is
attribute
is not
that in the example
really
an
just described,
independent variable
but
the
is
49
dependent
should
on
be
scope
what is
modelel
of
as such.
airport
distribution
number of movements
developed here,
and delay
by
airport.
path taken after
?he course
the primary
airport
accommodated can vary
the
area used,
purpose
w.hich is to analyze
on the
Thus
y,
nd how
the
number
of
aircraft
the
only
the
in the
that are
not
- under
takeoff and the
-taken in this
of
the
model
of capacity
of movements
operating rules of
schedule
shouldreflectt3is orientation
in that they
attributes
expands
direction of
uestions
by changes in the
the items
and thus
.4illremain fixed
c an change.
dictated
if one
suficient
classes
runways,
the airport,
fact,
even the apron
approach to the
is
on
In
analy;is
of aircraft
severe conditions
work
occurri n.
for
FLX3
include those
altered
except
in
extreme situations.
3.b
Selection of attributes
A wide
variety of attributes
could potentially
the schedule, including:
1)
ntry attributes
arrival time, departure time
type of operation - arrival, departure, through
2) Routing attributes
arrival fix, departure fix,
arrival runway, takeoff runway
apron area or a-te
3) Performance attributes
be in
50
*Class,% loaded or landing weight, noise, fuel
consumption rate
4) Identifying
at-tributes
airline, flight number,
index
number
(t, 2, 3, etc.,
i. e. a set of
numbers identifying aircraft which would be
without significance outside the model.)
We
consider
each
of
these
attribute
categories
in
turn.
Entry attributes
Entry attributes
where aircraft
describe when,
enter the simulation.
three ways an aircraft
- that
is the
taxies
to
remainder of
and
the day
hangar.
2)
airfield
at the
There
may use an airport:
aircraft enters
a gate
and by
then
or some
As a departure
-
beginning of
are basically
1) as an arrival
the terminal
either
area,
stays there
time later
lands,
for
is removed
an aircraft
the
implication,
that is
day and
at some
the
to a
on the
point
leaves a gate, taxies to the end of a runway,
takes off and
leaves the airport.
one that both
arrives,
lands,
takes off.
airports.
taxies
Touch-and-go
simulation are
negligible
3) As a through
to a gate,
of
and later taxies out and
operations,
not modeled
fraction
aircraft,
in FLAPS
operations
simulated
as they
at
major
by the ASA
constitute a
air-carrier
51
The point
n-try isL lifferent
of
through aircraft
for
on one hand anl deprt!ires
It would reduce the oosibiiities
3
point of entry times could be
a field-observable
arrivals
and
on the other.
f Confusion
if
these
defined to correspond both to
event and be
measured
at some convenient
point.
The choice
arrivals
of how
and for
difficult.
through
The ASA
runway threshold
this
is
not
threshold
land,
to define
due
out
A problem
field-observable
already
of entry
to be
simulation uses time over
arrival time,
experienced
aircraft turns
for arrivals.
a
the point
event.
obtained
includes
to runway
any
Lrom
delay
and airspace
for
very
the landing
arises because
The
observzed
watching
aircraft
the
aircraft
congestion.
has
T ais
delay is what the airport model should be trying to predict.
If observed
threshold times -were used for point
the model might
existing
give excellent results when
conditions that
times but. would be very
conditions.
produced
threshold
for different
The actual runway delay would be different for
the new case but the input
old delays.
simulating the
the observed
misleading when run
of entry,
data would implicitly assume the
This would cause the misspecification discussed
in section 3.a above.
If the base schedule is
an additional
course of
obtained from the OAG listings
error may exist.
action
ould be
In this case,
to simulate
a natural
scheduled threshold
52
time
by subtracting
scheduled
gate
subtracted
aircraft
some constant
arri ial
in
T.he OAG.
would be intende- to represent
required to
procedure,
times
time from each of the
land
however,
and taxi
would also be
widely known that airlines add
to
The time
the
time an
the gate.
This
incorrect since
it is
expected delay to trip times
when computing scheduled arrival
times.
Thus,
uncritical
use of the OAG information will, to some extent,
smooth out
the arrival pattern.
However,
time
there is unlikely
that corresponds
because under
great
to
extreme delays
distances from
aircraft
may
an
be
to be any field-observable
undelayed entry.
aircraft will
the destination
held
at
the
This
is
be delayed
at
airport.
departure
gate
In
fact,
of
their
originating airport rather than circle above the destination
airport.
Therefore the point of measurement of arrival time
should
be chosen
at
begins
to follow
the movement
threshold
time
the point
as the ASM model
phase
operations
of
arrival
time
for FLAPS
common approach path
is
is in slight
does follow the
to the
arrival/arrival separations
the model
of aircraft.
in the ASMI model
this idea
where
extent
of
The use
of
violation
of
final approach
imposing
on the landing
chosen to be
actually
minimum
aircraft.
at the top
since FLAPS does completely
final approach phase of landing (see section D.2).
The
of the
model the
53
For depar t ir
ai
ra
t
schedulei time to 1lae
use:
and th '
observable
ti.e
function of
certain
the aircraft
Cnters
stay at
has a scheduled
boarding
rrives at its
ateia-te, it
ate and the second
are required
from the first
time.
estimate
Once the
arrival
aircraft
taxiing to its gate.
time is
time drawn
time and a
scheduled departure
the first distribution should
of time the
requires for
include an
landing
ani
When the aircraft actually arrives at
the
gate
2)
the su:n of the arrivl
on-gate time
ate.
distribution is used as
Note that
the
raw the ninimnum time the
to
sum of the arrival
the
determined,
at the
stay
must
Therefore
of time.
is used to 3et the scheduled
The first
stay at the
a
departure time but it ms3t
ate for the miniimum lenn
class.
at
passengers,
twosetsof meanvalues and standarl d-iiations
aircraft
There
of
per aircraft
a
and
the
leave at the scheduled
he
gate
aircraft mnustbe
refue' inc,etc. If an aircraft
may still
the
that the
to complete
order
a
gate is
the
aircraft
An
generated
leave before this time.
some minimum time
in
c;annot be
leaves
departure time and will not
gate
ntry time as arrivals.
an aircraft
time
the time
mTodelin .z departures.
ir:
aircraft
these
minimum on-gate time.
is also
s-
se the sme
for
as the
directly
;:;
to
This value is both
the gt:.
Dyo4_t -Ir~
Through aircraft
Departure
n. obvious event
e
maximum of 1)
the scheiuled departure time and
titne
(drawn from the
at t,he ate and the minumum
3econd. iistribution)
is the
54
actual
departure
time.
The ASo
uses
tOdel
procedure save thrat the scheduled i epsrture
a similar
time is supplied
to the model by the external schedule.
Given the inclusion
timeit is
of an arrival
time and a departure
redundant to input a separate code forthe type
of operation (arrival, departure or through aircraft).
information
timer.
naiy be easily coded in the arrival
A negative
aircraft.
arrival time
A departure
arrival.
time of
may
and departure
signify a
infinity
This
departing
may signify
an
In summary, entry attributes included in the FLAPS
schedule are 1)
an arrival time at the head
approach path and 2)
of the common
a departure time from the gate.
Routing attributes
Some
aircraft
information must
take
be
provided
over the airport.
as to
the
As the AS-Imodel provides
no mechanisms for dynamically assigning
full set of information must be provided
aircraft
to routes a
to that
model.
will be discussed in detail in section II.F below,
important to be able to simulate the
aircraft
to runways and routes.
pre-specify
in
the
FLAPS schedule
that
airport.
Of the five attributes
above)
has
the
been
8,
9,
two that
discussed
we must try to
change on the
in the AST4 simulation
10 and 11 in the table
define
it is
only those routine
do not change as conditions
used
As
dynamic assignment of
Therefore,
attributes
(numbers 3,
route
in section 2.a
runway use should be removed.
above,
runway
assignment
is
As
not
55
The runw-~ys in :~se chin-e over the course of
predetermined.
the
and runway
day
dynamically based on the .thss of te
use, aircraft currently
are
tno aircraft
asinm eotn
made
runways in
aircraft,
waitinl to takeoff at each runway
and, perhaps, destination of the aircraft.
decision
is for an airline
to occupy a fixed area and have all of its
If this inflexibility
same set of gates.
flights use the
remain a-
The usual case
conditions.
of airport
independent
to be
-turned out
however,
of apron area should,
The choice
a problem
a particular
in
a
situation,
alter apron
special controller :nodule could be designed to
assignment.
The role
of arrival
and
departure
fix
information
in
the ASA4model is rather obscure.
Documentation iAplies that
aircraft actually arrive at this
point and are "vectored or
77 p.4).
put in holding patterns" (PMt'.
However, examination
code
does not show any such use of the
fix information save as a
way of partitioning total arrival
of the actual
program
delay among several categories of aircraft.
Fix information
has a
important potential
Aircraft that arrive from different directions may be
use.
put on different runways to
For
much more
departures the
aircraft
larger
diverting
that depart
distances
courses
segregate
information
is
aircraft
more crucial
streams.
in
that
on the same route must be separated by
than successive
(FAA 78 parag.
departures
340).
that
follow
Departure fix can
56
provide information
Departure
if
to decide wha-tseparation
fixes may also be used
it is
is required.
as a proxy for destination
desired to assign aircraft to runways on this
basis.
Performrance attributes
There is wide variation
in a number of resDects.
exit selection,
used,
noise
cargo,
consumption
vortex
These include:
number of
these it would result in a
correlated
most
aircraft
is
parameter
quantity of
speeds,
other
size
of
the
performance
then used internally
functions
aircraft
is
as an indication of the
The class
in
the model as
to
specify the
an
necessary
1) "Heavy" jets (B747, DC10, L1011)
2) "Large" jets (3707, DC8)
"Medium" jets (B727, B737, DC9, BAC111)
4) Large propeller aircraft (DC6, Convair 5830)
aviation
of
an input
Usually five classes are distinguisaed:
5) General
well
characteristics.
additional performance attributes.
3)
fuel
very complex and unwieldy model.
each aircraft generated.
to various
rules
if one were to use all of
Thus we include only aircraft class
performance of
separation
taxiing
ate.
the physical
with
speed on landing,
passengers or
generation,
rates, time on
Fortunately,
the erformance of aircraft
runway occupancy- time,
levels,
wake
in
57
Class 5 aircraft
for
ay be livide
high perfor-aance
aviation
lass 5 and class
. a',-*
rto
aircraft.
into
s should
nd small
e eIshasized
general
that
association of class categories to size of aircraft,
an obvious and useful procedure,
desired,
the
is usefull
to seg-ent
according to some criterion.
the
f
analyze
any
the input stream
For exanple, each class might
represent aircraft from a lifferent
be
while
not req. ired.
class- parameter 1may
be a3se to
problem where it
to
is
the
airline if this
as felt
major -performance-relateddifference
among
aircraft.
Identifying attrbutes
The
AS; simulation
model
requires
that each aircraft
be
identified by airline name anidflight number.
There are two
difficulties with using this procedure for the
rob ab 1 istic
schedule.
First, when the number of aircraft
replications then
the
there is no
same aircraft
from
Secondly,
this
meaningless
for any use of the
forecasting
revised by
aircraft
given
level
the
airlines.
of
varies across
unambiguous way
replication
to
replication.
identificaticn
model
rapid rate
Iote that
to identify
is
probably
in medium or long term
at
the
which
flinghts
airline to
belon.gs can be taken into account
are
which the
through the way
apron areas are assigned.
Airlines usually occupy one (or
sometimes two) apron areas.
The different aircraft fleets
of a large
airline
flying mosly
medium
and large
jets and a
58
small airline
flying mostly propeller
medium jets
can
be
modeled
aircraft with
by assigning
a few
different
percentages of the various classes to each apron.
There is a second dimension to identifying
that
is whether the identity
of each aircraft
retained during one replication.
aircraft completes
a
takeoff,
history of this aircraft,
how much delay
out
to
be
In
necessary
function of
is it important
e.
what
apron
for FLAPS
as
we
by the model
to know the
it came from or
want
about the aircraft.
internally
when an
This does turn
to
prepare
As this
aircraft identification
number is assigned
should be
other words,
it experienced on landing?
aggregate statistics
only
i.
aircraft
and
is the
in FLAPS,
this
and need not be a
concern of the analyst.
3.c
Relationship among attributes
The
question
attributes does
used.
by
of
the
not arise
This is because any
whatever
schedule.
procedure
In
is
relationship
when a
among
base schedule
method is
such relationship is determined
used
to
create
the
the schedule procedure being
external
developed here
the schedule is created internally by the model.
necessary to
aircraft
consider the relationships among
Thus it is
the aircraft
attributes.
Four aircraft attributes must
fix,
apron area and departure
be set:
fix.
class,
arrival
The obvious procedure
59
would be to define four
each
iulltinoiialdistributions and select
would restrict
modeled.
of situat ions
the rane
that
wherecertain types of aircraft
situations
or situations
certain
where certain
aircraft
types
a.ron
only GAalrcrcraft
modeled among the
of time period;
class as a function
The first
for
each
time period,
one set
for each
which give P(apron areal aircraft class)
given apron
the two
departure
and 2)
apron
wl.cih
give
of a particular
2he second
class given a time period.
multinomial parameters,
parameters:
is a set of multinom-ial
time period)- probability
P(aircraftcilassl
aircraft
two
These are set by two
area as a function of aircraft class.
matrices of parameters.
one of
these and similar situations
first orde-r interactions are
one set
general
(e. g. all jumbo jets must use
use). In order to handle
parameters,
g.
areas cannot accommodate
the aprons or there is a GAh'an-ar that
1) aircraft
(e.
to model
at certain periods
were restricted from oerating
aviation)
could be
that we would want
may be the case
It
'ho
wever,
This procedure,
attribute independently.
is a set of
aircraft class7
- probability of a
UJsed sequentially
area given aircrafT class.
enerate aircraft class and apron area.
Arrival and
simple
multinomial
fixes
distributions.
are
selected
See figure
II-3
aircraft attributes are selected.
from
for
a
schematic of
how
60
Aircraft
Multinomial
Parameters
Attributes
random
P(arrival fix) -
arrival fix
draw
random
departurefix
P(departure fix)
draw
arrival time*
used as parameter
random
P(class/time period)
draw
-
aircraft class
used as parameter
random
P(apron area/class)
- apron area
draw
*
From arrival rate function
FIGURE II-3.
Selection of Aircraft Attributes.
61
4
Modeling te
Level
This section
4.a
how the number and
discusses
of each aircraft
raised
of Demand
are determined.
the
hird
entry times
modeling
issue
in the introduction.
Probabilistic
schedule paranmeters
A number of
parameters
need
to
completely efine the probabilisti3
number of
aircraft
to
be
be specified
to
type of schedule.The
simulated
is
controlled
by
specifying two time-varying rate functions, one for aircraft
that arrive and-for through ai-rcraft, and .-rne for aircraft
that only depart.
The rate functions
one of a number of
incressingly
ould be specified in
complicated
ways:
stepwise
constant, piecewise linear, or second or higher order curve.
The data
that is typically
hour by hour flow
a
rates.
stepwise constant
unlikely to
available
This would
function.
jump suddenly from
then remain constant for an hour.
demand
is
seem to argue for using
But
one
on airport
flow
rates are
value to the
very
next and
Using a piecewise linear
function will ensure that flow rates in the simulation build
up and decline
linear function
gradually.
We thus assume that a piecewise
provides an adequate approximation to any
given demandprofile.
(See fi!ire
iI-4 for details.)
As
62
underlying rate function
piecewise linear
,\
function
I
flow rate
.IX
I
I
.
I/
t
I
I
function
I
II
I
I
I
i
Z
I
Time period
FIGUREII-4.
Rate function.
3
63
will
results
function
linear
below, use of the piecewise
be exolaine
in
simple
a very
for
procedure
probabilistic s ,l-iule genera.tion.
would be to use the
will control the
timess An obvious assumotion
of inter-aircraf
distribution
that
specifiel
density function must be
type of probability
a
the rate functions
each of
With
function. Data from Logan
exponential
Airport tends to support the validity
of his
One additional binomial oarameter is
percentage of
Whather
each particular
arameter
l'Iethodfor generating a
In this
are
section*
we
discuss
how
arrive
and for through
o set the
tns
ods.
inter-aircraft
times
mat-ters -re will confine
discussionto generatinginterarrival
that
departs is
ime-varying stochastic process
To simplify
generated.
to set the
throuah aircraft.
arrival aircraft
determined randomly usina this
4.b
neded
that are
arrival aircraft
ssumption.
aircraft.
used independently to generate
times for
our
aircraft
The sa-ne procedure
is
departure times for aircraft
that only depart.
The
the
basic
time to
procedure
be simulated,
from a distribution,
*
usel is to start at the begining
draw an
place tne
interarrival
of
time t(l )
first arrival at time t(l
The author wis.es to acknowledge the assistance of
Dr. William Duns3muir, Dept. of Mathematics, MIT
with this section.
),
64
time t(1)
arrivalat
is
of t(i)
the sum
until
thaa
reater
A problem arises,
modeled.
anner
h!e end time
to be
because we wish the
however,
rate of arrivals
to vary over time.
the commoncase
where interarrvai
We will first consider
tines are
e
assumed to
_xtensions to
and! then consiier
Poisson distibutel
likse
and proceed in
+ t2),
second
place the
2),
interarrival ti-e
a second
draw
he non-
Poisson case.
Two
basic methods exist or
and
the
time-soale
tr ansformation
involves
method
rejection
nethod-
samples
cnerating
from
The rejection
processes (LE'.78):
nonhomogeneoas Poisson
method
samples
generatin-
The
a
from
homogeneousprocess with rate equal to the maximumrate of
the time-varying process and then accepting or rejecting
each point of the homogeneous process based on a randon draw
of acceptance equal to the ratio of the
with the probability
rate of the time-varying process at that point over the rate
For many of the cases of interest
of the uniformprocess.
with significant variation between the
to airport analysts,
occasional maximum rate
more
off-peak
common
points which would
method
rate
would entail
this method
feasible,
of 30-35 aircraft per
however,
for
straightforward
this
of 10 to
20 aircraft
generation of
be rejected.
hour and the
a large
This method
per hour,
number of
is certainly
we prefer the time-scale transformation
application
as
eneration of the saipLe.
it
enables
the
65
The ti me-scale
transformaation
;metod
s "a
direct
analogue of the inverse probability in-tecral transformation
method for
generatin5
(continuous)
nonuniform
random
numbers." (LEI '73 .2) The method is thus analogous to the
way uniform random numbers in the range of 0 to 1 are mapped
into negative exponentially distributed randomnumbers. The
method is implemented
in the
should be
in
consulted
discussion).
Samples
followirln
parallel.
from
a
way (figure
with
the
negative
II-5
following
exponentially
distributed random variable of mean 1 are generated starting
at zero
and continuing until the
that are
enerated
has a value greater
of expected arrivals
sample values
than the total number
in the course of the run.
I,
Thisprocess
(l ) to x(I.
is represented in the figure as
number of points,
sum of the
Note
in the process x(i)
that
the
will vary from
replication to replication and will be distribut-edaccording
to the
with a
Poisson probability distribution
equal to the total
number of
being considered.
' he lower
the
function in
arrival rate
period.
The
upper graph is
which is
merely the integral
value of
the integrated
expected
This
x(i) ont.o the process
terms of
aircraft per
the integrated
of the lower
rate function
function
t(i).
for the case
raph in Figure II-5 indicates
number of aircraft expected to have
the simulation.
arrivals
mean value,
at
time
rate function
function.
any time
The
is the
arrived by that time in
is used
The process
to
map the process
x(i) whichL extends
6'6
x(I+1)
j
24
=x (I)_
o
,r-
1
2
U
c
x(3
o x(2
.
.x(
,,-0dXX(1)
1
r-
)
1
$-
1-4
,-
',
,
%
Time
time-invariant
process
00
.H
U
0
time varying process
10
_
0
e-,,
.H
a
8
#44
6
,*
U
w4J
CdI (D
*1-4
h
h
C
P41
.H
+jl
4
4j
4. 4
.94
2
0
1
2
3
4
5
Time (period function)
FIGRE II-S.
Rate
Function
and Integrated Rate Function.
67
from
zero
to total
of cumulative
dimension
onto
number
the dimension
will enter
arrivals
producing the
of time,
length
t(i)
the simulation.
will
of
consideration of
the following derivation of
results
for the type
the run
being
the times
that the
enhanced
this method
and numerical
t(i)
It is hoped
intuitiveness of
mapped
process
constitutes
be
in the
is thus
expected arrivals
This set of values
considered.
expected
zero to the time
extending from
aircraft
of
by
the equations
of cases in which we are
interested.
We will derive results
rate function
for the case
is assumed to
11-6 gives the
be piecewise
where
the arrival
linear.
Figure
nomenclature used in this derivation.
objective is to derive an expression for
of the arrival rate function.
Our
L(t), the integral
We can simplify this integral
by defining:
nP
C(n)
= LnP)
It is apparent
C(o)
=
(1)
i(s)ds
that:
=
C(1) = [R(1) + R(O)]*P/2
C(2) = [R(2)+R(l)]*P/2 + [R(l)+R(0O)]*P/2
=
[R(2)+2R(1)+R(O)I*P/2
and that
n-l
C(n) = P[R(n)/2 + R(0)/2 +
j-1
R(J)
1
n
N
(2)
68
Let:
l(t) - arrival rate function (aircraft/unit time)
t - time
N - number of periods of process
P - length of period
s - time from start of period n
n - current period
Rn
n = l(nP) rate at junction of periods n and n+l
1(t) > 0 at all values of t
We assume
R2
R1
1 (t)
Ro
R3
0
P
2P
2
1
3P
3
Further let:
L(t) - integrated rate function
L(t) -
t
FIGURE 11-6.
!.
NP
lJ(s)ds
Summary of Nomenclature.
N
69
be written as:
The above may also
C(n) = C(n-1)
+ [R(n)+R(N-1)]P/2
I <n
N
(3)
Thus:
L(t) = C(n-l) + [R(n-1)+1(t) s/2
but
l(t) = (1-s/p)R
(n- ) + R(n)s/P
(n-lP
t
nP
So
L(t) = C(n-l)
+
R(n-) +(1-s/p) Rn--l)+R(n) s/P] s/2
[2*R(n-1)+(R(n)-R(n-i)) s/P]s/2
L(t) = C(n-1) + R(n-l)*s + (R(n)-R(n-l))*s2/(2*P)
= C(n-1)
+
(4)
Wegenerate points x(1) to x(I) along the dimensions of L(t)
and we want to map them onto the dimension of time.
x(i)
gives the value of L(t) but we want to know the value of t
(or equivalency,
The value of L(t) must lie
(4) must be solved
for s and n.
between C(n-1) and
C(n) when t is in period
value of
set of C
L(t),
(n).
Therefore
n and s) for which L(t) = x(i).
n, so for a
n can be determined from examination of the
With n fixed,
(4) may be written
as
and solved
quadratic.
2 /(2P) + R(n-l)s + C(n-l) - L(t)
0= [R(n)-R(n(n-l)*s
a simple
Applying
the standard formula we obtain:
s = -PR(n-l)/w
2 + 2w(L(t)-C(n-l))/P]
±(P/w)*SQRT[R(n-1)
($)
70
where w = R(n) - R(n-l)
This is a well-behaved
always the desired
equation.
The negative
one.
The positive
root is
root represents
a time
beyond one end of the period in question when the projection
of l(t) based on R(n-1) and R(n) alone has a negative value
l(t) from the
area of the projected
such that the total
up to the value of the root is equal
beginning
of the period
to l(t).
See the'numerical
example in the following
figure
for an illustration of this.
The discriminant can be shown to be always greater than
or equal to zero.
inequality
We will prove that the following
is true:
R(n-1) 2 + 2[R(n)-R(n-l)]
<
(L(t)-C(n-1))/P
0
(6)
Proof
As
L(t)
0 < C(n-l)
only the term R(n) - R(n-l)
side of
(6)
L(t) - C(n-1) is largest,
from (3) it is known
R(n)
>
0
and
can be less than O.
be smallest
would
C(n) - C(n-1)
C(n),
when R(n)
0
P
The left
- R(n-l)
< 0 and
that is when L(t) = C(n).
But
that:
= [R(n)+R(n-1)]P/2
so (6) may be written
as:
R(n-1)2 + (2/P)[R(n)-R(n-1)] (R(n)+R(n-l))(P/2) ' 0
Simplifying:
R(n-1) + (R(n) 2 -R(n-1) 2 )
R(n)
2
0
>
0
71
As the above must be true
we have established
that
(6) is
true.
One other
R(n-l).
case must be considered,
namely? R(n) =
In this case (4) becomes
L(t) = C(n-1) + R(n-l)t
(7)
Thus
t = [L(t)-C(n-1)]/R(n-l)
Note that
should R(n) = R(n-i)
(n-l)P
<
t ' nP
(8)
= 0 then
C(n) = C(n-l) + [R(n)+R(n-)]P/2
C(n) = C(n-l)
and no points of the process x(i)
(and thus no values of
L {(t) will appear on this portion of the interval
(5) or (8) will ever be used in this situation.
so neither
Figure II-7
presents a specific numerical examplefor this case.
Extension to non-Poisson
rocesses
Although the above method was presented
Poisson processes
assumption.
functions
the derivation is
in terms of
not dependent on this
Tests of the method with other distribution
(normal, k order Erlang)
using the algorithm in 4.c below.
show correct results
The only caution is that
some probability density functions permit negative interaircraft
times and this must
be accounted
implementation of the process.
4.c
Algorithm for generated schedules
Step
1)
Step 2)
Input
P,
R(n),
N
Use (3) to find the set of C(n)
for in the
72
R0 =
Let
5
aircraft/period
R 1 = 10
aircraft/period
P =
From
1
As
(3)
C3
R 0 f R1
hour
=
(5)
C1 =
0
(5 + 10)2 = 7.5
applies
s = -(1) (5)
1
V
w
=
10
-
5 =
5
(2)(5) (L9t)-0)
2
n = 1
$
=
-1
+
For various
i
L(t)
1
2
3
4
2.5
3.125
7.5
0
'1
25 + 1OL(t)
values
s
of X i = L(t) this equation
Positive
Root tp(i)
-1+1
Negative Root tn(i)
-2
.0
-2.414
-2.5
.414
-1+1.5
.5
b
-3
1
-1±+2
gives
10
L(t)
5,
1
-1
5
o
tp(o)
FIGURE I1-7.
Numerical Example.
i
tp(4)
73
Step
3)
Step 4)
-et
i
=
1,
x(0)
= 0
X fromn te
Generate
istrib-ution function
chosen
with mean value of 1,
-1 ) + X
Step 5)
Set
Step 6)
If x(i)
Step 7)
Locate
Step 3)
use
Step 9)
t(i)
Step 10)
i = i + 1
If
xx(i
> C(LQ then
(5)
or
5
11)
Go
(3) to find s using
x(i) for L(t)
= s + (n-1 )P
for schedule
i > size of storage providel
to
Step
'arning,anl stop
4.
Comparison of the :Lehods of
The two methods of
the .A3li
base
complete)
< x(i) < C(n)
n such that C(n-t)
then issue
Step
stop (process
Demand Generation
demand generation
schedule and the probabilistic
1iscussed here,
schedule,
are
not equivalent even if the parameters of the two methods are
The
matched.
considerably
method.
aircraft
that
probabilistic
greater
variability
schedule
than
will be held constant in all
number
distribution
will
vary
attributes
the number of
replications
in the probabilistic
of aircraft
exhibit
the base schedule
in the base schedule
For example,
will
whereas
schedule.
The
will remainconstant
74
over
all replications
in
the
base schedule
whereas
distribution will vary in the probabilistic schedules.
example, if the base schedule contains 7% heavy jets,
all replications
heavy
jets.
average 7
using this schedule
The
set of
heavy jets but
replications.
distribution
probabilistic
of
aircraft
within a replication.
these heavy
positions
variance
up or
of the
size of the
schedule
for most
would be
down
over
time
the time
schedule aicraft
distribution
that reordering
moving aircraft
of
one or
two
Increasing
the
would increase
the
the .schedule.
In fact,- two replications
contain periods
aircraft types appear.
the probabilistic
in that the
vary
the lateness
lateness distribution
method might
sequences of
in
the base
situations
limited to
sort.
will
additional
greatly with regard to
via
would mean
aircraft
differ
altered only
which
7%
schedule might both contain
In
can be
then
To continue the previous example, two
jets appeared.
times
schedule has
attributes can
For
vary across
to the base schedule
replications of a probabilistic
7% heavy jetsbut
schedules
the percentage will
The probabilistic
variability by comparison
exactly
will have
the
of the base
in which
This
identical
difference with
schedule is of greater
consequence where
the demand pattern has significant peaks,
since performance
at peak demand is affected more
of
aircraft arrival
period.
than is
by such shifts in the order
performance
in the
off-peak
DEPARTMENT OF CIVIL ENGINEERING
Massachusetts Institute of Technology
MEMORANDUM
To .
T_
.LU.:
Institute
FROM:
V. H. Murphy - Room 1-281,
SIRTEcTr-
Mii
_1
-
.. --
no-- A=
..
_
DATE:
A~rcnlves
Ext.
March 20, 1981
3-7106
Paaes
nn Threses
Page 75 of the PhD thesis of John Nordin (Course I, 9/30) cannot
be
ocated.
76
ABC
D
1 3 2
2 3 3
3 2 2
360.3
361 .0
364.2
4 2 2
365.5
5
1
367.8
1
400.9
583.5 5 1
392.6 4 2
6 3 2
367.9
417.7
1I
7 2 3
8 3 2
9 3 1
372.4
375.5
376.5
41 9. 8
3 2
2 2
2 2
2
A B C
394.3
390 .3
424.
451 .3
432.8
433.7
4 2
3
2
393.5
452.7
424.3
41
2 3
15 3 3
396.1
424.7
2 1
16 4 3
396.8
421 -5
17 3 2
408.1
453.6
5 2
18 2 1
408.9
409.1
450. 3
398.6
431.0
455.0
439.3
12 4 3
2
1
18
2
1
19 2
471
.
5
2 2
414.5
439.6
2
23 4 3
417.8
454.2
2 1
1
13
3 1
1
20 4 3
402.0
419.6
390.4
41 3.6
459 .4
414.2
464.5
419.4
467. 9
464.1
419.4
1
Replication
1
2 2
4 2
2
1
4
1
3
1
3
1
2 2
22
52
1
2
2
1
51
414.1
2 2
22 3 1
E
F
G
397.4
2 2
3 3
444.1
413.3
1
425.6
4 t
2 2
D
390.9
392.0
402.5
404.8
410.1
412.0
21
A
B
9 3 3
400.6
412.3
Replication
411.5
1
1
3
2
2 1
1
387.9
1
20
1
8 4 2
2
428 9
445-5
19
436.3
2
14 4
15 3
16 3
17 2
2
2
386.2
11
14
5 2
7 3
!O
22
384. 3
414.2
405.7
409.6
369.7
382.4
3842
1
389.1
392.6
361.5
362.9
4 4 1
5 2 2
6 2 1
2
12 3 3
13 1 3
1
1
3641!
4
373.1
388.2
4
1
3 3 3
1
10 4 1
11 4 1
432. 3
1
2
D
2
Index numnbe
r
Aircraft class (I = heavy, 2 = large, etc.)
Arrival fix nr.uber
Arrival tine
Departure time
Apron number
Departure fix number
Table II-1: Probabilistically Generated Schedules
4
1
t
42
'
3
3
1
I
77
A B C
1 2
2 35
322
4 4 2
521
632
723
931
10 4 1
11 41
12 3 3
A
D
361
.1
3563.3
A
39¢.3
390
3
374. 9
363.0
366.9
374.6
3 38. i,
,92 6
417.7
380.5
41
384.0
382.1
373.7
383.3
390.5
4.33.7
'
1
2 3
3
3593.2
424. 3
403.8
424.7
1
20
2 1
21
22
23
2 2
3 1
4 3
41 0.1
421 . 5
45 = . 6
411 .4
444.1
414.3
412.9
428.9
445.5
414.9
415.5
424.2
471 . 5
439. 6
454. 2
Replication
A
-
B C
-
D
-
E F G -
2
2
432.3
452.7
235
442
521
632
723
1
1
14
15
1
4
432. 3
393.3
19
1
3
451 -.
424.1
1 3
401 . 9
5
32
22
22
3
13
16 4 3
17 3 2
18 2 1
1
13
1
493 1
2 35
!5
523
2 2
41
42
~F G
D
361 . 6
361 .3
394.4
4 2
3 2
363.9
376.2
390
00.9
5
2
4
2
1
1
2
1
375.'3
370. 5
385.3
581
.
375.4
392.2
400.2
399.4
399.0
9
33.5
417.7
41 9.3
2
2
2 1
22
21
34
2
23
2
1
3
4 3
1
ethod Schedules
413.3
415.7
421.
3
2
2
42
1
1
2
424.1
22
3
2 2
45;
4 33.27
432.3
452.7
424.3
2
1
4
1
2
4
1
4 2
424.7
2 1
421.5
453.6
5 2
428.9
412.
22
1
1
405.0
420.6
415.7
22
3
. 392.6
57.2
399·
Index number
Aircraft class
Arrival fix number
Arrival time
Departure time
Apron number
Departure fix number
Table II-2: Base
C
132
2
3 2
2
B
:1 1
2
I
.,
4
22
471 .5
22
439.6
2
2
454.2
Replication
1
1
2
78
aircraft but the order in which the aircraft
simulation has been shuffled.
enter the
The likely consequences of the additional variability
of the probabilistic schedule include both a larger variance
in performance. estimates produced by the model and a higher
level of delay.
The increased variance of model outputs is
an intuitively obvious consequence cf increased variation of
the inputs.
The higher level of delay comes from the
general observation that systems
operating
in very sto-
chasticenvironments do not perform as well as similar
systems in less stochastic environments.
Consider, for example, the family of single-server
queues that are Ek/M/1 (interarrival
times are Erlang of
order
k).
This family
includes
M/M/1 (k = 1) and D/M/I
(k = a) queues as special cases.
The variance of interarrival times declines as k increases.
It has been shown
(FIC 74) that the total expected waiting time decreases
monotonically
example,
as k increases.
waiting
2 at r* = .9,
time decreases
39% at r = .5,
For systems with u = 1, for
28% moving from k = 1 to k =
and 73% at r = .1
(FIC 74
pp. 901-Z).
Further confirmation of this point is provided by a
comparison between the two methods on a test case.
A 6 hour
simulation of a one runway airport was performed using
FLAPS. All aircraft
were through aircraft.
Fifty
r - utilization rate
u - arrival rate
79
replications
were performed.
figure II-8 was used.
The arrival rate function in
The only difference
was the schedule generation
method.
in the two runs
Each method scheduled
the same average number of aircraft into the airport in each
period. The results in table 11-3 show a halving of landing
delay when the base schedule method is used.
Variances are
60% to 90% lower in the base schedule method.
The different
underlying structure
and base schedules and their
of the probabilistic
different
effects
suggest
different applications for each method, The base schedule
is an appropriate model for analysis of near term changes in
the airport
environment such as the addition of several new
flights
or
the opening of several new gates in one apron
area,
or
for
conditions are
any case where current, eactly
to be altered
known
in some precisely
knownway.
The base schedulemethod also permits simulation
of any very
unusual
described
demand situations
statistically.
The
that
cannot
probabilistic
schedule
appropriate for longer term situations where
are not
should
as well known
be
studied
or when
over
a
be
the parameters
the effects of
variety
Situationsin this categoryinclude
of
all
method is
some change
demand
forecasts
atterns.
of more
than a year or two into the future or analysis of situations
involving major changes in the airport environment (new
runways,
new aircraft types, large demand shifts)
where
the
demandrate and pattern will be substantially different from
the present.
80
-4
0
(minutes)
4
Lateness Distribution
400
a>
(Base Schedule only)
/
30-
.4
$-4
205-4
1-i
1054
.,I
ct
I
I--
2
1
Replications:
Time periods:
Run length:
FIGURE II-8.
50
6
6
-
4
3
5
6
Period
hours
Comparison of Schedule Generation Methods;
Parameters.
81
Result
Landings
:D
Probabilistic
Bas e
Schedule
Schedule
- mean
-
s.
153.
- c. i.
- max.
Landing Delay:
- s. d.
1 54
4.5
minutes
0.2
2.8
6.2
2.7
25.9
- max.
end of
- mean
eriod ,:
1i .3
- s. d.
1.7
1.7
- min.
- max
mean
- s. d.
- c. i.
- min.
- max.
aircraft
5-L.
6.1
- c. i.
-
173
1.5
- min.
?akeoffs
1 50
0.8
- c.i.
lueue at
0.-3
136
10.2
- mean
aircraft
0.9
2.8
- min.
Landing
152. 8
1
9.3
d.
TJnit
0.5
2
2
26
10
127.5
7.9
2.2
1 4.7
111
1 25
145
1 38
air craft
2.5
0.7
Takeoff delay:
-
.
9.2
d.
- c.i.
2.6
- min.
1. 3
d.
i.
min.,
max.
minutes
33.8
41.9
- max.
s.
c.
17.8
5.3
1.5
9.7
19.7
- mean
-
S tandard
-
Lowest and highest values observed in
deviation
9 5% confidence interval of the mean
a nryone of th
replications.
Table II-3: Comparison of Schedule Generation
Method: Results
82
one type of schedule
Using
the
other
because
constitutes
of
the
schedule type.
a
in a situation
misspecif ication
different assumption3
Using the base
user knows exactly the aircraft
of
intended
of
the
implicit
schedule implies
ix,
for
model
in
each-
that the
number of aircraft and
aircraft
an
parameters,
time-of-day
distribution
inappropriate
assumption for many situations.
Because of the ifference between the two types of
schedules the model allows use of both the base schedule
-to
method (with the actual base schelule obtained externally
the model)
and the probabilistic
schedule method.
A third
the base schedule method may be used
option is permitted:
with the base schedule being created by using the algorithm
normally
used to create
probabilistic
was used to do the schedule
method.
schedules.
This
comparison given above.
83
D
RUNWAY OPERATIONS
Introduction
of
on runways
aircraft
activities.
landin.s
anrd formulate
The scope of runway
and for takeoffs,
operations
is to analyze the movement
cf this section
The purpose
are
followed
operations
as shown
from
of
a model
is di ferent
in figure II-9.
the
start
these
of
for
Landina
the
common
approach path, typically 5 or 6 miles out, through touchdown
on the runway, braking and exiting from the runway.
landing
the
movements
and its
operation
below.
clears
aircraft
are
moment they taxi into
their takeoff roll.
becomes
discussed in
a
,rouad
section
F
considered runway operations
Aircraft takeoffs are
from the
runway
OJnce a
position on the
Their movement
runway for
is followed until they
pass over the far end of the runway.
There
movements:
are
two
major
aspects
of
modeling
-runway
1) the performance of aircraft, i.e. how lon
an
aircraft occupies the runway and what exit an aircraft uses.
As
landings and
characteristics,
The
takeoffs have
they are discussed
separations between
runway.
This
very :lifferent performance
separately below.
2)
that use
the
successive aircraft
topic is discussed in
types of aircraft movements.
part 4 below
for all
84
- - - ; - y - -C - -n o A
-A
- - -
1
pati
direction of
operation
FIGUREII-9.
Runway Operations.
-c- -t - -- -
1 -
85
2
on Lrandinz
Performancs
Aircraft
We ill f+irst review to methods that have been used to
each
of
and disadvantages
to
odeling
the
n alternative
iscuss
andingan performance.
wastestedwithtwo sets of
to
In response
method.
problems of existing methods, we will
approach
the avanta-s
nd
aircraf't
anlin
movement of
model the
This new method
ata and the results
of the
validation are disussed.
2.a
Methods of representinf, aircraft performance
We are
in nodelin
interestel
of exit.
landings
probability
of time to exit woull'
class.
sirnulation
It
advan-tages.
than one larndin
of
informati on
prepared and input.
directions,
runway
for
exit
the
probably as a
e provided,
This procedure was used in the
(NOR 79).
can
provide
procedure has
This
the exact
desired and it is easy and fast to progran and use.
sets
for
exit and standard
average time to
of exit,
MITASI airport
For each
data directly.
function of aircraft
several
be used
then, the obvious way to proceed is merely to input
the appropriate
deviation
one runway is to
If only
of t he
runway occupancy time and
performance of landinq aircraft:
choice
two key aspects
ere
to be used,
behavior
If more
then additional
each runway would
need to
be
Note that if one runway is used in both
two sets of
information must be provided
as
86
travel time to a given exit from one end of the runway will
not be equal
to travel
time to the
same exit from the
opposite end of the runway.
The problemwith this direct input methodis that it is
not
behavioral.
The user is required to specify as an input
which is really a
an aspect of performance (exit selection)
result of
both aircraft
assumes that
method implicitly
exit
exit type
location and
characteristics.
The
occupancy
exit use,
time,
independent of
are all
each
If -theapproach speed of a landing aircraft changes
other.
or the
and runway
exit location changes,
time
occupancy
and exit choice
then,
reality,
in
runway
are also affected but unless
the user specifically alters them they will not change in
the model.
some of these problems is
A second method which avoids
to input two functions for
occupancy
lime as
probability
method,
of
as a function
using piecewise linear
simulation
occupancy time
determined
distance
function
of exit
the ASM airport
average
a
from
of the
occupancy
probability
parameter in
exit
of
distance,
functions,
(PA4A 77).
functions
is
used
directly
exit obtained
a binomial draw
actually exits at this point.
in this
in
2)
This
was employed in
In this procedure,
and probability
input
and
exit distance.
of
exit are
depending
exit from the runway threshold.
time
of
the
1) runway
each aircraft class:
the
way is
to determine if
on
the
both
the
The runway
model.
used
The
as
the
the aircraft
87
The procedure
performance if
distance
of
will
result
exits are
exit
probabilities.
moved,
to derive
However,
in
different
since
occupancy
aircraft
the functions use
time
and
exiting
changing approach speeds does not
change aircraft performance
since the functions do
not use
approach speed to derive runway performance.
Additionally,
the procedure as
performance to
implemented does not allow
be affected by exit type (90 degree, angle*, high speed) but
could easily do so
of exit.
by providing one function
for each type
The input requirements of this method are
than the first method discussed,
greater
though the absolute
amount
is not a majorburden.
The more significant
it is still
of
exit
problem
the "inputting
location
with this method
of conclusions".
If the effect
on runway performance is one of
questionsto be answered by using
results cannot be an input.
the
model,
airport model.
used to
the
then the
Having runway performance as an
input requires that a separate-, external model of
performance be
is that
generate this data
The method proposed
aircraft
for use
in the
in the next section
is
an attempt to solve this problem.
2.b
Landing performance logic
In this section we start
of the basic,
and derive
Exits
with the physical
well-known procedure used by landing aircraft
the underlying equations
with
description
an angle
to the runway
and parameters
of the
of 45 to 75 degrees.
88
process.
The relevant literature
the values
ha3 been reviewed for
of the parameters3.
It is unfortunate
data on
that many
aspects of this procedure have not been researched, at least
in ways that are helpful
for our objective of comprehensive
model building.
Data regardin.
runway occupancy
analyses are relatively
to date
times and related
scarce. Almost all work
has focus3ed on relationships
performancecaracteristics
types
and/or the
exits.
individual
of optimal
of specific aircraft
placem-ent and design
This emohasis tends
of
to
disregarA the operational need for consistent,
sufficiently low runway occupancy times.
While few question the
fact there exists a
disparity between optimal and - resently observed
runway occupancy times, little attention has been
directed towar~ds reasons for these differences as
they relate to airline, exit, 9.ircraft,
runway
nd
airport.
(KOE
7
p.1-1 ).
The published literature
tends to
hoc estimates of mean values
information
is available
of critical
the relationship
parameters.
on variances
distributions of parameters.
on
supply priarily
and
among
This scarcity
model of
developing a
performasnce
cannot
be
sense.
Nor
are
alternative specifications of
instead is
to derive
seems most likely
use
to
validated
in
we
able
always
the model.
a structure
values.
of the
Despite
a
What we
to be the case and limit
reasonable
still less
arameters.
us into
statistical
Some
on
Little work has been reported
information forces
that
al-
of
landing
precise
to
test
must do
model from
what
the parameters
this
in
disappointing
situation, it is poss3ibleto derive a -fullybehavioral model
of landin
performance that produces
cceptable results.
89
Aircraft Inln.in
. modeled in five se-nents
mrovements
:ar
(see figure 11-10):
i) final approach, 2) float, including
flare an:1 transition,
3) deceler actio
on, 4)
5)
exiting.
Each of thefive ophaseswill be considered in
For each phase we will consider
turn.
coasting to exit,
literature
information
in the
relevant to this aspect of landing and derive the
logic for that phase.
Final Approach
The
final approach
phase
refers
to the
section
landing from the beginning of the common approach
the aircraft
method of
is over the runwaythreshold.
modeling the
final approach
path
of
until
Thestandard
phase is
to
assume
that each aircraft flies at a constant velocity over a final
approach of
about
miles
apparently adequate,
in.length.
Thi3
assumption
is
as little
discussion of this prVasehas
been found in the literature.
An important observation is
that
care
mast
be used
specifying
approach
speeds.
obtained from aircraft performance data are
Minimum values,
probably lower
in
than speeds
typically flown.
The average
value of approach velocity is clearly a function of aircraft
type, varying from 140kts.
115kts. for a DC9.
for aircraft such as the B747 to
Thus a set of average approach speeds,
Va(-i), is specified for each aircraft class,
model.
amon
The standard deviation
aircraft
in
i,
to use the
of approach speed,
any one class is
approximately
triangularprobability
density function
is
Vas(i),
4kts.
A
often used
to
90
Float phase
R1
; ;^--
Deceleration
phase
I-- Il------CI~1-·1-~
Transition
Altitu
_
_--
Fla re
I
I
Final
I
Approa
4_
I
Velocity
v(i)
v(i)-Vfr
'N"
Nr--
Vc
·
I-- -
· N~
Ve (2)'
Ve (1)
----·-------- -- ·
Touchdown
Threshold
---
Start of
braking
Distance
v(i) - ApproachVelocity
Vf - Velocity drop during float phase
Vc - Coasting velocity
Ve(n) - Exit velocity for exit n
FIGUREII-10.
LandingAircraft Profile.
Exit
1
Exit
2
91
draw v.(i),
the a-tu1,
aircraft i,
from
determined
fo
a
-
voach
elocity for
ia(i)
ai
snd
i!).
iven aircraft,
then
a particular
Once v( i ) has been
the time the aircraft
requires to fll-y te approach path is !/v(i ),
whereC is the
the commonappro .ch
path.
len-tho
In summary tae parameters nee id
to model tnis
phase
are:
Va(ii). - mean
for each aircraft
approach speed,
class (knots)
2) Vas(i)- standard
deviation
of
approach
speed
(knots)
3) type of probability density function draw sampiles from Va(i)
4) C
- le-gt'
u.sed to
and Vas(i)
of ommonapproach path
(miles)
Float
The float
runway
hlase refers to
threshold
to
aircraft movement
from the
the point on the runway when all laniing
gear have made firm contact with
the runway and braking
may
begin.
This phase includes the flare and transition
maneuvers. 'ransition is the period from the point of first
touchdown of
main gear
contacted the run.way.
The
the
typical
tr.ansport
until
aircraft
the nose wheel has
is
intendingto come
over the runway threshold at an altitude
and
touch down on the
runway.
----
__·_I_
The aircraft
----
-----
l·---l-Y-
main
then
· ·- r -
of 50 feet,
3ear some distance
takes
several
I_-_lllll--·_l-L-lI-
flare
down the
seconds to
I___I·I__I_·___I___I__-
-
_
92
i . e.,
transition,
(HOR 75 p.
226, KE
process
have
the
nose
touchdown
gear
73 p.4-1).
shows that the mechanics of
the
Table II-4 lists
very subtle.
the literature
Review of
this
o
are
Parameters:
Df
- Actual distanceused by a iven aircraft
from
runway threshold to the end of the float phase
(feet).
-
A
Vf
-
v(i)
Va(i)
-
Vas(i) Xf(i)
-
rate
Deceleration
n air during
the float
phase (feet/s/s).
Total velocity drop during float phase
(knots).
Approach speed of aircraft i (knots).
Average approach speed of aircraft class i
(knots).
Standard deviation of approach speed of
aircraft of class i (knots).
of all class i aircraft
distance
Mean float
(feet).
of all
Xfs(i)- Standard deviation of float distance
class
Table II-4: Float
i aircraft
Phase Parameters
parameters for this phase
used in the derivations
Despite the
comprehensive
critical nature
Various authors provide
indicates (OR
and defines additional quantities
in this section.
analysis
occasionally on
(feet).
of
to
it seems
data on one or
the ranges
75 p.228)
of this
of the
process,
have
been
little
done.
more parameters and
parameters.
Horonjeff
that the floating distance is 1500
93
ft. for transport aircraft and 1000ft.
for twin-engine
general aviation aircraft.
Swedish measured this distance
at the Boston and Atlanta airports
of 1360 feet (standard
and
1509
feet
aircraft.
feet.
(3SWE
72) and found values
eviation
469 ft.)
(standard deviation
Large
aircraft
(DCS,
453
747)
ft.)
B727
of 1650
Swedish also provides
of the distribution of
which indicate that this parameter
for
had averages
Convair 580's averaged 930 ft.
selected graphs
for DC9 aircraft
touchdown -distances
is highly variable.
It
seems important therefore, to model this variation.
Horonjeff indicates
is about 2.5 f/s/s.
is
about
5
to
(BOE 69 p.3-164).
Boeing
to
that the in-air
He
also indicates
total
(HOR, 75 p. 2 2 9)
8kts
Time through this
be 7 to 11
deceleration rate
seconds.
as
velocity
does
drop
Boeing
phase is indicated by
Approach
speeds
have been
discussed above.
In addition
to the parameters,
the equations that govern this
more
detailed
information
we
we also need to consider
process.
assume
In the a.bsenceof
that
the
standard
equations for movementof a body under constant acceleration
are sufficiently accurate.
V = A*t + Vo
(9)
X = A*t 2 /2 + Vo*t
Equations
(9) and
(10)
(10)
state the time-distance-decelaration
relationship for a general
acceleration,
initial velocity, Vo, and time, t.
A,
distance,
X,
These two equations will
94
section to various
be applied at several points in this
runway performance calculations.
equations
Applying these
phase
float
the
using
parameters given above reveals the unfortunate fact that the
See figure
various given values are not exactly compatible.
with
a Va of
space
graph of the parameter
for the
II-11
a
20kts,
for an aircraft
typical value for aircraft like the
Figure II-12 shows ho: the parameter space moves with
B727.
values
differing
of
Va..
Hatching the given values of float
or a
distance will. result in either a very low deceleration
Reducing the distance brings the time in this
very high Vf.
phase
below
the
values
in the touchdown data.
deceleration occurs
seem.
since
significant,
If we
seconds.
8kts.),
model
Vf is
assume that
it
p.4-3).
two
It
is
D eceleration
takes only
transition
or
very
three
somewhat higher
(say
reason but
rates will be within
to include
the transition
In
out to cause problems.
necessitated
exit
this
(KOE7
Logically float distance should be increased (to
around 1800ft)
turns
Koenig indicates that some
that
then deceleration
still low.
the transition phase
in the transition
unlikely
the
Swedish's data apparently does not
distance.
include transition
Some of
the literature.
due to the omission of
problem may be
would
in
was
determined
higher braking
selection
that
the course of testing
longer
rates to
orobabili ies.
phase but
This
float
the
distances
achieve the
rapid
this
correct
deceleration
95
4.0Tf =5 seconds
Vf = 10 kts
Vf
= 8 kts
6
.i
7
( )
8
i.
1-1
Vf = 5 kts
i
1.0
Vf
= 2 kts.
ci·-,
-,,, 111_.'"·
0
__
_I
500
t*.
-·-;--····i-,
_1
1000
1500
2000
Float distance (feet)
Va = 120 kts.
FIGURE II-11.
____YIPr__U·_^UUYl___liilll-i-il_
Interrelationship
Phase Parameters.
of Aircraft Floating
---IIIIII -_l-m_-XL_L__IIII_
96
resulted in
unacceptably low
would be possible
by
increasing
to reduce te
Vf
still
braking needed.
the
high
end
runway occupancy
significance
further 'to
Unfortunately
of
times.
of this problem
redluce the amount
a Vf of 8kts
the reported
It
range.
of
is already
at
author
has
The
discussed this problem ith individual pilots and has read a
numberof operations oriented articles for
fly
These sources inlicate that aircraft
at 1.3
times
the stalling
stalling speed.
speed
private pilots.
the
and touch
final
approach
own at
or near
For typical air transport aircraft this
would involve a velocity drop of 30 knots.
^elocity drop were taken after
if al
of this
the threshold was crossed it
would result in unacceptably large deceleration rates.
may be then that some deceleration occurs
the threshold.
direction
8kts.
of
We chose to resolve
leavirlg float distance
Rigorous resolution
availability
of better
measure all relevant
data.
float distance.
fast approach
It
speeds
lonaer distance
at 1500ft.
and
Studies
would seem logical
(for their class)
type with slo,,er approach
speeis.
await the
in order
of parameters.
been found on how Va
down the runway
Vf at
are needed which
parameters for each aircraft
has
rossin-
this problem in the
of this problem must
to permitstudyof the interaction
No information
rior to
It
that
is related
aircraft
to
with
would tend to float a
than aircraft of
the same
On the other hnd,
the
97
4. 0 -
3.0 t = 5
--
.A
ul
OP
cH
2 .0
t = 7
v~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I
I =
i
L
v0
-
-
140
t = 10 ---
120
1.0 .
I
0
0
^ -- r
500
1000
1500
--
r---.------L-t---
2000
Distance (feet)
Vf
= 8 kts
FIGURE II-12.
.I_,
......
·-II..-. -.aY·a"-·I-~~-'"'"""`s""
Effect
of Va on Floating Phase Parameters.
98
correlation between the
two is most unlikey
Therefore the
following compromise
lieu
describing the
of data
procedure is
correlation.
in
used,
A mean
and standard deviation of
distance (Xf(i))
to be perfect.
float
float distance
The actual
(Xfs(i)) are specified for each aircraft class.
that any given aircraft takes to float and to
distance (Df)
transition are drawn according to the following equation:
Df =
+ B(v - Va)/Vas
where
Vas is
(11 )
the standard
actual approach speed of the
deviation
of
aircraft.
Va and- v is
the
We have omitted the
subscript i on v(i) and Va(i)' in the equation and folloing
discussion for clarity.
is to
have actual
actual approach
term, X,
The intent
of the chosen equation
float distance be
speed and a
an equal
function of
random component.
The first
is intended to represent
this random component and
the second term, V(v - Va)/Vas,. is intended to represent the
contribution of
distance.
X
approach speed to determining
is
assumed
to
be
drawn
actual float
from
a
normal
distribution with:
E(X)
= A
VAR(X)
where E(X)
variance
E(Df)
variance
is the expected value
of X.
= Xf,
= C
We
wish
V(Df) = Xfs 2
of the
two
terms
of X and VAR(X) is the
to select
and
the
A
+ E(B*(v - Va))/Vas
+ (B/Vas)*(E(v)
- (Va))
and
C so
contributions
are equal.
values:
E(Df) = E(X)
A,B
Taking
to
that
the
expected
99
but as 'the expected
E(Df)
=
Thus
A should eual
alue of v is Va
A
the
expected value of Df which is Xf.
Taking variances
VAR(Df) = VAR(X) + (B/Vas)2
= VAR(X)
2
+ (3/vas)2
* VAR(v - Va)
* VAR(v)
(/Vas)
2
* VAR( Va)
But VAR(Va) is zero and
VAR(v) =
Vas
50
VAR(Df) = VAR(X) + 32
f_we wish th
VAR(X)
two parts to have equal weight then
= VAR(Df)/2
or
VAR(X)
= Xf s2'/
andr
vAR(Df)/2 = 32
or
B = Xf3/s'SQRL(2)
where SQR7T(2) is the siare
root of 2.
To summarize:
X is normal with mean Xf and standard deviation Xfs/SQRT(2)
and
Df = Xfs*(v
- Va)/(Vas*SQRT(2))
The application of
the following example.
an averageapproaci
spe.:
(12)
this formula can be
Suppose tat
of
ts.,
12' ts
illustrated by
an aircraft class had
standard
de~viition
100
of approach speed of 4kts., a mean float distance of 1500ft.
and a standard deviation of
all the aircraft
float distance of 500ft.
of this class that were
an approach speed of 124kts.
mean) would have a float
modeled as having
(1 standard deviation
distance
Then
(Df) described
over the
by
Df = C + 500(124-120)/(4*SQ.RT(2)).
Simplfying
Df = X + 35 5
Fast
aircraft
of
a given
taking a longer distance
slower aircraft
of
model v is first
class are
to flare
Df.
and to
the same class.
transition
Then,
and Xfs(i).
than
Then X is
X and v are used to
assuming Vf =
8kts.,
we solve for t
place
of Vo and v - 8
using equations (9) and (10) with v in
in place of V.
as
When implementing the
chosen randomly from Va and Vas.
chosen randomly from Xf(i)
determine
therefore modeled
The resulting value of t is time in the
float phase.
Deceleration and coasting
Deceleration and coasting is the
the
begining of
braking to
the
phase of landing from
moment of
exit from
the
been given
to
runway.
It
appears that
little attention
measuring actual deceleration rates
has
for transport aircraft.
Boeing does present (BOE 69 p.3.60) a very complete equation
for
acceleration and
runway as
a function
deceleration of
of thrust,
an
drag,
aircraft on
lift,
the
velocity,
101
brakin
and
rua-iW- 30ooe but
oe-
r t
oro ,neff (DR 7~. .223)
not
vario
conszn
ns
in ti't
ne. 'e i,
inicatee
tha' dece]lerati.on avera.,es3
ve value
f/s/s.
may ori-:inait fro1 tudfies on prior t
aircrf
types
like the 377 and
ooera.t
fran
nort
deceleration
DC9 that are dez; ndee to
m ht
have
-to
dependinq
on whether
used an- indicates
tht
varies
moderate
frown5.5f/s/s
or
hard brakin ;
NHoinformation is
on how this .-ould vary over A.cr
provided in ,ithe
seem
wouid
that
surprisingly since
occupancy time .
to calibrate
lsing mean
be
lower
as-
alsi
on
wet
to
the
ichane has been found.
information that
fThe
is
source
r
ul
but no infotrmation
compared to dry runways,
ofte
' tt;
na manitude
n 4.t,.. 0+ oI
cass
deceleration
to
moderate br kin', is
from his data,
more typical.
-how
this
o e...n_
Koeni
states
to airr.t.
(KOE7r p.4-1 ) tnat deeier'ition
locical
hi on:er
Horonjeff does not indicate
rtes.
-val1u
e might v a ry
value
mht vry fron aircraft
1Of/s/s
te i:troduction of
and thus
fields
h is 'ure
it
is usually co lected
is
reafily
observable)
is
(not
runway
in the next section we use this inforZation
the
anding
values in
model, and we find that
performance
of 5.25
the range
to 5.75
feet per
second squared -with
' a standard deviation of 0.75 f/s/s gives
acceptable results across all aircrafftclasses and runways.
Li ttle
deceleration
on the
rnway.
infor nation
rates
it
vary
was
found
urin., the
seems louicai
about
time
how
aircraft
when an aircraft
is
that.ircr:ft laiitain
full
102
deceleration down
to some safe speed
low deceleration rate)
taken in
taxi which is 10 to 20 kts.
found that a
results.
occur at a
coasting speed
(at a
exit to be
on the runway.
logical that this would
than aircraft
it was
until they are near the
order to minimize time
also seem
and then coast
It would
higher speed
In the validation
of 25 knots
gave good
For simplicity, we assume that the coasting phase
is.conducted at constant speed.
Exiting from the runway
There are various types of
vary from
high-speed exits
exits from runways.
to sharp 90 degree
sometimes even greater than 90 degree exits).
These
turns (and
The speed at
which aircraft may
clear the runway will
the type of exit.
To use the model, an exit speed, Ve,
specified for each exit.
Suggested
vary depending on
is
values for Ve are zero
kts. for 90 degree exits, 10 kts. for angle exits and Ve = 30
for high speed exits.*
An
important
interaction
question
is
between deceleration
whether
there
rate and
exit
is
any
location.
One possibility is that pilots would try to leave the runway
closer to their intended terminal gates. Koenig divided his
data between
"motivated carriers" who had an
exit early and other carriers,
of runways
On a majority
examined motivated carriers had runway occupancy
times of 4 to 6
seconds less
(KOE 78 p. 3-3).
On several
*
who did not.
incentive to
than the
other
remaining carriers
runways
Conversation with Professor Odoni, MIT.
there
was no
103
data
:J3es n ot
vailable
oe-nigdoes not r port
since
rocess,
were motivate
this
.ocrmir
the fLitting
for
at -arly
to ex i
begins to
'he time the aircraft
- odel this
An extension of FLAPScould
iand.
the
ach runw-ry. HIowever,
is 'known at
of each aircraft
which airlines
aircrarzt is tracked throughiout
the ,round destination (apron
model, since eac. particular
Thereiore,
the simrulation.
area)
of a model of
FLAPSfor implementing such a
xist in
basic frameawr' does
The
odele .
' i_2ference.This beh'ivio r -wes not
significant
interaction.
a second, more limited
Because of th e daa limitations,
and exit location,
interac-tion between deceleration res
dependent only on runway onditions,
was eveloped.
found to be usefuil in enhancing the performance
avoid lon
caused Dy narrowly
normnalbraking
periods of coastir.g
missing an xit.
is
no close
rollout, it is assumed the
to make the
searlier exit.
braking being within
aircraft.
on trhe' iunway,-
usin.
an aircraft
erceived as "close")
subsequent exit
ilots
by less than some critical
vi 11 iss an exit
amount (so that the miss is
If
as
f the nodel
It is based on the idea that
across several runway.
would like to
It
thus necessitating
and there
a lon_
ilots will employharder braking
This is conditional
on the harder
the performance capabilities
of
the
Conversely, if a long rollout is inevitable iven
it is assumed that a pilot will
the placement of exits,
elect lig'lter brsking to reiuce runw'-i occunncy time.
ii-·--l-----a.---r.--xLu-(·
·-- r^i
---·-
li--l-ui
· ·--L1I··--
·-- ·----- -- -·------------
·-··-- a-Lrnn
ra·
--
· ·--lxx
104
Experimentation
600ft.
as the
bound
on '"lon,
with
this
definition
showed
that
"near miss" and
of
the
narrowed
roll"
predicted andactual
model
performance.
using
as the lo-er
divergence between
deceleration
Aircraft
only if they were on the "wron.?" side of
rates were adjusted
nalrier braking was employed
average braking rates, that is,
iust missed exits only if
that
on those aircraft
original braking rate was below -average for
their
that aircraft
Aircraft with lon, rollouts were decelerated more
only if their' original- braking rate was above
class.
slowly
average.
phrases are
Because the deceleration, coasting and exit
closely related, we summarize them together.
Once all
specific
a class
mean
Ve(n)
negotiate exit n.
speed at which
is the maximum
that is
deviation.
and standard
Ve(n),
is
aircraft
can
For each exit, n, on the runway an exit velocity,
specified.
ontact
Aircraft
Ar,
constant rate,
assumed to decelerate at a
drawn from
solid
deceleration phase begins.
with the runway, the
are
gear have made
of the landing
Note that Ve(n) is direction specific.
A
high speed exit in one direction
is a very sharp exit in the
other
direction.
that aircraft
first
exit for which
Ve(n)
It is assumed
the aircraft
or less for that exit.
adjusted either up or down to
and the runway occupancy
time
will take the
to a speed
can decelerate
The deceleration
rate can be
minimize near misses
for aircraft
of exits
on long rollouts.
105
This
determines where aircraft
The aircraft.
is assumed
had when enterin7
'c ear
to i.tul1ly
the landin.g
runway.
brake from the seed
(Val - 3'kts) to a coasting
tis::ri:
it
speed
Vc, which is a secifie:
value con.stant across all aircraft
types. The aircraft coasts until it is near the place where
it will clear the runwaywhenit resumes decelerating at the
previous rate to arrive at the
chosen exit with speed equal
to Ve(n).
2.c Validation
Both Swedish an1d Koenig report data on runway occupancy
times
The
for a number of airports,
anding
runways and aircrafttypes.
performance model
described above
against this data for four airports.
.
two Boston
runws3.s (data
from New York LaGuardi.a,
KI3,78).-
from SJE
The model was run for
72)
and for
Los Angeles and Buffalo
For the Boston airport
w'as-checked
one runway
(data
fron
three different cases were
run for each runway, one for each of three aircralt
odels.
The Koenig data is for "'class 3" aircraft which include
BAC111, DC9 and B727 types.
parameters
and the
__IWI___LI___WWYnX_11-^11·._1111^1^
that
the only change of
to model these cases -as to change approach speed
airport specific
exit speed.
data
Note
paramnetersof exit distance
and
An adjustment between the Koenig and Swedish
sets had to
be made as
incompatible.
Koenig reports
than Swedish.
his
_-
.
the
wo sets
of data
consistently earlier
are
exits
liscr epancy was resolved by usin, tnhe
IXI-i
-
106
specific float distances reported by Swedish to fit the
Swedishcases and the specific deceleration rates reported
by Koenig when fittina
Swedish does not
the Koenig data.
report deceleration rates nor does Koeni report float
.distance. . A. longer float distance and lower deceleration
Table I-5
rate was used on the -Koenig data.
describes -the
Value used for
Swedish data
Koenig data
Parameter
.
.·.
Deceleration rate:
mean
standard deviation
p. d. f.
6.00
5.25
.75
.75
normal
normal
Floating distance:
mean (DC9,B727,3707 )
mean (class 3)
standard deviation
Approach speed:
mean DC9
mean B727
mean B707
mean class
1500
(not used)
(not used)
2000
450
knots
120
4
Coasting speed:
in float phase:
4
25
knots
8
knots
Near miss cutoff*:
600
600
Increment on deceleration rate*:
1.0
Critical coasting, distance*:
p. d. f.
s. d.
feet
feet
s. d.
- probability density function
- standard deviation
*see text for details
Table II-5:
Landing
feet
125
140
3
drop
fL /ss
450
1 !5
standard deviation
Velocity
Un its
.
Model Validation:
Common Parameters
_ _------· _·1-111--·1__111
_·_·II_
I·-----I
107
commrnonassumptions
Exit
Runway
us-!
'Distance
Type
4500. feet
Boston
Logan
The specific
Ifor each case.
runways
Va
7000
High Speed
90 degree
30 knots
4150 feet
Ti
50 knots
0
27
Boston
F
J
Logan
10
5200
33L
6800
N or-th
New York
22
Los
Angel as
25R
7650
8
4189
4955
9
51 60
10
6233
"7
1.0
Angle
.ide 90 deg.
3678 feet
6
La Guardia
n Speed
10
0 knots
90 degree
90 degree
[i gh Speed
90 degree
90 degree
0
30
3.
0
O0
0
31
32
4136 feet
4666
90 degree
45 degree
33
34
5515
6787
7424
45 degree
45 degree
45 degree
15
4768 feet
5178
6203
45
90 degree
15
0
45 degree
15
35
Buffalo
7
8
10
15
15
15
dezgree
93 degree
7997
knots
0
II-6: Landing -'odelValidation:
Table
Case Descrition
used for the validation are described
The procedure
used to validate
in table
the
model was to try to
find a set of parameters (A, Vf, Vc, D, Ar,
produce
acceptable
results
aircraft types without 1)
for the parameters,
_
___
I
__
_C__
I_
CI
I_
across
II-6.
Ve)
seve ral
that would
runways
straying beyond reasonable values
ani 2) without extensive alteration
_·I_
and
_II
__
______
of
108
values' over the cases bein!? considered. The presentation of
the model in the section above discussed a number of these
the final
presents -the results for
Table II-7
tradeoffs.'
model specification.
The model
The major
matches the
sample
be considered.
data -
size of the existing
exit.
So
exit
First,
in
"tNorth",
B707's
exit in 51
time reported
occupancy
4 and
to
So it
B707 average
per
quite
Swedish reports
72 -.89).
For exit
seconds.
For
exit
Thi
seconds.
second
using the
reductions
for DC9 and 3'727 using
exit on the same runway.
more data taken,
12
be
time when
additional runway occupancy
exit compares
3L.
the small
truth
707's exit in 837
7650 feet down
32 second
further
down,
runway
note
Secondly,
exit by exit runway occupancy times (SiE
6800 feet
well.
only 2 or 3 aircraft
distributions could
different from those reported.
T,
uite
B707 aircraft on
iscrepancy is for
Two factors should
runways
two Logan
in
the further
may very well be that were
runway occupancy tiraeswould
decline from 55 seconds.
The model's performance
on the Koenig data is close but
not generally as good as on the Logan data.
to spread
aircraft out
over the exits
indicate should happen.
to be low.
A
Model
The model tends
more than
the data
runway occupancy times tend
Sample size is not a problem here.
number
parameters to
of
changes
bring the
could
in the
be explored
predicted prformance
--
-.__L-·--l_-~.-·
---------
I
model
intocloser
~ i -11~·l~-P···--
-11---·1
-
·
109
Runway occupancy
Air craft
Exit
type
1
4
5
ev.)
(15.0)
0
2000
(18.5)
2000
.20
50.
.8
.17
47.5
.64
.56
.36
45.3
.44
53.2
.50
.50
15
.85
53.2
60.2 (15.2)
2000
2000
Boston Logan runway
.74
.16
.06
.04
'odel:
.66
.29
.04
.00
42.4
40.9
.41
.20
. 32
07
49.1
.33
.46
.16
.OO
43
.2
.3
.2
.06
55.4
50.2
3707
.06
8
35
.54
4
52
\ 7.9)
( 9.8)
( 9.0',)
41
9
2000
uardia runway 22:
New York La
3
Actual:
>iIodel:
.01
.02
. 07
. 07
59
.4
. 06b
.0
26
43.3 ( 9.5)
.51
47.8 ( 7.8)
2000
.37
44.9 ( 7.9)
2000
52.6 (14.1 )
48.5 ( 6.9)
2'000
Adjustel
mod el:
Los Angeles
21
33L:
Atual:
3727
Class
mean(st.
4lodel:
3707
Class
3
Actual: .80
3727
DC9
2
Lo-grn runway 27:
Boston
DC9
time
number
.01
09
.53 .00
14
runw~ay 25R:
3
Actual:
.02 .14 . 55
Aodel:
.06
.25
.05
.19
.41
.25
.08
.15
.10
. 72
.02
.26
.20
.43
.1 1
1 38
Buffalo runway 23:
Class
3
Actual:
Model:
Table 11-7: Landing 'lodel
· 1-··-----··-_----_-rr--rrl·-
55. 9
53.7
Validation: Results
( 5.7)
( 9.0)
1 24
2000
110
agreement with te
the variance
ata.
The obzious
solution,
in the ranlc;n variables,
so few data
exist
parameters.
Variance
o th.
is 'hard to evaluate
variances3 of
in aporoach
of reducing
a
number of
as
the
speed and float distance
account for m0ostof the variance in performance, but these
values
are
-lso the
best documented
and thus
the
most
difficult to justify altering.
One possible change in
parameter values is presented in table II-7 for La Guardia
under the title
of "Adjusted illodel".
This is intended to
show that t edegree of discrepancy in
is the model
in line
with the uncertainty in the parameters.
The adjusted model
for La uardia differs from the original model in that
the standard deviation of flcat distance is reduced from 450
to 300 feet,
and 2)
from 5.25 to
5.75 f/s/s.
average deceleration
rate is increased
These changes bring the results
into line with observed ata. The same chanes on the other
test airports,
however, do not produce similar
Extensive model fitting
the scope of this
and sensitivity
improvements.
analysis
is beyond
work and was not done.
It is worth emphasizing again that no attempt was ade
to fine tune the model for runway specific behavior.-
Obviously such tuning of deceleration
rates,
coasting
speeds, floating distances and exit velocities could cause
an exact match of predicted to actual behavior as the model
has many more parameters
points.
Doing this,
than there
are independent
data
however, would negsate the value of the
111
exercise
as a validation.
the text
is to answer
model accurately
landing
This is because
the
represent
aircraft
or
is
the objective
question:
can this form
the major
modesof
appears from the results given
of the
behavior of
odelnecessary?
a more detailed
of
It
above that the present model
is quite satisfactory.
3
Aircraft Performance on Takeoff
The principal issue in
runways is to
modeling departure movements on
determine how long each
aircraft will occupy
the runway.
Mluchless analysis of this issue has been done
for takeoffs
than for landings.
There are no studies of
to the landing studies reviewed above.
takeoffs equivalent
The only information
available
is
runway occupancy time
data.
This is somewhat surprising since the determination
of the minimum required length of runways is set primarily
by the requirements for takeoffs (HOR 75 pp.66-78).
There are
absence of
proper
a number
analysis
location
in this
of
Whereas landing
of reasons
I
I
·-- I---·
··-II
I
First the
not
runway occupancy time
arise
to affect
I-
·--. --
--------
takeoffs.
there
is little
takeoff performance
the grade and orientation
-
of
minimized by
of the runway.
as will be seen in the next section,
-
for the
question
for
can be
location of exits,
designer can do
other than changing
Secondiy,
area.
exits does
accurate placement and
the airport
that may account
---·--.----
·----·-·-
the rninimllm
·--·
I-
-
1.
112
separation between tk.eoff's is both simpler and shorter than
IPinally, the dynamics of takeoffs are
between landings.
less
simpler and
for
combination of these factors may account
The
ladings.
than for
variable
the comparative
neglect of analysis of takeoffs.
In view of
this situuationthere is little
that can
be-
than
to adopt
a
to represent
done
this
model us-ing
simple
operation
other
runway occupancy time
as the primary
A mean and standard deviation of rnway occupancy
variable.
time for each class of aircraft are used as inputs to FLAPS..
runway occupancy time is
Each aircraft 's actual
Irawn from.
this distribution.
The primary use in FAPS
of
occupancy
runway
is to
time
determine the time each aircraft needs to cross taxiways and
intersecting
runways
while occupying
needed
assess
proper
to
movements.
aircraft
To derive
separation
To
runway lengths,
runway occupancy times
from a standing
start
6000 feet down
If X is distance,
(9) and (10):
X =
(a/2)t
2
and
t = SQRT(2X/a)
at the end
the runway.
point from the start
for
intermediate times
accelerate uniformly.
This is
the runway.
conflicting
we assume
adjust for
different
are defined as time
of the runway to
Then time
that
a point
to any intermediate
can be found as follows:
t time and a acceleration,
then from
113
Let T be time to 6000 feet
T = SQRT(2*6000/a)
or
2/a = T/6000
so
t = SQRT((T2/6000)X)
or
t = T*SQRT(X/6000)
4
(13)
Separation of Aircraft Movements
4.a
Introduction
The
separations imposed
major factor
in
determining
major area of work for
This section
between aircraft
the capacity of a
improving capacity
discusses te
are both a
runway and a
(SIN 7S p. 3-1).
procedures and rules by which
aircraft
are separated on a runway that is being used either
for landings, or for takeoffs or both. A discussion of
separations involving operations on parallei or intersecting
runways
is
presented
introduce the
Each
the
type
in section II.E.
framework necessary
of potential conflict
appropraite rules
separation formulas.
translated
We
will
to discuss
will
this
first
topic.
then be analyzed and
into consistent
minimum
114
4.b
Conceptual Framework
Separations
operations
other.
are required
which
are
to
maintain
potentially in
the safety
conflict
with
of
each.
They are intended not only to prevent collisions but
also to eliminate
the hazard
to aircraft
of encountering
the
wake turbulence of large aircraft.
Obviously the concept
of aircraft.
As
landings and
of a separation involves
there are two types
takeoffs,
there are
a pair
of runway movements,
thus four
categories of
separations for a runway:
1) Arrival/Arrival (A/A) Arrival movement followed by
another arrival.
2) Arrival/Departure (A/D) Arrival followed by a departure.
3) Departure/Arrival (D/A) Departure followed by an arrival.
4) Departure/Departure (D/D) Departure followed by another
departure.
The first
term
that has
already
f the pair
begun
refers
its
to the type
operation.
of movement
The second
of the
pair refers to the operation being scheduled.
Some separations
times
between crossing
distances.
either
as
internally
wake
are logically
FLAPS allows
a
time
or as
reference
issue
to cover the
point,
a
distance
and the
and
same distance,
Because
times
the
as
be input
converts
the run.
different
terms of
others
all separation types to
to a time for use during
turbulence
require
some
specified in
each
of the
aircraft
majority
of
115
separation types involve
a matrix of values,
one for each
possible pair of aircraft classes.
Aircraft
point
"cleared"
the aircraft
delayed,
a
save
real
occurs
at
some
through to
Beyond this clearance
not diverted
the
takeoff roll.
as aircraft
to
movements
when
while spacing
accomplished
runway.
takeoff
begin the
is less clear
movement.
committed an-d is
For
approach pattern
been
are
or
case where an actual collision becomes
clearly
-permission to
point
is
in the
danger.
commitment
operations
by air tr-affic conrtrol to proceed
completion of the desired
point
runway
undertaking
a large
The close cooperation
this
controller
of
gives
For landings
are funneled
the
into the final
and sequencing
extent
point
has already
upstream
amongvarious
from
the
controllers
means that the point of transition from terminal airspace to
-the landing runway is
aircraft
blurred.
at some point
converge onto a commonfinal approach path, usually
5 or 6 miles from the
discussed,
interarrival
is
runway threshold.
the portion of flight
separations
convergence to
point of
are
applied,
the final approach
point at which to assume
The
However,
commitment
This.
as will be
where the final
so the point
-pathmakes
of
a convenient
that landings are first committed.
is significant
to
the issue
of
aircraft separations because the separations are checked and
enforced when an aircraft is
to a runway operation.
first eligible to be committed
The separations
re applied aain3t
116
aircraft
that
already
the
run-ay
performance rules
until
the first
more
than one
the
operation
in
If
accordance
are not Umet, the
before the aircraf
can be
minimum
pplicable separation controls
to
the
sections. If
is heId
Ihflere
are met.
applies,
committed
with
aircraft
timewhXenthe separations
separationtype
the
aircraft proceeds
discussed in the previous
the minimumseparations
longest
committed.
requirement is ,net,
separation
execute
are
all
must be
met
This means that
the
the release
of the
aircraft.
The
entire set
aircraft.
On a
arrival/arriv-al
used.
of separations
runway used
separation
On
a
do not
just
for
departures
for runways
runways used
time,
each
arrivals
the
will be the only type that
only
runway,
departure/eparture
separation
is relevant.
situation
apply to
using
mixed
for both arrivals
only
the
To discuss the
operations,
and iepartures at
it is necessary to anticipate somewhat the
of airport control below in section II.F.
is
that
is,
t'he same
iscussion
Discussions with
airport personnel and controllers indicate that runways used
for mixed operations are operated in one of three ways (Also
see WEI
1)
80 p.37).
Arrival priority.
over
priority
scheduled
using
the
In this scheme arrivals
departures.
to meet
A/A
adequate
separation
Arrivals thus
separation
without
need
on final
are
only
iven
be
approach
consideration
of
117
departures.
whenever
Departures
the
space
are fitted
between
separation
D/D separations)
for departures,
is
not
Departures can
next
arrival.
The
addition
to
but the departure/arrival
for
schedulina
of
adequate time exists
D/A separations
arrivals
permits.
is thous used (in
used
only go if
between
arrivals
arrival/departure
separation
in
arrivals.
before the
are used to assess this, as
explained in the operations section below.
Occasionally in
is- incorrectly
system.
the literature this mode
re-fer-ed
to
as
a
of operation
"preemptive
priority"
It is actually a non-preemptive priority system, as
once a departure operation (the lower priority) is committed
to
a takeoff
roll,
the
appearance of
a higher
priority
arrival does not cause the takeoff to abort its roll.
2)
Alternating
operations.
between arrivals,
one departure
Here,
when necessary,
added spacing
is used
to
insure that at least
can be released between
successive arrivals.
Implementation
of this
procedure
requires
that all
four
separations be used.
3)
Departures only.
In this
method,
departures have queued up for takeoff,
off" until
the departure
acceptable level.
queue has
used only when many
landings are "turned
been worked down to some
This method differs
from the case of a
departures only runwayin that here, arrivals continue to be
assigned
to
the runway
runway to open
__111_·
__1______
_
and form
again for landings.
a queue
This
waiting
for
the
method will need
118
only the D/D
will be
separations
whenever
a transition. period
committed
to
land
it is
in effect.
during which
complete
their
There
arrivals already
operations.
A/D
separations will be needed for this case.
Throughout the remainder of this
the
three operating
runways.
schemes as
Our attention
work we will refer to
"modes
of operation"
will be primarily
directed
for
to the
first two modes.
4.c
Arrival/Arrival separations
Arrival/Arrival separations have probably been the most
carefully
analyzed
in
generally accepted
the
literature.
procedure for studying this
HOR 75 p.140-5,
the cited references.
the
revised slightly
for use
possible
classes.
These
minimum
allowable
distance
at any
matrix
leading
are
between
the
both are
are then
separations for use
in FLAPS.
aircraft
maintains the
a class
of which are in
of minimum separations
separations
point after
These distance separations
in
We will
in FLAPSand then derive
combination of
aircraft
aircraft
See
the revised procedure.
The method begins with a
each
a
Wewill then explain whythis method
the specific formulas for
for
details
now
case.
-.;EI 80 pp.43-9 among others.
briefly outline the technique,
must be
There is
It
and
stated as
given
on final
translated
is
trailing
pair
the
of
approach.
into time
assumed that
each
same, constantspeed,
119
As the minimum separation is
Va(i) during final approach.
applied at the
point
and 2)
faster than trail aircraft - opening case,
are of the same class and thus
lead and trail aircraft
speed may be included in either case.
these
time separations
each
time
to
Trail
The situation in
aircraft faster than lead - closing case.
have the same
Lead aircraft
1)
considered:
aircraft, two cases must be
which
the two
of closest approach between
allow for the
is added to
a buffer
are determined
imprecision
Once
in
aircraft
This resulting separation
positiong at the approach gate.
can then be combined with information on the mix of aircraft
classes
to derive the capacity
One modification
FLAPS.
In the
of the runway.
is necessary
to
use
this system
work this poses
no difficulties.
the simulation
structure it would
scheduled only upon arrival at
this is
not what
inaccurate
results
position of an
technique the
standard presentation of the
point of reference is the runway threshold.
in fact
in a
in
For analytical
Directly translated into
aircraft are
imply that
Even though
the'threshold.
it will
happens,
simulation
as
not
long as
aircraft on final approach is
cause
the actual
not needed in
the simulation. However, since it is our desire here to be
able to model
dependent
runway
operations
and apply
separations that depend on the distance of aircraft from the
runway threshold*, we must change the
point
of application
of the A/A separations from the threshold to the beginning
*
One example of this would arise when deciding to release
_______
120
of the
commonapproach
path.
This willensure
delay of landing operations due
will
be
applied before
the
that any
to congestion of the runway
calculation
of the
time
of
arrival at the threshold is perf-or-med. Thus the actual
position of the aircraft on final is available to be used in
the simulation.
Simulations,
-like
the ASM model, that
impose A/A separations at the threshold restrict the analyst
to specifying time separations for these cases.
Closin
case
Figure
II-13
presents the time-distance diagram for the
closing
case.
Table
II-8
defines
common
terms
used
throughout the separation discussion.
As this is a closing case, Va(j)
> Va(i),
the minimum
separation applies when aircraft i is at the threshold.
The
resulting time separation at the approach gate (Saa(.i,j)) is
the time i
takes to fly the final
the time j requires to fly
approach (C/Va(i))
down to Raa(i,j)
less
miles from the
threshold.
In addition,
errors in
gate.
a buffer
timing the
separation.
chosen
will
needed due to the inevitable
arrival of
It is convenient
control directly the
is
aircraft at
to parameterize
If an average buffer
the
the buffer
fraction of aircraft that
size (B)
with Zaa = 1.65, for example,
violate
the approach
separation.
In
so as to
violate the
of Zaa*Bsaa is
then 5% of the aircraft
summary
we
impose
departures on a runway that intersects with an arrival
runway.
a
121
Runway
Threshold
Approach
zate
11
C
Ti
Va (i)
IN
Cl of lead
:raft
i
of trail
--- -1·--- t j-i
Saa(i,j)
C
C - Raa(i, )
Va(i)
Va(j)
B=Zaa*Bsaa
Arrival error distribution
FIGURE II-13.
Arrival/Arrival Separations: Closing Case.
122
C
- Length of the commonapproach path
Va(i)
- Average seed on final approach for class i
Vas(i)
- Standard Deviation of speed on final approach
v(i)
- Actual speed on final approach for aircraft i
(knots).
- linimum distance required on final approach
(miles).
(knots).
for class
Raa(i,j)
i (knots).
between class
(miles).
i in lead and class
inimum time separation
j following
Saa(i,j)
-
Bsaa
- Standard deviation of error in arrival position
Zaa
- Number of standard eviations of the arrival
error distribution to be used in setting
buffer length dimensionless).
- Average buffer length (seconds).
that Raa
B
b
Tag(i)
Tt(i)
to be imposed on class j
at the approach gate when class j follows
class i on f nal aproach in order to insure
is met (minutes)
at approach
gate (seconds).
- Actual buffer length imposed on at given aircraft
(seconds).
- Time that aircraft i crosses the approach gate
(minutes).
- Timethataircraft
i crosses the threshold
(minutes)
.
Tc(i)
Nt(a,b)
- Time that aircraft i clears the runway
(minutes) .
- Jormal distribution, truncated at plus or inus
2 standard eviations with mean of a, standard
deviation of b.
A number of these terms
figures II-13 and 14.
are shown graphically
in
Table II-8: Terms used in derivation of separations
123
Threshold
Appro,
Runway
Saa (
B
t ime l
ing
aircraft j
Saa(i,j)
=
B
FIGURE 11-14.
=
1ing
Raa
(ij )
Va (i)
Zaa*Bsaa
Arrival/Arrival Separations:
Opening Case.
II____
124
separation
of:
Saa(i,j) + b
(14)
where
Saa(i,j) =
and b
/Va(i)
- (C-Raa(i,j))/Va(j)
is drawn from
Zaa*Bsaa
a normal
and a standard
(15)
distribution with a
deviation
mean of
of Bsaa.
Opening case
Figure II-14
pre3ents the case
The same terms are used here
Raa(i,j)
where Va(i)
> Va(j).
as in the closing case.
applies when trailing aircraft
Here
i reaches the
approach gate.
The time separation is merely the time it
takes the
first
landing,
buffer,
is
b,
added
j,
as before.
to fly Raa(i,j)
miles.
A
The separation is:
Saa(i,j) + b
whe re
Saa(i,j)
= Raa(i,j)/Va(i)
(16)
Note that should Va(i) = Va(j),
at
all points
reduces
when both
pair of aircraft
its
separation
proceed,
Va(i)
are on
applies
final and
(15)
to (6).
Once the appropriate
begin
aircraft
the separation
met.
an. actual
and Vas(i).
the time
needed
+ b is
the second aircraft,
descent
is
Saa(i,j)
from
the
Once an
is not allowed
approach
gate
aircraft
is
approach speed,
This actual
j,
drawn for a given
v(i),
until
permitted
is
to
the
to
drawn using
speed is used to determine
to fly from approach
gate to threshold.
125
Numerical values
-
Raa(i, j )
Raa
conditions
in which
for situations
miles except
is 3
(IPR)
rules
fl ight
instrument
nder
wake turbulence must be consi.lered-.For visual flight rules
no formal
conditions
(VFR)
values
has
come to
be
but a
set of
of
actual
as typical'
recognized
The two sets are given in table Ii-9.
conditions.
operating
standards exist
Buffer - Thnemost often used values for the buffer size
are Zaa = 1. 55 and Bsaa = 1
If we
-Va(i) -= 140,
assume
those shown
lower left elements
may
= 1
tlhat result are
(aa)
Note tiat the
matrix are opening cases,
the
rocedure
arise
as. to
formulas for Saa(i,j)
the
assume that
has the same approach velocity,
validity
of
the
since the separation
bove,
separation procedure described
that approach speeds
for i
re closing'cases.
Analysis of the
uestion
6-1).
then the set of
in the lower part of table II-9.
upper right elements in each
A.
marker
at the outer
4-1,
11 Okts.
120
(small), respectively,
(heavy), 2 (arge),
time separations
(SIN 75 p.
seconds
each aircraft in a class
Va(i),
whereas it is known
vary among aircraft of
a given class.
We can calculate the actual separation that results when the
aircraft separations are determined
fixed
Va(i).
separation
separation
'le let
R
under the assumption of
indicate
the
actual
closest
when a
between two arrivals that results
+ b is imposed on aircraft with
of 3s.aai,j)
_11____1_11________--
126
MinimumSeparations (miles):
IFR Rules
Trailing
Class - -
i
Lead Class -
1
4.0
2
3.0
3 3
V'R Rules
2
5.0
3
6.0
3.0
4.0
3.0
2
1
3.6
2.7
1.9
1.9
3.0
Derived Time Separations,
1 .9
minutes (Saa(i,j)
3
4.5
2.7
1.9
+ B):
IFR Rules
VFR Rules
Trailing
Class - -
1
Lead Class -
2
3
1
1.99
2.36 . 2.73
2
3
1.99
2.10
1.80
1 .92
Class 1 is heavy jets,
1
1.51
1.58
1.69
2.24
1 .86
class 2 large jets,
Minimurn3eparation data from HAI 73 . 3-3,
also
see
3
2
1.84
1.53
1.44
2.13
1.67
1.36
class 3 small jets
EI 80 pp. 36-3.
2able II-9: Arrival/Arrival
actual approach speeds v(i)
Separations: Typical Values
and v(j).
We examine only the
more complicated closing case.
The desired minimum distance seoaration, Raa(i,1),
used
to derive a
marker.
The same
time
3eparation,
formula
(13)
Saa(i,j),
carn be
used
is
at the outer
in "reverse":
what separation R in fact results when
given an Saa(i,j),
the aircraft fly the final approach not at Va(i) and Va(j)
but at v(i) and v( j)?
The actual separation is given by:
127
Saa(i,j) + b =
(C-R)v(j)
/v(i) -
for R:
Solving
R = 3 + v(j)*(saa(i,j)
+
Inserting Saa(i,j) from
R
-
(17)
C'/v(i)
(15):
= C +
v(j)*[C /V-a(i)
(C-'aa(i ,j))/Va(j)
b
/v(i)
(1)
This describes
te actual separition.
Taking expected values:
E(R) =
+
/Va(i)*E(v(j)) -
(C-Raa(i,j))/Va(j)*E(v(j))
E(b*v(j)) - c*E(v(j)/v(i)
Simplifying:
E(R)
= Raa(i,j)
+
As b and v( jj are
*Va(j
'(bxv(j))-
a(i)
*E(v(ij)/v())
uncorrelated
E(bv( j ) ) = EZb) E(v j))
=
E(b*v(j))
*Va(j)
=
Zaa*Bsaa*Va(j)
The remaining term E(v(j)/v(i)) cannot be evaluated exactly,
unless
the probability
istributions
of the vi)
for all.
classes of aircraft are known.
As v(i) and v(j) are uncorrelated
E(v(j)/v(i))
it is known that:
= E(v(j)*E(1 /v(i))
Therefore:
E(v(j)/v(i))
= Va(j)*
(/v(i))
The expected value of 1/v(i) is not kno'wn.
However, in the
cases of interest v(i) is on the order of 120kts. with a
standard deviation of 4kts.
Because the mean of (i) is
large rel ative to the spre
of v( i), we assume that
I--·L--aYsl·--·11---111.-..__.
128
E(1/v(i))
can
be adeq.a-tely
approximated
by
1 /Va(i),
and
therefore
R =. Raa(i,j)
proving
+ Va(j)*Zaa*Bsaa
due to
that the average error
the assumpotion of
fixed arrival speeds is insignificant.
Note
that
the
second
term
represents the contribution of the
average separation.
Using the
above,
Va( j)*Zaa*Bsaa,
buffer to increasing the
typical
values,
as indicated
above (Va(j)-120 i'ts.,Zaa=1.65, Bsaa=18 seconds), this term
4.d
1 nautical
in practice of approximately
has a value
ile.
Departure/Departure separations
is much simpler than
The procedure for D/D separations
for -the A/A case.
as
regulations
conversion
Separations are directly specified by
mininmum time between
is- necessary
Additionally the
departures,
(FAA 79 para.
trailing departure
the end of the takeoff runway
340,
at
until clearance is given,
As with A/A
is needed.
rino
80 p.33).
remains stationary
any error in beginning the roll is usually
no.buffer
TWEI
so
A.
neglected.
so
Thus,
separation there
is a
standard minimum, supplermented to avoid wake vortex problems
behind heavy
aircraft.
Typical D/D separation
values are
given in table I-10.
The separation between departures is also a function of
the
route
aircraft
use.
Shorter
D/D
separations
are
129
IFR Rules
VFR Rules
Trail ing
Class
--
Leading class -
Class
1 is heavy
1
2
3
1
90
120
120
2
3
60
60
60
60
60
60
120
120
60
50
60
45
60
35
(values i.nseconds)
Typical Values
FLAPS therefore
separations:
on divergent
routes (ATCp.
allows the sbmittal
number)
(as indicated
of two sets of D/D
and
one
by havi ng
the same departure
when successive
diverging courses (different fix
departures
operation
complicated of
problems
numbers).
to be
separations
single runway
considered:
are
by
separations.
1)
The
far
the
There
spacing
of arrivals
to permit
leave between successive
basic time/distance
at least
landings.
diagram for this case.
the
2 ) The
one departure
Figure
most
are two
rules governing
release of one or more departures between landings.
_____
have
Mixed Operations
Mixed
U
95).
one for use .%hensuccessive departures fly on
the same course
4.e
90
II-10: Departure/Departure Separations:
permitted between aircraft
fix
3
jets.
Data from HAI 73 p. 3-5
Table
2
1
II-15 is
to
the
Several terms
130
Approach
gate
C
Threshold
Tag(i
)
time
aircraft
j
In general Tag(i) + Sxda(i,j) need not occur at time x
as shown here.
FIGURE II-15.
Separations
for Mixed Operations
Single runway.
on a
_____1__·____1_1_1III1I____IILI__
131
used in the
erirations
Rm(k,j) - Tae closest
arrival
3eparations ar3
of :ixei operation
istance
of class
to the threshol
j mnaybe :¢hen a
an
ep.rture
of cla3s k becins a takeoff roll ( miles).
Used to deter:n.ine
to set S (, j).
Sda( k, j)
- TTheaxinu
if
interval
a tkeoff
may roll
ani
allowei between the
ba ginninc of final. ,po.?rozn of arrival
class j an tn, beginning, of
takeoff
roll
of cla3-3 k. Derived from Rmn(k,j).
nen .s3cne1ling arrivals
when the. ruinay is oprate
i lternating
Applied only
mode usin, v c-'lclat
Sxda(i,j)
D/A seprations.
- Tan mininum time sepratio.n
aircraft t t ~ a-3p
oah
i noosea
on
1ass
gate whenclass3
j
aircraft follows ai z.ass i aircraft.
Aplie.
only when tne runway is operated in alterriatin=
;nodeusing se,.ified sparations.
Zxla
- Numberof stan.iar'
error
dAstributio
buffer a3soCi-te1
~e,;iation of t
with Sxia(i,j)
Bsxda
- Stand
Tc(i)
- Timethat landing airraft
ri.i deri
tion
arrival
used to st the length
of
of error in arrival
position at z.'ppro:ah ate a:ssociatei w' .t
Sxdai,j) (se
3on:isi
i clears the runway
(clock time).
Table
II-11:
erms UJsel for Mixed Operation
3eparations
defined
in table
II-1 1.
Release of departure
Any time
departures,
with any
Thl3s,
a
runway is being used for
the takeoffs
arrivals that
on the runway nust
have alraady
this type of separation
operating
mode for
this
ray
alternating, ieparture only).
·_
_·I
q__ll_
both arrivals and
2iost
be
not interfere
begun their
descent.
et regardless
(i.e.
arrival
of the
priority,
132
(HOR 75 p.
1)
there
145-7) that a takeoff cannot begin
are
no aircraft
arrival is
farther from
distance.
We
the threshold
minimum
where j is the class
Rm(k,j),
roll unless
2)
the next
than some
critical
on the runway,
refer to this
and
critical
distance
as
of the next aircraft to land
is
Rm(k,j)
to the class of the next takeoff.
and k refers
is
in this situation
takeoffs
rule governing
The basic
typically 2 nautical miles for all k and j, however we allow
the case where Rm(k,j-)varies across aircraft classes.
Spacing of arrivals
The normal
between
than
landingss tht
successive
one,
departure
this is
However,
one,
and
sometiMes
not the case for
all A/A
airs and
is a
where
A/A
und er
V'FR
conditions
land ings.
To rectify
than under IPR rules.
landinr=s andl taseofls
in capacity between
operated to allow at
runways are often
every
arrivals.
this,
Some pairs
as the
departure
applying an
A/A
in
takeoff,
least one departure
This is
additional separation
between
of landings
separation
is
will not
already
be affected
by
for
a
adequate
to roll.
In the standard
example
and
(WEI 80 p.61-7).
pair of landings
accomplished by
more
the
attendant accumulation of departures queuing for
between
time
between
3eparations are shorter
the imbalance
allows sufficient
can takeoff
problem
particular
often
A/A separation'
treatment of this problem
the A3S4 model),
arrivals
(used,
for
are schedule:l when they
133
Thus, in
reach the threshold.
order
the
to calculate
a
earliest time that the arrival could cross the threshold,
applied from the
-may be directly
separaticn
minimumtime
This time is
time the previous
departure began its roll.
markedas St(k,j)
in the figure for mixed operations.
set
is
of St(k,j)
originally stated
as a distance,
as
probably
separation would
This
separations.
to
generally referred
The
the
D/A
have
been
and converted
Rm(k,j),
to
St(k,j) by the formula:
St(k,j) = Rm(k,j)/Va(j)
will
'use the
to it before
applied
separations
even
though
Thismeansthat any
is
that
eparation
scheduled and has
runway before
the
figure
The mixed operations
arrival.
change
the takeo-ff is scheduled -
will use
the. takeoff
this
is
An arrival
runway.
the
they
scheduled in the sequence
are no longer
nowaircraft
at
- closerto wherethey
One aspect of
sequenced.
arrivals
not schedule
at the approach gate
threshold but
are in fact
does
FLAPS
However,
the
shows this.
(II-15)
intended to allow alternation
of landings with takeoffs cannot be applied whenthe arrival
reaches the threshold.
St(k,j)
or from
Rather
Rm(k,j)
the approach
applied at
derived separation
e
must work backwards from
gate.
We
continue
a D/A separation,
_·
__
_
_____
·I
as the
·
I
__
standard
D/
to
term this
at the risk
of some
because its use is
confusion with conventiol nomenclature,
the same
that can be
to find a separation
separation:
to
____I_·I________
separate an
134
arrival
from
a
previous
takeoff
when
an
alternating
operations mode is being used.
Obviously,
necessary.
no
more spacing
Any
the
model should
calculate
the
the second landing
the runway,
and
the
However,
runways
efficient manner.
are
is
minimum
it would seem that
based
on
landing of the pair clears
will just be Rm(k,j)
miles
its
roll.
can
always
not
the
D/A senaration
takeoff
intervening
added than
beyond
Therefore,
so that when the first
Rm(k,j),
out
spacing
additional
requirement is 'wasted time.
should be
begin
operated
in
such
an
Often the "gap stretching" procedure is a
blanket increase of the shorter A/A separations from 3 miles
to some
longer distance.
separations
specified
in the
same
D/A -
Calculated
manner
the
model
b,
buffer,
to
be
in the
drawn
distribution Nt(Zxda*Bxda,
analogous
label
to Zaa and Bsaa.
a separation
separation".
to delay
applied
as
the D/A
of. two ways:
1)
is given directly and is
the
A/A separation.
calculates the
The specified
internally based on Rm(k,j).
is given as Sxda(i,j)
FLAPS allows
in either
D/A - the D/A separation
Speified
applied
to be
Therefore
figure.
Bxda),
minimum- time
D/A separation
It may have its own
the
from
2)
where
truncated
normal
Zxda and Bxda are
It may appear contradictory
between
two arrivals
a
to
D/A
We label it Sdax(i,j) because of its function:
an arrival a
sufficient time behind
the previous
landing to allow a departure to leave between landings.
135
The calculated separation is represented by
the figure.
nor the point
The best
of Sda are the same as for Sxda.
of reference
to understani
rule for
the subscripts
Note that neither
may
the Sda(k,j)
scheduling
of arrivals
da(k,j) in
be to state
ay
the resulting
and then. explain
how it is
derived.
Under alternating operations using calculated D!
Rule:
separations,
landing
aircraft
(j)
after Tc(i) - 3da(k,j) + b,
may begin a descent only
where Tc(i)
is the
time the
previous landing aircraft (i) clears the runway-andb is the
buffer associated with this case.
In the mixed operations
figure (II-15)
the small x enotes this time.
The rule is erived in the
following
mrayroll is
landing clears the runway, Tc(i).
time
the
that a t akeoff
approach.
miles,
this
If
implies
than C - R.( k,j)
aircraft j
it
Thus,
the length
miles
uses to fly
j
the final
the
annot
this distance
is C
have flown
ore
The time that
is (C-Rm(k,j))/v(j).
j cannot be
approach within
out on
miles
approach
on final at Tc(i).
would seem that aircraft
start down
Rm(k,j)
of the final
anding
that
previous
time the
If k is to depart,
subsequent landing, j, must be at least
final
The earliest
way.
allowed to
(C-Rm(k,j))/v(j)
of
Tc(i).
this time cannot be used as just stated.
However,
the
time
aircraft
I
LI--·11
the
controller is
j at the approach
---
-.
positioning
gate,
-
the
-----
the
controller
arrival
At
of
does not yet
-
136
ill fly on final.
knowthe exact speed that the aircraft
The controller only knows the typical speed of the aircraft.
That is,
advantage
and take
model
the exact
of
the landin
would be
to schedule aircraft j
allow j to
rule regardless
-o only
possible flight paths
From this it
can
fastest possible
from
aircraft
be
j
that began their descent at
Tc(i) - w
Zt
is
a
tolerance
separation should be.
Rmn(k,j)
miles out
then
Tc(i),
slower
w -w^ill be even
farther
the t ime
should be
= (C - Rm(k,j))/(Va(j)
Sda(k,j)
where
Sda(lk,j)
so that the
Theefore,
away from the thresiodoc(i) at
of
"cone"
that leaves at time w.
at the point
a.t
c3se
Rm(k,j)
violate
if we chose w
seen that,
arrives
worst
sho'ws the
for an aircraft
thresnold just
runway
the
II-l5
to
procedure
to a
cannot
when it
Figure
of v(j).
according
the
approach speed
A aore valid
orecisely.
schedule
ahead in
to project
it tw.ould be erroneous
Therefore
are known.
is unknown but Va(j) and Vas(j)
v(j)
'able
+ Zt*Vas(j))
value
indicatlng
(19)
how
safe
the
I-12 summarizes the scheluling
rules for the mixed operations case.
137
Aircraft being
scheduled
k -
takeoff
Rule - commit if. and only
lode of
if, the followin,7
are met:
operation
-
(all)
1) D'D separation
2)
o aircraft
met
on runway
3) Next landina is at least
Rm(k,j) miles from threshold
j - landing
Arrival
1) A/A separations met
Priority
Alternating
Priority
calculated
separation
1) A/A separations met
2) Time
is after
Tc(i) -
1(k,j)
from (19)
Alternatin.g
1) A/A separations met
specified
2) time since last comittment
of a landin.- is reater
Priority
separation
then Sxda(i,j)
Table II-12: M.ixed Operations: Summary of Rules
I_
+ b
where Sda is found
138
E
DEPNDENT
1
Introduction
RUNWAY OPERATIONS
This
section
discusses
how
aircraft
movements on dependent runways are modeled.
that
are
used are
similar
to
separation
The procedures
those discussed
above
in
section D for the single runway case, but there are a number
of complications when the two operations being separated are
on different
occur
runways.
- A/A,
separations
A/D,
and. the
The same
D/A,
D/D
point of
basic types
- but
the
application
of conflicts
values of
vary.
the
Where
parallels to the single runway analysis exist, the procedure
for dependent
runways is not
repeated,
rather
the single
runway procedure is referenced.
There are several
each other.
may depend on
They may 1) be physically intersecting, 2)
parallel or 3)
centerlines.
ways that two runways
intersect along the projection of the runway
We will discuss the first two cases in detail
as they represent the bulk of airport conditions.
case will be
be
discussed only briefly.
We will
number of configurations can be reduced
The third
show that a
to one of the first
two cases, but we will not attempt to show that all possible
configurations can be so modeled.
Table II-13
gives nomenclature
used in
this section.
Some items are repeated from the table giving single runway
nomenclature (Table II-8).
139
- Length of common approach path of the
C
runway used for arrivals
Raat(i,j)
(miles).
Parallel runways used for arrivals are
assumed to have common approach paths
of eaual length.
- Minimum distance separation imposed between
a landing of class i and a following
landing of class j on a parallel runway
(miles).
Saat( i,j)
Sadt(k,j)
- Minimum time separation to be imposed on
class j aircraft at the approach -gate
when a class j follows class i on final
approach to a different runway (minutes).
- Maximum interval prior to a takeoff of
class k clearing the intersection with
the arrival runway that the next arrival
of class
Tag(i)
Ti(i,l)
j
If aircraft
Tc(i)
j)
Rmt(k,
is allowed
to begin final
approach minutes). May be specified
directly or derived from Rmt(k,j).
- Time when aircraft i crosses the approach
gate (minutes).
- Minimum of the time when aircraft i
clears the runway or crosses the
intersection with runway i (minutes).
i is a takeoff,
Ti is always
the intersection crossing time.
- Time when aircraft i clears the runway
(minutes).
- The closest to the runway threshold an arrival
of
class
j can be when a takeoff of class
k clears the intersection or takes off on
a different runway (miles).
Zt
- A measure of tolerance
for the "worst
Va(i)
case" situation (number of standard
deviations).
-Average approach speed, class i aircraft
Vas(i)
- Standard deviation of aproach
Tto(i)
- Average takeoff roll time to 6000 feet
Ttos( i)
- Standard deviation of takeoff roll
time to 6000 feet for an aircraft of
class i (seconds).
- The distance from the threshold of runway
(knots).
class i aircraft (knots).
speed,
for a takeoff of class i (seconds).
Xi(1,m)
1 to the intersection
Table II-13:
I-
·I
---
of runway m (feet).
Dependent Runway Nomenclature
--·I ·I---· ---I--
140
Each
operation
and
is
geometry
discussed
It must be remembered that, as in the single
independently.
a number of separation types may be applicable
runway case,
to the
of
type
must all be met
given situation and they
before an
operation may be committed.
2
Intersecting Runways
every
Almost
operates some or
major
airport
most of the time
York -La Guardia
Airport
(see
United
States
with intersecting runway
Boston Logan Airport (see
movements.
the
in
Chapter IV)
Ii.3)
chapter
and New
are
two
examples.
2.a
Arrival/Arrival separations
As far as can be determined, airports are not currently
operated with
could
arrivals on two intersecting
accurately enough to
intersection.
Although
Evidently
cited, it turns out that,
still true.
Washington,
Consider,
figure
ensure separation
this ability does not
counterexamples to
the statement
on closer look,
for
II-16.
instance,
at the
yet exist.
above could
be
our statement
is
Dulles
Although
This
the position
could project
only be done if controllers
of aircraft
runways.
it
airport in
might
appear
initially that two runways are operated there simultaneously
for landings, this
is not really true as
landings are not
141
w ay
'a y
The taxiway system has been simplified
FIGUREII-16.
_
C
_
_I· I
I
_
Dulles International
_ I
Airport, Washington D.C.
I
___
_________
_
__
_1_1
_I
142
assigned to the secondary runway unless the pilot can assure
the
controller that
primary runway.
be analyzed
the aircraft
This is a
will stop
short of
"hold short" situation and will
in part 6 below.
As explained
separation is. imposed between
the two
there,
de facto two independent runways.
case would depend on correctly
as at
Given
these are
Accurate modeling of this
estimating the percentage of
aircraft (primarily general aviation at Dulles)
Logan airport
no real
operations.
that landings on the secondary runway hold short,
the secondary runway.
the
The same
Dulles and
assigned to
situation occurs at Boston
is modeled
in chapter
IXV
below.
Since A/A separations
runway case,
the
it is simple to
intersecting runways
imposing
will be needed for
a
time
described below
that arrivals
case.
on intersecting
2.b
This
using
for the parallel
is accomplished
the
same
runway case.
runways
by
procedure
It
could be
may be
studied
selection of separations,
no data exist for this case,
this
extend the same capability to
separation
this way with a proper
the parallel
in
but since
it is not possible to confirm
..
Departure/Departure separations
The basic
1111,
1121)
there is a
rule for the
intersecting
is that aircraft may
case (FAA 79 para.
not begin a departure if
takeoff rolling on the other runway
but not yet
143
across the intersection.
in
figure
II-17 is
occupancy
rule.
directions
there
the
kind used
Effectively,
viewed
As
is
as
the two
having a
runways
no need for any
when
the area marked
single
point in
in-trail
both operations
were
"a"
aircraft
different
separation of
using the
same
runway.
2.c
Mixed operations
Separation
when they
of landings
are on
and takeoffs
different runways
problems as the single
from each
involves the
runway case:
release
same two
of a departure
and gap stretching for arrivals to allow departures.
these separations are considered
other
Again
independently of any other
separations needed such as is required, for example,
if the
landing runway is also used for takeoffs.
Release of departures
Figure II-18
case.
Aircraft
land.
gives the time-distance diagram
in part a
to release a takeoff.
landing, j,
is made whether or not
akeoff k is
able to go if the next
k crosses the
I
For simplicity
_I __Y__
intersection.
Note
runway prior to crossing the
the departure may rol:
clears the runway.
_ I_
first to
a decision
should landing i exit the
intersection,
I
is the
is at least Rmt(k,j) miles out on final and will
be so when the takeoff
i
figure
When this aircraft clears the intersection of the two
runways at time Ti(i,m),
that
of the
for this
s soon as the landing
we use
· __
Ti(i,m)
·_
as the
I__
144
-i
I Departures
a
·IC
FIGURE II-17.
J
Intersecting
RunwayDeparture Operations.
145
Tag (i)
time
!
.ng
i
i,1)
Tag(j) -
i)
Sdat(k,
Rmt
k,m)
- It t<)
'I
a) Time - Distance
area
H---
d
-D
- LU
rnwqv
I··1- 1 (nartlr
'\U--k- - YJI-- )
b.
/
Rimt(k,j)
I,
i
M
I
l~~~~~~~~~~~~~
Diagram
J
Ysss IIIllAl~
.
_
_~~~~~~~~--
C
Caircraft J
area:
b) P o s i t i o n
lo f
~
aircraft i
/
Air c r a f t
-I
roo-
War
!l
m
Ill
vls 11
(arrivals)
a t~
aircraft k
b) Position of Aircraft at
Time = Ti(i,l)
For clarity, buffer is omitted
FIGURE II-18.
_
Mixed Operations on Intersectiong Runways.
_11
1-._11 --.
-----
146
minimum of the
clear the
time across the intersection or
runway
of aircraft
i.
position of all active aircraft
Figure.II-18b
takeoffs means that the
must
any
contain
aircraft
shows the
at time Ti(i,m).
used for-releasing
not
the time to
at
any
The rule
area marked "d"
time
while
the
departure is in the area marked "e".
This procedure is
that the
order
complicated in practice by
future position of
to
determine
controller cannot
takeoff to roll
the
aircraft must be
adequacy
know exactly
of
the fact
estimated in
separation.
how- long
it will
down to the intersection.
The
take the
The controller
must estimate the distance from the threshold of the landing
when the takeoff reaches the
intersection.
As before,
we
assume - a worst case procedure is used.
If,
for instance,
the departure has a takeoff runway
occupancy time of 34.seconds
to reach 6000 feet then,
(5 seconds standard deviation)
using
equation (13),
its time to
reach an intersection 3000 feet down will be 24 seconds with
a standard
deviation
position of the
even
if
it
of 3.5 seconds.
The uncertainty
arrival is much less than
is
assumed
that
the
only
in the
for the takeoff,
information
the
controller has is Va(i), Vas(i) and the present position.
120
knot
currently
seconds
arrival
3 miles
with
uncertainty
a
which
with
out
a standard
deviation
will reach a point 2 miles
standard
exists
deviation
of
in the landing's
1
of
4
kts.
out in 26
second.
time
A
The
to travel a
147
than the controller is able
given distance is probably less
to
estimate but
takeoff.
the major
uncertainty is
we neglect any
Thus
still with
variation in
effect of the
assume that the position
arrival speeds and
the
of the arrival
20 to 30 seconds ahead can be estimated accurately enough to
decide if
the separation is
We then
met.
compensate for
this by using a more generous
estimate for the value of Zt,
the "worst case" parameter,
when computing
takeoff
detailed
to
will need
of
study
get to
this
precisely controllers
ase
intersection.
should
judge the 2
also
A
more
consider
how
(Rmt).
In
mile cutoff
will they prohibit a takeoff if the arrival is
other words,
projected to be 1.98 miles out
intersection?
then merely
the
the
how long
The
procedure
to check
when the takeoff crosses the
for releasing
the location
a
departure
of arrivals
is
and insure
that the separation is met and will be met before allowing a
The rule is: do not release
takeoff to roll.
runway 1 unless the next landing, j,
miles out
least Rmt(k,j)
a departure
on
on runway m will be at
at a time
= (Ttc(k) + Zt*Ztos(k))*SQRT(Xi(m,l)/6000)
(20)
from the present, where Zt should probably be 1.65 or more.
Providing space
takeoffs and
between arrivals to
landings is accomplished
procedure as with
the calculated
The specified separation is,
JI
I
-
·-
-------
, I -.-..,I
.
as
same general
by the
the single runway case.
and the specified gap
allow alternating
We permit both
stretching procedure.
in the single runway case,
_
__
___
148
second time
merely a
The
maximum
two
of the
between arrivals.
separation imposed
is used
separations
control
to
arrival/arrival spacing.
The calculated
more complicated than
the notation introduced in
Using
aircraft j on runway m must
C - Rmt(k,j)
cannot have flown more than
miles by Ti(k,m).
will be in the future at the time aircraft
to estimate
we
Thus,
j is being scheduled.
formula
be at least
This means that it
Rmt(k,j) miles out on final at-Ti(k,m).
However, Ti(k,m)
the point
for single runways because
of reference is changed.
the last section,
runways is
separation for intersecting
use the same "worst case"
as we
Ti(k,m)
did
in studying
the
procedures for the release of takeoffs.
The time that aircraft
will take to fly C - Rmt(k,j)
j
In the notation
miles was given in the single runway case.
for the intersecting case, this is now:
Sdat(k,j') = (C - Rmt(k,j))/(Va(j)
operation
runways
is
complete rule
The
mode (calculated
+ Zt*Vas(j))
(21)
therefore:
Under
alternating
separation)
with
intersecting
do not release a landing
j until the time:
(22)
Tc(i) + T - Sdat(k,j) + b
when
i is the previous
given by
(20),
landing
Sdat(k,j)
associated with this case.
on this runway and where T is
by (21)
and b
is the
buffer
149
3
Parallel Runways
The air traffic control rules
and not
very complicated
control
(FAA 79)
handbook
parallels
any one
in
available to
entirely
in
the
author
agreement
can be
conditions (IFR or VFR)
approach
but by
the
Further complications
controllers
two
use
two
a unified
p.96 -7,
runways
but
summaries of
nor
The
not merely
the
and ..the
weather
the amount of offset of the
of divergence in
are-induced
by the
the missed
para.
fact that
rules
for
not official rules,
744).
local
situations
let alone
airport.
We
of possible dependencies and
will briefly outline the range
detail the rules necessary
to support the
The primary variable
analysis of all of the possibilities.
degree of
framework
KAY 79).
consistent from airport to
then consider in
for
complete
are neither
"marginal weather"
published or even
affecting the
Two
runways (FAA 79
between IFR and VFR that are
rules
discuss
affected by
and the degree
paths of
not
(HOR 75
separating - the
two thresholds
does
place or in
appropriate separation
distance
The air traffic
codified.
in several contexts.
presents the rules
rules
easily
for parallel runways are
dependence is
distance separating
the two runways:
4300 feet or more
Runways that are separated by this distance or more are
completely
independent
(FAA 78 para.
i
·
·
--
under
all
operating
conditions
1103c).
·-----I
--
·--
-·-------
-
--
·---
--·--
--
150
2500 to 4300 feet
In this situation the runways are independent under VFR
Under
conditions.
IFR
separations
arrival/arrival
are
Departures are independent from operations on the
imposed.
other runway .(SIN 79 p.4-6).
700 to 25'00 feet
extent
that an
arrival
runway.
on one
must
runway
be over
the
the other
be released on
a departure may
threshold before
to the
the runways are dependent
Under VFR conditions
Under IFR.conditions the runways are essentially a
in. terms of
single runway
on one
operations
separ.tions:
runway must clear operations on the other runway by the same
have to clear
amount they would
the operation
if it were on
.the same runway..
Less than 700 feet
The two runways
runway under
are essentially a single
all conditions.
There are
where the type
additional breakpoints at
of dependence does not change
number
of
ways
dependent and of
that
two
parallel
very difficult to
the
other
hand,
was
runways
can vary,
construct a model that,
automatically imposed the correct
In view of
can
be
of separation (not
the.fact that the type
merely the length of the separation)
on
but the value
imposed does (MAY 79 pp. 4-7).
of the separation
the
various distances
on
it would be
the one hand
set of separations while,
flexible
enough
to
--111111--··-
permit
151
experimentation.
Instead we will establish a procedure that
can model the possibilities mentioned above.
3.a
Arrival/Arrival separation
The only
literature
two possibilities
for A/A separations
dependency
and
2)
adjacent runways.
on parallel
a minirum
imposed or not.
A/A separation
time
in
the available
runways
between
are 1) no
arrivals
on
-,Thus,this case can be modeled by having
the user designate whether two
separation
mentioned
parallel runways have an A/A
If they
that is calculated
do,
then we impose an
and applied
in
the same
manner as the A/A searation used when the two arrivals
on the same runway.
May indicates
that the
were
value of this
separation will vary from the standard values given above in
table II-9
to
a simple 2 mile separation
of arrivals depending on distance
the
"single
identical
the
(MAY 79 p.6).
Note that
runway" case can be modeled by imposing the
A/A separation
runway and 2)
between all pairs
on both
arrivals on
separation
is
1)
arrivals
on
the same
different parallel runways.
specified
in
units
of
If
distance
(Raat(i,j)), then this procedure assumes that the length of
the common approach paths (C) are equal.
is specified as a time (Saat(i,j)),
If the separation
then the length of the
approach paths may be unequal.
I
`*L--- -
-
-·-
_
_I_
_
_
152
Departure/Departure separations
3.b
independent or 2)
The
operations.
used
of D/D
it is imposed in the manner
3.c
if so,
runway case.
of the single
Mixed operations
to be
of priorities
there
of
are two
and
(arrival priority
modeled
cases of dependency
The possible
alternating operations).
the most
types
three
are
In addition,
exist.
dependencies that can
types
there
as
situation,
complicated
parallels are
on dependent
Mixed operations
are
A/A
a flag to
and,
is to be applied,
if a D/D separation
indicate
with
As
separations.
are modeled by providing
separations these cases
in table
as given
separations
runway
(MAY 79 p.5)
the latter
only example of
single
for
II-10
1)
either
have a time separation between successive
same values
the
are
runways
parallel
on
Departures
) no dependency, 2) single runway case and 3) touchdown
The first
case
and
the
functionally
analysis
and
simple
actually
conditions
to
when the
has touched
analyze.
controller
takeoff
The
poses no problem.
single runway
identical to the
formulas
The third case requires
directly.
arrivel
of course,
situation,
second case is
release of the
before
necessary
by the arrival
allowed.
used
there
rule but
is
limited
to
see that
the
the relense
of
an additional
This
case
is able
down n order to
is
to
ermit
apply
153
the departure.
can
This occurs primarily with VR
happen under
IF.Rrules
with
visibility at ground level.
A/A
separations
are
1.9
a low
miles or
more
redundant
good
all VFR
all
and
IFR
A/A
When the buffer is added
it means that the second
will be at least
touches down.
ceiling but
Under existing rules,
separations are 3 miles or more.
to these values,
rules, but it
landing of a pair
2 miles out on final when the first landing
Therefore, under existing rules, it would be
to
check
the
position
of
the next
arrival.
Despite this fact, the mechanism for checking is included in
the model to
permit the analysis of
closer A/A separations
should they be used in the future.
The
parallel
procedure
runways is
runway case.
applying
used
for
exactly
alternating
the same
as
operations
for the
a
Additional separation is provided
user
specified separtion
or
by
on
single
either by
calculating
additional spacing needs, as in the single runway case.
Should the arrival/departure
form mentioned above
dependency be of the third
(departure
arrival is over the threshold)
may leave
then,
currentrules adequatespacingalready
operations.
would
Were shorter
be
The
separation and
next
as explained,
under
exists
to alternate
A/A separations to be
straightforward
operations.
when the
to
analyst
provide
can
use
for
the
used,
it
alternating
specified
D/A
et the values for all closing cases equal to
Rmt used in this case.
This
will
insure that arrivals
are
at least Rmt miles apart at the threshold.
11
I_1I__
1
_
_ I^_I
_
· __
IIY--Y--·IIIII___
-.
154
4
Projected Intersecting Runways
A number of 'airports have runways that are not parallel
but do not intersect physically.
and Chicago
Mo.,
O'Hare
by the procedures discussed
runways diverge
When the two
two sections above.
they are independent
Wichita)
slightly (see figure II-19a,
under. certain operating
A number of
are three examples.
these situations can be modeled
in the
Wichita, Ks., Kansas City,
arrivals on- one
1)
conditions:
runway, departures on- the second; 2) mixed operations on one
If the runways are operated
and departures on the second.
they may be modeled as if they
direction
in the converging
This may be valid as a departure on one, for
did intersect.
example, may be held until the departure on the other runway
This procedure
flew past the projected intersection point.
would
more
be
likely
to
be
true
when
the
projected
point is close to the real ends of the runway,
as it is at Kansas City (see part b of the figure) than when
intersection
the intersection is far from the runway end.
In
it may
other situations
be more
appropriate
regard the two runways as if they were parallel.
on
one
have
may
to have
cleared
the
to
An arrival
before
runway
a
departure could be released on the second.
Whenthe
projected intersection
one runway but on the other
part
c of
the
figure,
as
is
beyond the end of
runway (see O'Hare
well
as
example in
the Dulles
geometry
-- l--LIIllC1-·
·
155
IN
a) Wichita,
Kansas
b) Kansas City, Missouri
Airport
Airport
c)
FIGURE II-19.
1___11
1
_
_·
ii
Chicago O'Hare Airport
Airports with Projected Intersecting Runways.
I
I-Y.----·-IIXI
_
_11--1_
1__.
156
then a "hold short" situation may be in
referr'edto above),
effect and the two runways are independent.
It
may
be
not
possible
to
all
model
projected
intersecting runways in the manner outlined above.
discussion that in
clear from this
it is
can
above
models discussed
parallel
or
the overwhelming
projected intersecting runways,
majority of cases with
intersecting
However,
the
be
brought to bear by making the appropriate adjustments in the
model's parameters.
5
Assignment of Aircraft to Runways
5.a
Discussion
more than
Whenever
landings or takeoffs,
the active runways.
one runway
aircraft must be assigned
FAA
assignments.
are
there
was
model
assignments.
to one of
as being made dynamically and
criticized
for
prespecifying
runway
Consideration of airport operations shows that
several
factors
from
that
can
influence
FLAPS provides several
Therefore,
runway assignment
which
one of
the
selected as appropriate for a given case.
are
either
In the demand section (II.C) reference
was made to runway assignment
the
use for
is in
identified,
several
problems
assignment will be discussed.
in
runway
modes of
modes
may
be
After these modes
modeling
runway
157
Direction of approach or departure
When runways
directions,
the
then the choice of
direction
in different
are available for operation
which
from
runway may be determined by
aircraft
the
approaches
the
airport(for landings) or the direction in which the aircraft
(for takeoffs j).
wishes to depart
operated as a North airport and
or the other half of O'Hare
each with
a South airport,
Traffic is routed on to one
runways.
landing and departure
is often
Chicago O'Hare
in order to avoid intersections
with traffic coming from the opposite direction.
in FLAPS.
information
fixes
and departure
Arrival
provide the
directional
Wemodel this type of assignment by
providing two two-dimensional matrices, one for landings and
one for takeoffs.
giving the
probabilities
conditional on
landings,
Each matrix provides a set of multinomial
probability
the relevant
type of
using a
runway,
fix (arrival
fix for
of
When
fix for takeoffs).
departure
an aircraft
becomes eligible for a runway operation, the appropriate set
of multinomial probabilities is sampled to obtain the runway
to be used.
As
of how
an example
consider the
following example.
arrival runways
A,
B and C and
All arrivals from fix
arrivals
Y
·
ILClur-----·
this procedure
u·-l·
Suppose there
two approach
1 will use runway A.
use A, 20% B and 30% C.
would be
used,
are three
fixes 1 and 2.
Half
of fix 2
In order to affect this in
-----
158
FLAPS the follwing matrix, X(f,r) would be specified:
r-
f -fix
Then
runway
A
B
C
t
1.0
.0
.0
2
.5
.2
.3
would first have an arrival
each aircraft that arrived
f,
fix,
assigned
would be
Then row f of
to it.
used to set the
the above matrix
odds in a multinomial
draw which
will randomly determine runway assignment.
Apron area
As the
direction out of
the airport from the runways
so too can the destination
can influence runway selection,
Pilots may choose between runways based
within the airport.
on their' intended apron to avoid excessive taxiing. This is
a less significant factor than the others mentioned here and
was not needed for any of the
runs.
validation or application
Therefore this option was not modeled. If necessary,
it could be added by providing
a matrix of probabilities
of
runway assignment as a function of apron area for landings
and takeoffs.
Aircraft requirements
Aircraft vary greatly in
vary in their length.
Not all
runways that
might be
use all
their performance and runways
of the largest aircraft can
available.
FLAPS allows a runway assignment mod e
To
model this
based on the class of
_ · - I
_.
159
the aircraft.
This operates
in an analogous
fix-based assignment above.
of probabilities
giving
to the
aircraft class a set
For each
runway to be
fashion
used as
a function
of
aircraft class is given.
Noise abatement
In order
to reduce
the impact
under the flightpaths,
operations
equitably
to
to
noise.
entirely
exposure
of people
assignment
An attempt may
expose
Noisy jets,
to
a
percentages to
areas
more
using
the
modeled
for instance, might be
runway
to noise.
away from.
also be made to
residential
This could- be
aircraft class mode.
assigned
on residents
aircraft may be directed
"noise-sensitive" runways.
"balance"
of noise
which
avoids
All Classes
balance the
extensive
may be
number of
given
aircraft
going to any one runway.
A second
also
be
assignment
useful
assignment.
operation,
mode is provided
here.
This
is
a
by
FLAPS and may
simple
multinomial
If three runways are elibible for a particular
then a
probabilities
draw from
can be
made to
a set
of three
determine the
multinomiail
runway to
be
used.
Cperational considerations
If
airports
capacity in
to
an efficient
traffic should
them.
are
utilize
manner,
be assigned to
their
then
limited
it would
runways as to
runway
seem that
fully utilize
In particular, if one runway has aircraft waiting to
dlL --- --------- -- ·---
9lllllslli~~~~~surarsarurr~~··rrurrr~^l----·-
160
another runway is
move and
vacant,
should be sent to the empty runway.
FLAPS
a
has
new aircra't
To model this procedure
ru-nway -assignment mode
that
directs' each
the shortest queue
the runway with
aircraft to
then any
waiting to
use the runway.
The shortest queue assignment procedure is likely to be
combined with some limitations on the ability of aircraft to
use
Assignment
runways.
shortest
queue of
any of
aircraft
class may
use.
assignment
implemented
is
aircraft a set
class of
the runways
- Therefore,
particular
Then,
queue
the shortest
for each
which runways
of flags indicating
aircraft may use.
that class of
which a
by specifying
in FLAPS
the
runway with
may be- to the
when the aircraft
becomes eligible for a runway operation, the model scans the
set of runways
this class
active and
that are both i)
of aircraft.
The
aircraft
2)
usable for
is assigned
to the
runway with the smallest queue of aircraft awaiting service.
In
summary,
assignment.
and
may use
FLAPS
allows
four
modes
of
runway
Landings and takeoffs are considered separately
different modes
for
The
assignment.
modes
allowed are:
assignment
1)
Multinomial
2)
Multinomial
as a function of aircraft
3)
Multinomial
as a function of fix
4)
Shortest queue of acceptable runways where runway
acceptability
is a function
class
of aircraft
- -
class.
-
161
These
of
modeling
represent an
capabilities
airport
used by the
assignment method
the
over
operations
in
advancement
prespecified
They
ASM model.
permit a
Mode 4,
wider range of real-world situations to be modeled.
makes it possible for the airport planner to
in particular,
and
evaluate
the
runway
alternative
investigate
assignment
policies with respect to their impacts on airport delays.
5.b
Sequencing of operations
As discussed
previous parts
in the
of this
section,
once aircraft are assigned to a runway they-do not move on-to
the
runway
until
all
runways other
scheduled (i.e.,
then a problem
than
of
the runway
when two
control
traffic
If these separations
separations are met.
on
air
relevant
nvolve aircraft
the aircraft
being
or more runways are dependent),
in properly sequencing or
alternating these
operations can arise.
We
illustrate
following
example.
has begun
arrives
arrivals are
Suppose
dependent parallel runways.
jet)
landing on runway
needed approach
I I
-
2.
Because
imposed at the threshold.
is relatively
gate separation
IIII 1 -
fed
to
3 (small
class 1 is
all separations with it as a
non-class 1 aircraft arrives
I--C----··
being
the
A class 1 (heavy jet)
1.
and wishes to land on runway
trailing aircraft are
through
An arrival of class
the fastest class of aircraft,
another,
difficulty
the potential
-
Thus its
large.
If
on the first runway,
e·11-.--.1
1-1
111-_1_
162
its
required A/A
separation is
1 aircraft,
so it becomes
class
its operation.
from
this
deferred again.
stream of
eligible
Now the class
new landing
on
smaller than
the
to land and begins
1 aircraft must be separated
1
runway
In fact,
that of
and its
should there
arrivals on runway 1,
landing
be a
continuous
-the aircraft on
needing a long separation will not
is
runway 2
be allowed to land until
an arrival appears on runway 1 which requires.an even longer
-
A/A separation..
This is not a realistic
busy
are
much
alternating
mechanism
more
mode.
pattern of use.
often
operated
In order
is included
successive landings
to
in FLAPS
to begin
in
force
an
explicitly
this to
which does
on a
Runways when
occur
not allow
given runway
a
two
unless no
other runway has aircraft waiting to land.
The same difficulty logically
takeoff runways
so
no
but
specific
included.
is not often
mechanism
for
exists for two dependent
a problem
in practice
alternating
The reason it is not a problem
takeoffs
is that seldom
there two dependent runways used only for takeoffs.
of
requirements
above.
landings
(A/D)
act
and
the
to
prevent
attendant
the lockup
is
are
Usually
one or both of the runways will have landings as well.
presence
and
The
separation
described
163
6
Special Problems
This section
considers three
special situations
that
can arise and how they are modeled within the framework that
has been
set up for
runway operations.
here because they involve both
They
are covered
aircraft performance and air
traffic control procedures.
6.a
Displaced runway threshold
A runway
may be operated
that is,
the aiming
physical
end
description.
of
with a
displaced threshold,
point for landings
is moved in from the
the
runway.
for noise abatement.
the runway is
available
the
Occasionally
for takeoff
as well.
also use
the full
runway.
Arrivals may exit beyond
is located
length
Operations
length out
there).
of the runway
used in the calculation
to be safe
chapter
including
to the
for takeoffs
=
--
31YY
.-L·IIIIP·IIIII*···Illl(l(i.ly*-
is
direction may
physical
end
of the
the far threshold (if an
sense that
may
"use" the
full
the entire length is
of whether the runway is long enough
has several
some with
that end of
Logan airport (see
runways with displacedthresholds,
displaced
thresholds on both ends of the
runway.
"
a
full lengtn of
in the other
for this kind of aircraft.
IV)
II-20 for
rolls from
Departures
in the
The
the threshold
moved in
exit
figure
This technique may be used to raise the flight
path of landings
runway.
See
sl--
--L- -L------·IIICIIIIY. ..-IVIOI.LII----·li-··ll
164
Direction of operation:
Direction
1
Direction 2 -
Altitude
50 ft.
path of landing aircraft
_
-
- displaced thresholdactual threshold
physical length of runway
(a)
Takeoff runway
_______________________________________
A
k
Landing runway
(b)
FIGUREI1-20.
Displaced RunwayThresholds.
165
This feature can be modeled by the procedures described
in this
section.
If the' threshold for takeoffs
been moved in (to Y),
then the
runway can be modeled as if
it actually .began at Y rather tha.nX by
to
(direction 2 in the figure)
full distance
use the
located
in the area beyond
for
and if it is necessary
an
landings,
exit may
be
the end of the runway.
If the landing and takeoff
thresholds
are in different
then the analyst can model the situation by viewing
places,
the one real runway as two runways,
for takeoffs.
The runway
runeay modules.
shifted
placing the runway
When. the runway is modeled in the other
end keypoint at Y.
direction
has also
one for landing and one
is described
so that one module
takeoffs begin
and the other
ends where the
The
operated
dependent
two
are
separations
runways)
as
as to
operationally.
This
procedure
threshold is.
The
in part 3 (parallel
two modules
make the
ends where
parallels.
imposed are those described
so
as two
on the same centerline but
Each module is
(part b of the figure)
to the model
will
a single
result
in
runway
correct
Before a departure can roll on the takeoff runway
behavior.
module any arrival must have cleared or be at least Rmt(k,j)
miles away
from the threshold.
If
alternating operations
are in effect, the procedures described in part 4 will allow
space
*I
for departures.
By describing
modules,
the performance
modeled.
Landings will touch down
`---I""I
""
of
--
the one runway
aircraft
will be
as two
correctly
in the correct place on
--
c--"-
------------------
166
the runway
and roll across
cross various
time to
runway in
should
takeoffs
landings and
two runways
of the
onto whichever
be directed
operating the
When
intersections,
direction both
the other
amount of
the correct
as-taking
be modeled
takeoffs will
-,that
will ensure
oint
takeoff rol.l
The shifted
time.
at the appropriate
intersections
is
placed in the right position.
Should
it be the case that both ends of the runway have
displaced thresholds, the runway may still be modeled by the
procedure.
split runway
modules
be
should
ends of the two runway
The opposite
to have'one runway module end
positioned
and the cther
where takeoffs begin in the second direction
end where landings
runway module
the second
touch down in
direction.
6.b
Hold short arrivals
A hold short
arrivals are
directed onto a
where
a situation
is
arrival procedure
the restriction
runway under
that they be able to "hold short" of some point, usually the
intersection with
for an example.
up
(discussed above)
situation
is
and at
trivial
independent runways
runway is
This procedure
to
Logan (see
model
for arrivals.
assumed to stop
as
used
is
I-21
figure
capacity
This is done to increase
runway.
another
See
another active runway.
by opening
at
Dulles
This
chapter IV).
is
two
arrival on
one
intersection,
the
the
As an
short of the
result
167
/ Arrivals
f
Departures
'7
/
/
/
/
/
Runwa);
(D/
tr
Departures
_w--.Y
...ZArrivai
s
-- ----TRunway
Landings
FIGUREII-21.
__
----
1
on 1 exit at A or before.
Hold Short Arrivals.
I·___I__ __
·1 _
U--LI·Y-
--
----1___111_1_
168
operation on the other runway
Correct modeling involves assigning arrivals
first arrival.
to
proceeds independently of the
the proper runway in a correct manner.
The
runways
operations.
will
not
independent
be
takeoff
for
Using the example of the figure, departures on
2 must clear departures on 1, and departures on 1 must clear
arrivals and departures on 2.
are
the
same as the
These particular separations
ordinary dependent
runway separations
discussed above.
This
short
hold
procedure is
used
sometimes
on a
In other words, not all the arrivals
conditional basis.
This is the case in the Logan
will be able to hold short.
Small aircraft hold short,
examplebelow.
need the full
length of the runway and
but large ets
with
thus interfere
In the fi'gure example
operations on the other runway.
heavies on 1 maynot be able to stop short of runway 2.
This
can be
modeled in an approximate
an arrival separation
on the two runways.
way by imposing
The value of the
separation will be zero for all pairs of arrivals which will
does
hold short.
greater
than zero
The
value of
for those
intersection.
For
the
pairs of
arrival on the hold short runway
separation
will
aircraft where
be
the
does not stop short of the
the example of
below demonstrates how
short runway
on the hold
not conflict because the arrival
the figure,
this would work.
are the arrival/arrival separation
The
the table
two matrices
imposed on each landing.
·---11111·111·311··CII- -
169
X
The entries mrked
value
greater than zero.
will inore
runway
1
table
n the
are
set to
A landirg on runway 2 (to, matrix)
oFeretions on runway 1.unless
is a. class
intersection.
1 and
If the
an appropriate
thus will
runway
the leanding on
not stoy
1I landing is a
non-ze-ro separation provides adequate
before
1,
class
the
the
separation from other
aircraft crossing the intersection.
Class
Trailing
Lead
a.c. on runway
Trailing
Lead
a.c. on runway
a.c.
a.c.
or
2:
: 1
Intersection
Runwaysfcr
3
X
0
0
X
3
X
o
0
i
2
3
I
X
X
2
0 O0
:
j'?
6.c
2
2
runway
or, runway.- 2
1
0
0
0
0
departi.ires
commercial jet departures usually
be 7000 or more feet in length.
need to
Aircraft used for business
or private flying need only a small portion of this distance
to takeoff.
aircraft,
If
they start in the same
then they
will take a
location as larger
ong time to
fly down the
length of the runway, blocking other movements. To reduce
the
QIC~~~~~II"~~~-~"~~-------'
rrunway
~---IY···---PI-YI·L-·IC--^--LILI
occupan.-cy time on
takeoff, sm11
. ..
. i_. . .
aircraft
I_-·--·IIII·1--·----*·
may
·L·ll----·---·l_------i-_l_--l^__
.
170
depart at some
intermediate point a good
distance down the
departure runway.
This carnbe modeled in FLAPS
displaced threshold.
shorter and
as an extreme case of the
In this case the second runway is much
begins at
the point
from which
the departure
will roll.
7
Comparison of separation methodologies
Consideration of the methods used
separating aircraft was deferred
of
the
analysis
of
aircraft
in the ASM model for
until after the completion
movements
on
runways
and
separation procedures between conflicting operations.
was
done
because
proper
comparison
procedures involves the issues
of
ASM
and
This
FLAPS
of aircraft performance and,
in particular, dependent runway separation rules.
Now that
this has been presented, the methods used by ASM to separate
aircraft will be described.
cannot accurately
The reasons why the ASM method
represent certain cases modeled
by FLAPS
are discussed.
The method used
two principles:
by ASM to separate
1)
single
runway
aircraft relies on
occupancy
rule and
2)
separations imposed as
a minimum time between
the runway thresholds.
The first point simply means that no
more than one aircraft is ever
the runways.
crossings of
allowed to occupy any one of
Crossing a runway does not count as occupying
171
it.
The second
point
is
If operation Y is to be
X by an interval
implemented
in the following way:
separated from a previous operation
t or more;
the procedure
is
to hold Y at
its runway threshold until t seconds after X has crossed its
runway's
threshold.
landings,
types.
This
takeoffs
procedure
and between
It is used when the
or on different
runways.
is
operations
two operations
The
used
result
of
operation
runway
is that each possible
separation.
a matrix
of
takeoff) ,
a lead operation runway,
is
considered
Each of these
eparation
different
are on the same
combination of a lead operation type (landing,
trail operation type,
between
a
a
and a trail
different
;Upe of
eparation tyyes is specified by
v-alues tines or distances)
for each
combination of lead aircraft class and trail aircraft class.
For example,
a matrix of
separations could be specified as
applying between a leading arrival on runway 1 followed by a
departure on runway
could be
specified
2.
to
An independent
apply between
set
of separations
arrivals
runway 2
on
that are followed by departures on runway 3.
The ASM
easy to
procedure
describe
situations
in a
procedure relative
is that,
1-
and
has certain
strong
permits modeling
unified
framework.
of
points.
a wide
The
It is
range of
defect of
this
to the methods discussed above for FLAPS
as is the case with
many other
aspects of the ASM
model,
it sometimes ignores
thev
;us parameters of the airport.
certai.
cases can only be approximately
modeledby ASM.
CI -I I---I- -·--
·- I
1- 111-
important interactions between
1 I-
As a result of this,
I
- -
-··-I· I
^
172
One
such
situation
departures on
runway.
must
one runway from
the separation
of
arrivals on an intersecting
As has been stated, the rule is'that the- departure
be held
until
intersection or
modeled in ASM
each
involves
class
threshold
the arrival 'has either
exited,
crossed
whichever occurs first.
by the analyst calculating
of arrivals
will
to the intersection
the
This is
the average time
need to travel
from
the
and using this time as the A/D
separation.
We refer
S*.
to this average
This will be applied
departure is
begin
to be
time to the
in the model as follows:
scheduled, it will
until a time S after
its runways' threshold.
intersection
not be
the previcus
This differs
4hlern a
allowed to
arrival. has cros-sed
from the
actual
of holding the departure until after the mi.nimum of
Wihen
arrival
crosses
runway.
If
the intersection or
most
intersection,
insignificant.
or
all
then the
arrivals
of the
difference
average
time to
between
crossing
the
rule
the
clears
the
arrival
exit
after
the
-error introduced is,
The error would only
as
in practice,
be the absolute value
actual time to
crossing
for the landing, perhaps
3 or
and
4
seconds.
S is actually
a
function
of
the arrival
class.
The
following discussion does not depend on this, so, for
simplicity we assume S is independent of the arrival
class.
173
The difficulty
significant
with
fraction
intersection.
the ASM procedure
of
arrivals
exit
If S, as defin.dabove,
then
separation,
serious errors
to
be
held
will
for the
the
result.
When an
the departure
full time
S after
the
This error could be 15 or 20
arrival crosses the threshold.
seconds and, in
before
is used as the A/D
arrival exits early, before the intersection,
will continue
comes when a
some situations,
could
be
enough to mean
that there will not be sufficient time between arrivals to
permit a takeoff.
to reduce
S
In this situation the analyst could elect
to the average
departure.
That is,
that the arrival
average time
will block
the
S would now be set to the probabil.ity
would cross
to
the arrival
time the arrival
the
intersecticn times the
the intersection plus the probability that
would exit
early times
the average
length of
time the arrival would be on the runway given that it exited
early.*
This value for S may also cause erroneous behavior.
is true that this method will
departure
down,
the correct
delay,
interval after
on the average,
the arrival
It
each
touches
Nonetheless, this method may introduce a significant
bias to the results.
operations,
Under
the arrival priority mode
of
some departures will be able to go while others
will not have
sufficient time between
arrivals to
do
so.
This decision will often depend on whether the arrival exits
*
_
II
I__
The latter
term might itself
be a weighted
average of
times to several exits before the intersection
_
I_
I
1_1
_
_
I
____
174
early
or late.
Taking the
average
runway may significantly change
arrival
time on the
the fraction of interarrival
gaps that can accommodate a departure.
For example,
touchdown
suppose that
of a class
the time
between
the
3 arrival and a class 4 arrival is 90
seconds and that the average time the class 3 arrival blocks
the departure
intersection
is 45 seconds if the
arrival
and 30 seconds if it
does not.
releasing a departure
requirement for
crosses
the
Then. if the
is that there
be 50
seconds from the moment the takeoff begins to roll until the
next arrival
allow
the
touches down, the actual behavior will be to
departure
exits early
go almost everytime
(as 90-30
arrival exits
50).
to
50) but almost
>
late and crosses
If the
average
out to be
average will
bias results
takeoff.
never* when
the intersection
time for
runway turns
the first arrival
the arrival
below 40 seconds,
towards
<
(as 90-45
to block
then using
letting
the
the
the
more departures
If this average is over 40 seconds, then using the
average time
will
bias
results
towards
letting
fewer
departures takeoff.
This same problem occurs
parallel
runways
that a
are used
departure must
identical difficulty
with parallel runways.
with the
hold until
with using
separation
the
When
requirement
arrival exits,
average arrival
the
runway
occupancy time will occur,
*
The exact fraction would depend on the standard deviations
of buffers and approach speeds and related factors.
175
An additional
in
interested
studying
runway
the analyst
the effects- of changes
or new runway exits
performance
Changing
occur when
problem can
occupancy times
in aircraft
and capacity.
on delay
changes
is
the
separations
In the ASMmodel this
imposedin the cases described above.
interaction can be modeled only by the analyst recalculating
the average runway occupancy times.
aircraft
or
performance
congestion can take
model
outside the
type
place,
with
The interaction between
of
for the cases
time.
will
and
described,
only
be specified
a
but also in other
D/A separations
the intersecting runways case,
In
This is
depends on runway occupancy
where the separation
to prevent an arrival from being
too close
departure crosses the intersection.
to the threshold when a
will be specified
This time
delay
analyst intervention.
problem not only for the cases described,
situations
on
exits
as
a minimum
the time
between
when the departure leaves its threshold and when the arrival
crosses its threshold.
time the
arrival
Thus, it is based,
needs to
in part,
cross the intersection
on the
with the
arrival runway.
The separation
previous
FLAPS
sections
uses
the
--
does
exact
or clears
intersection
war
methodology
control
the
biasing
of results
I
release
described
not suffer
time
the
from
an
runway,
also
these
arrival
problems.
the
as appropriate,
to
prevents
explicitly couples
___
and the
crosses
This
of derartures.
and
in this
any
aircraft
176
performance
procedure
to
will
the determination
aircraft
A
performance.
This
separations.
FLAPS
with
facilitate experimentation
assess the significance of proposed
on
of
to
changes in runway exits
further
advantage
of
the
procedure in FLAPS derives from the inclusion of the landing
of section ' II.C.
performance model
means that
This
entire set of responses induced by, for example,
90 degree exit (exit velocity O
(exit
parameter,
runway
kts'.) can
velocity 30
rather
occupancy
separations.
than by
times
and
kts.)
the
changing a
to a high speed exit
be tracked
by changing
one
first
manually
recalculating
then
manually
recalculatig
r
177
F
CONTROL OF THE AIRPORT
1
Introduction
The previous sections of this chapter have examined how
the various
pcints we
operated
portions
have seen
in a
of
an airport
how a
number of
operate.
given airport
different
At
several.
be
facility can
modes.
For
example,
runways may be in an alternating priority mode or an arrival
priority
mode.
We
did
not
consider
at
length
the
motivations forchanging these policies.
The purpose of this section is to analyze the causes of
changes in the way airports
of changes
will also be examined.
to identify
effects.
set of
the major causes
of the
a complex
These
policies
set of
the resulting
alter the
see
"operating
that
two
majcr
and some minor factors can
responses
include
is
of change "factors" and the
We will
factors (weather and congestion)
cause
Our method of approach
they can
airport.
The frequencies
of changes and
We term these causes
possible parameters
policies"
are operated.
runway
in operating
assignment,
policies.
aircraft
performance, and air traffic control separations.
The frequency with which
occur
should
means that
have
a
models for
I I·
analyzing airport
dynamic capability
operating poiicies.
-
changes in operating policies
------.
operations
to
follow
changes
Correct modeling
of the
transitions
in
_____
178
from
one
set
of
operating
rules
to
another
will
be
discussed.
It will
be
existing models
shown
that
the
restricted
ability
to analyze situations involving
of
changes in
operating rules limits their applicability and increases the
difficulty of their validation.
We
will propose
capabilities that
advance over present models.
are a
significant
We will show that the type of
changes in operating policies encountered in practice can be
described
as one
of two
- changes
kinds
certain time and changes triggered
condition on the airport.
procedures
in
response
generalize them for use in
triggered at
a
in response to a certain
Wedevelop each of these specific
to
a
specific
factor
and
then
modeling changes caused by other
factors.
2
2.a
Weather
Summary of effects
Weather
operation of
conditions
an airport,
have
a
rofound
changing a
effect
number of
on
the
operating
policies.
Separations
As indicated
in section
II.C,
different
apply under NVFR
and under IFR conditicns
spacing.
The difference in capacity
and,
separations
for arrival/arrival
therefore,
delay
179
is significant.
would be from
per hour
A typical
reduction in
40 landings per hour in V
in IFR conditions.
separations
can
That
scheduled after the
conditions to 30
Transition between
probably
instantaneously.
landing capacity
be
is,
modeled
the
first
types of
as
occuring
aircraft
time of the transition
to
be
merely uses the
new separation.
Dependencies among runway
As
seen
in
s
II.D
section
(also
reductions
in visibility
previously
in.dependent- parallel
This
also reduce
will
increase delays.
see
and cei.lina can make
the
.runways
capacity
of the
instantaneous.
of these changes will require several minutes
not do so until
a pair
IV)
of
inter-depe.ndent.
As with separations, change
can probably be considered
and will
chapter
airport
i
and
dependency
2Mhefull impact
to
ake
effect
all a rcraft scheduled under the
old procedures have cleared the runway.
Runwayconfiguration in use
By runway configuration we mean
the airport's runways
them),
for which
takeoffs or mixed
the choice of which of
are active (have traffic
operations
operations)
they
are active
and in which
assigned to
(landings,
direction they
are to be operated.
Aircraft
must land into the
velocity of the
wind and the direction
wind can dictate which
and
runways are usable.
The runway configuration in use often changes several times
during the course of a day at a typical airport.
1
C__· _I
_
_·
_
_
_
__ _·I
_
180
at La Guardia for
Information on configurations in use
one
week in
December,
During
author.
was made
1978-,
seven days
available to
of 2.4
an average
changes
configuration.were made each day between 7 A.M.
On
no
day
was
the airport
in
and 10 P.M.
entirely
operated
the
with
one
configuration.
affects runway use
way that weather
A second
is that
of lighting and landing aids
during low'visibility a.number
(visual approach slope indicator, instrument landing system)
may become required
for landing.
Each runway
is equipped
with various combinations of these aids, and this can govern
which runways are open for use.
Transition
complex
and
between
cannot
be
considered
Once a change
instantaneously.
must begin
configurations
runway
to be directed
to
is
fairly
take
place
is decided upon,
aircraft
new runways to
be used.
to the
For landings this may mean that, for some time, aircraft may
continue to operate
close to the
that has
on the old
approach
begun
runway endpoint
gate to be
taxi to a
to
runways,
will often
as they may be too
diverted.
takeoff
or is
at the
to continue
to the
runway
be allowed
runway and takeoff.
Once no more aircraft
old configuration,
operations will
configuration.
described
earlier
Separations
Any departure
remain to use the
begin to
use the
can be provided in
in this section.
the manner
If the direction
of a particular runway has changed then,
of use
at a minimum,
_·.--- l·--·IIIIIC--·
new
all
181
aircraft
on the runway will
have -to be
cleared
operations can begin in the opposite direction.
mean that any takeoff
have to have
operating
under the
climbed out before
runway in the new direction.
before
This would
old regime would
ny landings
could use the
There would likely
be a delay
of several minutes between the last takeoff in one direction
and the first
landing in tile other direction.
To model the transition
used.
At- the designated
time
is
the followin.g procedure
of the changeover -the runway
assignment procedure is changed to assign any new departures
from the apron
to the new runways.
At changeover plus Cx
minutes t}-e run-ay assignment procedure
any new arrivals
to the new arrival runways. Operations are
scheduled to meet any relevant
specified
runways.
s charnged to assir
proer separation
If a landing
separation,
the user having
between the old and new sets of
on a runway will
use the runway in a
different direction from. the previous landing, then it is
not
allowed to
until
Ca minutes after the
runway.
different
not
begin its
If a takeoff
descent from the approach
previous takeoff has cleared the
on a runway will use the
direction from the previous takeoff,
allowed to begin its operation
currently
on the runway have cleared.
until
....
runway in a
then
all
it is
aircraft
Times Cx and Ca are
set by the analyst.
1IP-"-ssl·"--·--·nsrrar^..·l.
gate
___
1S2
Aircraft mix
Landings
in bad
weather
also
require both
pilot skills and on-board navigation aids.
be permitted to
takeoff may still cancel
to bad weather in surrounding area.
have limited capabilities for bad
be flown more
constitute
weather.
their flights due
Small aircraft tend to
weather operations and to
a
Therefore,
smaller
training for bad
light aircraft
percentage of
the
will probably
mix
during
bad
Procedures for changing the aircraft mix over time
were given in the demand section, II.C,
Runway
in
Pilots who might
often by pilots without the
weather flying.
specific
above.
ssignment
The result of
the last several factors
will be shifts
the
runway
landings
overall
departures.
assignment
for
and
This may imply either changes in the percentage
assignment or a change to a new mode of operations.
Aircraft performance
Rain can reduce the effectiveness of braking and change
exit selection
for landings.
Taxiing speeds
are probably
lower in bad weather, as pilots tend to be more cautious.
2.b
Implications
for analysis
Being able to follow changes
capability
conditions
for airport
can
course of a day.
change in
models..
several
in weather is a necessary
This
is because
weather
different ways over the
Changes in visibility
may mandate a change
183
in flight rules
often but
(VFR to IFR or reverse).
not always associated
direction can
weather.
change several
The result
operating in the
Low visibility
with rain or
times a
is that it
snow.
day in
is
Wind
any kind
of
'is rare to find an airport
same configuration,
using the
same rules
for an entire day.
If we wish to fully analyze how airport operations,
models must have an ability to
effect
during
the
course
of
alter
a
the conditions
our
in
run and to model the
transition from one configuration to the next.
2.c Evaluationof existing
The ASM airfield
models
model has
follow weather-induced
a very limited
changes in operating
ability
policies.
to
No
changes in separations, dependencies or aircraft performance
are allowed.
One
change in the active
However,
duringany ru.n
this is done at
halving the number of runways that
time.
Because of
model,
changes in aircraft mix
simulated by
schedule.
the expense of
may be active at any one
the schedule techniques used by the ASM
assignment (i. e.
be
runways is allowed
and minor changes in runway
relative probabilities of assignment) can
the user
suitably
constructing the
The MITASIM model has no ability
base
to model this
type of changes.
The limitations
analyze
this
--
------
type
on the ability
of
I
change
of existing
result
irn a
models to
significant
---LJI
.._
II
184
constraint
on the data
that can be used to validate
the
models.
A natural
procedure
for validating
such a model would
be to take measurementsof flow rates
characteristics,
such
as
etc.
was done at
at an airport
O'Hare
in
delay, aircraft
for one or two weeks,
the summer of
i977.
This
record will typically show some change in operating policies
every 2 to
4 hours.
one may combine
appears
more
comprehensive
If a capacity analysis
the records of a given
than
once during
validation
comparisons between the
the
will
is being dbne
configuration if it
study
involve
period.
a
Any
sequence
model and data obtained
of
under each
operating policy.
Analysis of the models' performance
is foreclosed as
practical
matterby the existingmodels' lck
simulate alterations
in operating
delay performance is
desired,
different
periods
with
rules.
of ability
If
appropreate due to the difference
operating
to
matching of
no combination of
constant
a
data from
policies
is
in initial conditions for
each period.
Modeling of
successive
offers
the
changes as
time periods
best
a sequence
would be
explanation
of simulations
difficult.
of why
this
An
is
the
of
example
case.
Suppose an airport uses one set of operating rules before 12
noon,
and a second from noon onward.
Assuming the airport
was essentially empty at some early morning time, the period
185
before noon can be simulated without difficulty.
Simulation
of
accurately
the period
unless
1)
the condition
to start
between
after noon
the second
the
and
making the
second run
The demand
rates in
the set
of
at noon can be used
and 2)
the .model
second
The first
be performed
airport
of the
-run of
first
represented..
until
cannot
operating
problem
may
of the model
this warmup
conditions
at
at the end of the first
can
be
be approximated
by
with a
noon
in
the second
significant depending
run
at noon
The more congested the airport
run.
transition
The secorzd problem,
ade.
warmup period.
period would. be adjusted
at noon, the more important
policy being
rules
the model generated conditions
closely approximate
really was
transition
on the
time,
is
may
type of
this
metching.
or may
change in
not be
operating
The lull in operations. caused by changes
in runway configurations will be hard to model.
The problems just discussed in terms of validation also
appear when existing
Investigations
policies
of
is an
models are used for
the
effects
important
issue
of
airport analysis.
changes
in
operating
These
for controllers.
effects cannot be analyzed using existing models.
2.d
Modeling of policy changes
Changes
airport.
in
weather
They occur at a
conditions are
certain time,
dependent on certain airport conditions.
external
to
the
rather than being
In order to model
186
we need
them,
at any desired
operating rules
easy to
very
do.
read at
values
parameter
its specified
change.
3
3.a
involve a set
See chapter
changes
the
to implement
of orders
in
changes
IV for severial examples.
Congestion
Summary of impacts
The buildup in
the number of aircraft
or takeoff can trigger changes
that this
most obvious way
arrival
priority
occurs
the
queue has been reduced
There are
if the
departure
imposition
of
priority
number
to some acceptable
occur as a reaction
queue
mode for
continues
alternating
priority
See section II.G for definition.
then
is
in the
a
rises
of departures
of aircraft
possible
The
from an
a switch
The alternating mode
a number of
shifts that could
is in
when the queue
above some critical value.
maintained until
waiting to land
in operating policies.
mode to an alternating
mixed operations runway
*
each
Cliangesin runway
involve simple changes in command values.
configurations
a run
of
Most policy
are implemented.
of
parameter
and the
time,
be
a file
of
During each replication*
names and values.
order is
input of
and a set
of a time
in
changes
This turns out to
time.
allows the
FLAPS
orders, each consisting
arbitrary
to permit
a procedure
departure
value.
"second order" policy
to congestion.
to
grow
rules,
First,
despite
then
the
the
187
controller may elect to change to the departure only modeby
halting all arrival operations on the runwayo
A
might
shift
configuration.
configuration
be
made to
are
Airports
with
make available.
conditions
new
run
capacity
However,
runway
weather
due to
a lower
used,- then congestion
the
using
that
if,
for e-xample,
abatement considerations,
configuration is being
normally
highest
the
entirely
an
noise
capacity
may
induce
a
change to increase capacity.
Even
more subtle
changes
in
operating policies
are
possible
if controllers can anticipate the traffic demands
immediately ahead.
Then, for example, they may elect not to
change operating policies if they expect
of arrivals.
It
a lull in the flow
may be that some responses to cngestion
are best described as changes in runway assignment.
may
be
a
runway
nominally in
congestion some aircraft may be
runway.
Congestion
performance,
movements.
as
may
use
but,
There
during
severe
directed from it to another
induce
changes
in
aircraft
controllers urge pilots -to expedite their
The extent
to which such procedures
are used is
unknown.
A
wide
range
of
capabilities
to
alter
operating
policies in response to congestion is necessary for studying
which policies are most effective.
It may be that
certain
commonly used policies are not optimal.
_·__I____·_
____
__
___·
I-----LI-__-lll
·_
188
3.b
Evaluation. of existin,
-r!odels
Both the ASMmodel and the MTASTIhImodel (NOR 79)
have.
a capability to automatica
lly
alter the operating .mode for a
mixed - operations
The A.S:'
specifying
runway
a critical
q-ueue length
model
and
does
a time
this
by
interval.
Then, each time an arrival is scheduled, the departure queue
for the
value,
runway is
checked.
If it
is above
the critical
then the specified time interval is added to. the A/A
separation.
The MITASIM
model employed.a
the ASM. procedure in-two
-queue lengths
for
the
respects.
are -specified:
from arrival priority
transition
arrival priority.
several aircraft
method that
one
First,
for the
"downl'from
arrivals
is
lower than
provided.
model permits the more
Lack of
-···IIIIIYYII---I-
'of the
a second
to
the latter
value to
be
rapid alternation
The second change is
of extra
uses
space between
the
described in section
"calculated
II.D.
Neither
complicated changes discussed above.
more complicated policy alteration
the ability
policies.
MITASIM
"'up"
pr ori ty
the first,
which the amount
separation" procedure
transition
alternating
By specifying
manner in
two critical.
to alternating priority and
between the priorities is prevented.
in the
improves on
models
to
be used
options reduces
to explore
optimal
189
Modeling of congestion induced changes
3.c
cannot be modeled through
Changes caused by congestion
This
the same procedures used for weather-induced changes.
is
-
the
because
ai rcort
triggering
operating.
What is
condition.
That is.,
external
external
is not
is one aspect
but
(weather)
factor
is
to
the
the airport
of how
the definition
the exact situation that
is
the
of
causes the
changes, queue length, for example.
Modeling of these changes is
a set
of
(such
conditions
that
greater than X aircraft)
analyst
what
designates
value
(X).
When
automatically read
allows only
as
takeoff
occur,
3
The
are to be set and at what
a
of parameters
list
is
Currently FLAPS
and changes are made.
two general types
on runway
queue
willi trigger an event.
conditions
they
done in FLAPSby defining
1)
of conditions:
queue on runway X has more that Y aircraft,
and 2)
takeoff
takeoff
queue on runway X has less than Y aircraft.
can be
made when
the condition
takeoff queue is added to
(condition
in parameters
restraints on what changes
There are no
2),
the
is true.
the
or subtracted from
(condition 1)
relevant
Each time
condition
is
and
checked
triggered if true.
Extensions
to
FLAPScan be made to enlarge
the above
set of conditions.
-
-I-
I
----L-L·
-I
Il-----a
I
--
-LII
190
4 Other factors
A number of additional factors may occur that result in
changes
policies.
in operating
subject to a
curfew
to control noise
Logan Airport
lanes.
When
ship
several
where
a liquid
natural
it may
leaves Boston Harbor,
LNG
makes its transit,
inactive for intervals
often
not occur
Accidents
exposure.
runways overfly
gas (LNG)
tanker
several runways
20 minutes
several.hours.
enough to
be a
shipping
enters or
'Whilethe
not be overflown.
of 10 to
entire process may take
does
be
Perhaps an extreme example is provided
may block a runway.
by
runways may
Certain
are rendered
at a time.
The
Fortunately,
issue to
major
this
be
analyzed, but it does illustrate the limitingocase.
Whatever motivates
the two
procedures described above
capability
change can
to model
them.
be described
under a specific
policy
the changes in - operating policies,
change
provide a
As long as the instigation
as occuring
at a specific
set of airport conditions,
is
aircraft parameters
wide ranging
describable
in
terms of
specified so far,
set up above can be used to model it.
then
of the
time or
and the desired
the runway
and
the procedures
191
G
1
STATISTICAL ISSUES IN MODELING AIRPORT OPERATIONS
Introduction
This
section will
which are pertinent
we
will first
airport operations.
as an event paced
digital simulation,
briefly
statistical analysis of such
survey
the current
simulations.
of current work relate directly to
wish to analyze,
considerations
to the analysis of
FLAPS is implemented
and
discuss statistical
the type of situation we
but the airport environment poses a number
we draw conclusions about
area
The ASM model is briefly evaluated
each of these topics.
what output
In ech
the statistical features relevant
for airport simulation.
consider
of
Certain aspects
of significant problems for the statistician.
with respect to
state
statistics
Secondly,
are required
we will
by the cases we
wish to. analyze with FLAPS.
2 Survey of Statistical
Issues Relevant to Simulation
2.a Simulation context
In order to understand the application of what follows,
it
is
neccesse.ry to
simulation
discuss
from a statistical
A simulation
such as
the basic
point of view.
FLAPS is
based on
description of how the airport operates.
__
__
concept of a
a stochastic
The computers
used
192
to
implement
Thus,
simulations
are
completely
deterministic.
some way must be found to simulate randomness.
This
topic is discussed below under section 2.b.
This probabilistic base to- simulation means
outputs of
a simulation
analyzed as such.
are random
identical
produce a
variables and
mus-tbe
Each "trip"" through the simulation is but
one realization or replication
the
that the
case
with
of the simulation.
different
different realization.
random
Methods of
Running
numbers
will
reducing the
significance of variation among replications are discused in
section 2.c
Of major significance to the analysis of simulation is
that
its
outputs
example,
inherently
if the airport is
experienced
is
are
aircraft
very congested,
by a typical aircraft
very likely
will
complicates
autocorrelated.
then the delay
is likely to be large.
that
the
delay experienced
also
be
large.
application
For
of
This'
by
it
following
autocorrelation
estimation procedures
considerably.
There are two fundamental approaches that are
obtain
the
true
autocorrelation.
average behavior
...
.
.
|
.
.
.....
over the entire
The second procedure
is to make many shorter
....
.
.
..
.
.
..
.
..
..
.
..
at
.
.
of
Average behavior is obtained by
computing estimators
each starting
presence
One approach is to run the simulation for
an extended period of time.
.
in the
used to
.
someinitial
duration of
the run.
replications,
condition (usually
empty and
193
idle).
Average behavior is obtained by computing estimates
across the
several replications.
There are
statistical tradeoffs between the two methods.
creates certain problems for the analyst..
a number
of
Each method
Someof the more
significant issues are reviewed below in section 2ed.
2.b
Random number generation
The subject of
and
complicated.
bibliography
Fishman
with
developments is
and before
how to generate random
cites
491 entries
(FIS 78 p.350)
on this subject.
such that much of
has been surpassed.
attempt to
contribute
numbers.is vast
1972
The pace of
the best work from 1972
It
is not our purpose to
to the theory
generators (RNG), but ayone
a
of random number
who constructs
must be ensitive
to the ways the
model .
a simulation
use of ar RNGaffects the
Choice of random number en_;rator
Much has been
correct
choice
the analyst,
of
RNGs.
(FIS 78
This
pp.
345-91 )
on
the
choice poses difficulties for
as RENGs
may be machine dependent,
written in
are usually
assembler language and exceed the abilities
most application
For
written
example,
oriented users to meaningfully
even
the
GPSS simulation
of
test them.
language
package
employs a RG with so many problemsthat it leads Fishman to
this conclusion:
expect
to
scientific
1_1
defend
basis."
LC
"Anyonewho contemplates using GPSScannot
his
results
(FIS 78 p.
_ _
successfully
on
a
truly
66)
_I_
_
194
congruential
numbers,
use today
of RNGs in
The majority
(MC)
are multiplicative
a stream
which generate
generators
which are uniform on the-interval from 0 to
Z(i),
f
the largest integer capable
being stored in the machine.
The Z(i) are divided by this maximum size to obtain
number
uniformly
on the interval
distributed
used by all MC generators
formula
Z(i) = A * Z(i-!
The user
of
0
r(i), 'a
to 1.
The
and the
RNG
is of the form:
(modvlo M)-.
supplies a
starting seed
for Z(O)
recursively generates-the series Z(i).
The ASM model uses an
= 2051
undocumented MC
This-form
= '2
and M = 4194304
enerator with A
restricts the
initial seed Z(0) to odd numbers,
and the FAA routine has a
mechanism to insure that,
user inputs an even eeed,
it
by
is "bumped"
provision
p.87)
is
replications),
therefore be
10
the sample
as
the numbers
by the
replications,
not
odd value.*
inputs given
(for
outputs and
This
(PMM 77
use. in ..
10
1001 to 1010 inclusive.
that sample
the case
next
number seeds
random
runs reported
those
to the
1 unit
valuable
include
if the
It mav
validation
FAA are really based on
6 different
Pour replications may
be doubled,
10.
replications beginning
with
the seeds
(1002,1003),
(1004,1005), (1006,1007) and (1008,1009) being the same.
*
These observations are based on a listing of the code
of the AS.M model.
195
The
routine
(LEW 69).
used
It was
in FLAPS
used in
was
the
developed
FORTRAN
IMSL
package.
It uses
A = 16807 and M = 2147483647
This is a
variety
of MC generator
multiplicative congruential
by
Lewis
statistical
=
231
-
1.
known as . a prime modulus
generator.
Fishman
applies a
large number of tests to several generators of this
form and
his conclusion
is -that this one is acceptable
382).
concerned about
Users
elect to
change
the quality
(FIS 78 po369,
of the
A to one- of the other values
RNG may
that Fishman
tests which perform somewhat better.
Use of random number generators
Several authors
emphasize
that
(FIS 78 pp.35-6,
the correct
use of
SCE 74
a RNG
in a
pp.
144-7)
simulation
involves not only choosing an acceptable algorithm, but also
I)
having
ach process
in the model use its own independent.
stream of randomnumbers
and 2) explicit identif icaion in
the simulation outputs of the first and last seed used. The
first point allows for more reproducible experinents.
The
user may change one process in the simulaticn,
without
disturbing the sequeince of random numbers used in the other
processes.
of the
This allows a clearer
change
in the outputs
examination of the effects
than would be the
case where
all the random number streams were changed. Seeing the final
seed used
exactly the
that
_
L_
was
allows the analyst to
same random
altered.
variables except
This
__
prove that two
also
allows
cases used
for the
the
process
running
of
196
independent
experiment
The
experiments
as the first
ASM model
FLAPS allows the
by using the
seed
generation
of these
printing of beginning and
one for
FLAPS uses three streams of random
and one
for general
may specify any seeds for these streams,
are provided
procedures.
ending seeds if
calculation of separations,
of schedules
in the first
in the second.
provides neither
the analyst -so requests.
numbers,
last seed
one
use.
The user
but default va'ues
from the table in FIS 78 -p. 486 to be
apart in the
sequence generated by this
for the
RNG.
million
Preliminary
runs of FLAPS indicate that each stream may be called on the
order
of 100,000COtimes
in a "moderately
Generation of non-unifcr
There are
density
There
for generating
functions.
FLAPS allows
numbers
needs for random numbers
other than uiform.
catalogued
larige" run.
are a wide variety of techni ues
a
wide
variety cf
See, for example,
the user a
with distributionLs
choice of six
probability
FIS 78 pp. .92-480.
probability density
function forms whenever a random variable is to be used:
1) Deterministic
2) Normal
3) Normal
- using the central limit theorem with user
specified truncation
- using a formula from Box & uller
(BOX 58, also see FIS 78 p. 410)
4) Triangle - convolution of two uniform numbers
5) Erlang
- with user controlled order (k)
( k = 1 is negative exponential )
6) Uniform
197
This allows
results
the
user to experiment
to different
with
probability
the sensitivity
density function
This may prove useful in view of the scarcity
about
the exact
probabilistic
of
forms.
of information
form of many key airport
parameters.
2.c Variance reduction techniques
There has been considerable interest in developing ways
to controlstochasticity
inlsimulations in order
more
estimates of
accurate
pp.05-263,
FIS 78
stratified
sarupling,
simulation
pp. 114-126).
control
to obtain
ou-;tputs
Techniques
variates
and
LE 74
such
as
imortance
sampling are -not directly applic-ale for use in a simulation
that has both
multiple inputs and multiple
as
outputs,
is
the case here.
One method
which may
antithetic variates.
be applied
The basic
idea
is
is the
technique of
that the variance of
the simulation outputs may be reduced by having each pair of
replications
negatively
follows:
use
correlated.
where
procedure is
r(j).
One
If replication
variables r(j),
s(j),
streams
With
of
random
way
i uses
to
-
r(j)..
started again with a
the
MC type of random
method proves easy to implement.
of C
i + 1 should
For
that
are
is
as
achieve this
a stream
then replication
s(j) =
numbers
to 1 random
use stream
replication
new seed for
i+2
the
the stream
number generator,
this
It has been shown (KLE 74
198
pp.254-6)
if
that -streams
the seeds. used
M - Z(O),
process
where
to start
Z(O)
the
second
stream. s(j)
is.
is the seed used to. start the first
and M is the modulus of the RnG,as indicatedabove.
When analyzing
replication
However,
Thus,
r( j) and s(j) will have this property
can no
each
the
replications
the outputs from this
longer
considered as
pair of replications
degrees of
freedom
is no longer
this technique
be
n-
(KLE 74 p.
1
199)
situation., each-
can be
in
independent.
so considered.
any average
but n/2 -
.
also reports
across
n
The source of
its successful
application 'to a number of simulations.
The procedure
easily
2.d
added
was not included
in FLAPS but
could be
as an extension to the model.
Output analysis
There is much work reported
of a simulation..
However,
few
on analysis of the outputs
advances have been made in
analysis of the particular type of simulation represented by
FLAPS.
We
will first discuss why
multiple replication
FLAPS must be run
type of simulation and
are produced for this situatiorn.
number of problems and techniques
as a
how estimators
We will then
discuss a
used to analyze this type
of simulation.
Overview of analytical framework
The basic
complicating factor in
outputs is the presence
of
analyzing simulation
autocor.relation.
There are two
199
distinct
approaches to
dealing
with
methodoperatesthe simulationr as
this
roblem.
One
a single long replication
but attempts to manipulate the outputs to ex-tract meaningful
estimators.
final
Ar:alysis focuises o
condition
bias and various
values from
autocorrelated data.
the regenerative
series
condition bias,
methods of estimat ing
techniques are skipping data pints
time
initial
Amongthe
ean
latter
or blocks of data, using
nature of queueing systems and performing
analysis
(GOR 69
vE
L
71,
rp.27795, -S
74
pp. 8 7-9O, FIS 78 pp.219-273).
Implicit
assumpti;on
state
in
all.
cf these
that the
system
condition.
constructing
+fac that
procedures,
being
Since a
however,
is the
is
steady
modeled
significant
an airpcrt simulation
in a
reaso-n for
in the first place2 is the
the airport is seldomn in steady state
we cannot
use a single long experiment for our analysis.
If accurate
estimates
und er
varying
of
the
loads is
perfcrmance of
to be obtained
an a rport
then the model must be
formulated and run to makemultiple replications
time
and
eriod.
the
Only in this
range
of
time
of the same
way can the average performance
typical
pe rformances
be
determined.
Unfortunately, little analysis has been done on the multiple
replication case.
multiple
Even the infrequent paper studying of the
replication
case,
such as
TUR
76,
is
often
liilli
· · *LI*C---·Il··-··-·-·------
concerned with steady state situations.
_I_
I
_______·__·ll·__IIL___lllnU--·l-
I-IIO(LI-···aPI··*i
..
.I
200
The standard treatment for multiple replication
simulations is to assume that each replication is
of observations of an output
independent and that any set
across replications will be normally distributed, permitting
use
of the classical
(KLE74 p. 85-6).
is some performance statistic,
For example, if X(i,j)
as average delay to
all landing
such
in period j of
aircraft
and I is the number of replications
i,
replication
process
estimation
be
to
run, then the estimate of the true average landing delay in
period j would be:
X(j) = (1/f)
the standard
I-
x(i,j)'
(23)
i=l
of x(i,j) would be-:.
deviation
I
2
}-1
.- (l/I)*
Finally, the 95%
2
I
(24)
[. x(i,j)]
i=l
confidence.interval of the mean .would
extend- from X(j) - Xc(j) to X(j) + Xc(j) where:
Xc(j) = Xs(,j)*t(.025,I-1)/SQRT(i)
The term t(.025,
n) represents
(25)
the t statistic
for a 95% two
tail confidence interval with n degrees of freedom.
Assumption of normality
-An assumption of the classical estimators
is
that
the
distributed.
underlying
process,
X(i,j), is
given
above
normally
The question naturally arises of whether this
model will generate normally distributed
data,
and
if
it
does not, how dependent our estimators are on the assumption
of normality.
_.._____· UIQLIIY·IIIILWU
··I·· .
201
The central limit theorem is general enough that it is
not implaus-iblethat estimators across replications would be
normally distributed.
454-7,
Kleijnen discusses (KLE 74
also. see GOR 69 p.
theorem
called the
280)
us,
"stationary
where we want to
individual
terms
r-dependent central
to
are
processes
from
theorem applies to
and that we have no idea how fast
Reportson
actual
the
distributional'
simulations
The only
stationary
it converges.
form of
are
of
The conclusion is that
the distribution of X(j) is asymptotically normal.
would be that the
and the
themselves averages
successive points' of a time series.
caveats
limit
the case of interest
compute estimates of X(j)
x(i,j)
87,
a' form 'of the central limit
theorem" which applies specifically
to
p.
rare.
date, generated
FLAPS supports
investigation of the question of distributional forms of the
simulation
output by
printing
replication by
replication
values, should the analyst so elect, for the majority of the
statistics that are collected.
one
such
case
as a
question of normality.
We
report here results for
preliminary
investigation
into
the
Thorough investigation of this topic
would be a major research undertaking.
The case that was used
is described
in section
III.B' as
a part of the New York La Guardia airport capacity runs.
use the single runway configuration.
found by
F'AP3 to be
departures
·I
-`I-.--------
II
--.
The IFR capacity was
approximately 26.8
per hour.
Fcr
_
I
the
We
arrivals
tests of
_
__I____
and 26.8
normality
this
_
202
configuration was run for 50 replications of 4 hours.
Both
the arrival and departure streams. had an average demand rate
of 0.8*26.8 = 21.4 aircraft per hour.
in the arrival process,. the
Note that due to gaps
departure process is operating
at less than 80% of capacity.
Table II-14
The normality
presents summary
of 3 variables
statistics for
the run.
was investigated:
1) Total average landing delay
2) Total average takeoff delay
3) Number of landings in the 2nd period
Period
Landings
Landing
Delay
Takeoffs
Takeoff
Delay
1:00
to
21. 0
(4.2)
4.1
(4.9)
21.9(4.1)
3.2
(2.5)
2:00
1.2
1.4
1.2
0.7
4.5
83.9
Entire
run
82.4
3.2
(7.7)
(2.9)
(9.5)
(1 .5)
2.2
0.8
2.7
0.4
Results given as:
mean
(standard deviation)
half width of 95% confidence interval
Arrival and departure flows:
Negative exponential interaircraft times
Average of 21.4 operations/hour
Remaining parameters:
Described
in section B.1 of chapter
III
Table !I-14: Normality Test: Summary Results
203
The
test
for
normality used
(SHA 65), described
of
was
the
as among the most
different types, of
departures
Shapiro-Wilk
test
sensitivJe for a number
from normality
(FIS 78
The Shapiro-Wilk test sta'tistic varies from 0 (all
p.72).
to 1
at one point)
data grouped
(perfectly
normal
data).
For n=50 as used here, critical points (FIS 78 p.319) are:
Critical Value of W
Level
.01
.10
.930
.955
.50
.·
974
.90
.985
.95
.988
-i gures
statistics
II-22
and
and IT-23
the values
present
of
the
graphs
of .the
Shapiro-Wilk test
statistic, W50, for each one.
The interarrival
time
aircraft
between
exponentially.
by the
process
to t his
arrivals
simulation has the
distributed
The srvice time distributicn,
distribution of the
buffer on A/A
normal.
Therefore,
we wculd
landing
delays
be
to
as controlled
separations,
expect the
somewhere
nega.tive
is
distribution of
between
those
two
distributions
Takeoffs are also generated with negative
exponential interdeparture times. However, the service time
function cannot be characterized in any direct way. D/D
separations are deterministic
for any single combination of
aircraft classes but
take on several values
combinationsof classes.
--
L
-__1
I
--
I
I
.-
-------- r-
across various
The arrival rocess interferes
___
_
204
mean ±1 st.
0
-
deviation
-
.2
1
10
U
'H
8
W50 =.815
-
P>
6
0;-
4
r=
;z
2
CW
0
0
2
4
6
8
10
12
14
Delay (minutes)
a)
Landing Average Delay
mean + 1 st. deviation
1?
0
U
r.7
0
.,I
,.H
r-o
P-4
ar
.-
.
1
10 8-
W50 =.899
$--
04j
6 I
4 2 -
|
E
zj
F:
0
71h 11-1
7
1
-
S
- -
0I_
t
w
2
|
--
t-
=
.
71
4 Fhl
~
i
i
i
L
10
12
14
Delay (minutes)
b)
FIGURE II-22.
Takeoff Average Delay
Distribution
of Average Delay.
205
mean + 1 st. deviation
I.
7-
I
--
.W0 = .966
6-
50o
.r.
4-
U
O
(o
i
O1
G)
r4
i
I
I
I
I
I
I
21L
I
m
r.
Il
0
-1
I
/
x./
30
-0
I
number of landings in second period
FIGURE II-23.
---
---- -- - - -
Distribution of Number of Landings.
----
-------
----- ------------
206
with. the
landing
distribution,
expected to
The
process,
sum
result in a
further
of all
these
complicating
factors
more normal-like
the
might
be
distribution for
takeoff delay than landing delay.
The statistic for average landing delay to all aircraft
is graphed in figure II-23.a.
There
chance in -a hundred
that the
underlying process
normal
this
and generate
distribution
than Gaussian.
is much less than one
distribution
produced could
be better
The distribution
could be
of results.
The
described as
gamma
of average takeoff delay,
in part b of the same .figure, is closer .to being symmetrical
than landing delay,
is still
below the
samples from
The value of the.test statistic, .899,
.01 possibility
a normal population.
of being
It is
generated by
unclear whether
takeoff delay appears more normal than landing delay because
the
fundamental process
is more
normal,
or because
,the
average value of takeoff delay
is lower than landing delay.
The lower
mean that the
overall average may
distribution produced here
is merely a scaled
takeoff delay
down version
of the landing delay distribution.
Delay to an aircraft cannot,
of course,
be negative.
It may be that at low values of average delay this fact will
lead naturally to the one-tailed form of delay distributions
we see here.
Higher average delay values
might result in
the distribution converging to a more Gaussian form.
207
Only one distribution
plot-ted.
The
of the number of
operations was
one chosen was the distribu'tion of the number
of landings in period 2, shown in figure II-23.
In spite of
the fact that the underlying distribution for this statistic
is discrete
the Shapiro-Wilk test is the second
mostsensltive
among tests for normality for this specific
problem
of
and that
(FIS 78 p.
the
three.
73), the distribution
We
can reject
normality at a very low
.50).
However,
as
period,
while scoring higher
to the
may
of
the simulation,
be taken to indicate that
than either delay process.
conclusion
which
emerges from this
preliminary analysis is that more attention
to the
question of
complex simulations.
of
this test covers only one
full length
on W50,
this process is more normal
The tentative
null- hypothesis
significance level (between .10 and
the fact that
opposed
the
is the most normal
the distributional
should be given
form of
oiutputs of
The assumption of normality
may not
always be justified.
In view of
the
non-normality of these
reassuring that
the
classic estimators
out to
be robust
normality
test
does
using
Xc may
p.335, 346).
same is not
_
t statistic
be used
depend
of Xs,
on
true for any inferences
nor
normality,
as presented
Both the cited authors
I----·------IIYY
for Xs and
it is
Xc turn
from normality.
not bias the estimate
the
estimate of
under departures
outputs,
(BOX 53,
Non-
does the
so
SC
the
59
ake the point that the
abcut the distribution
I
I
208
for Xs to be calculated,
Were confidence intervals
of Xs.
on the
depend critically
validity-would
their
underlying
In summary, it can be concluded that we
X(j) being normal.
may use the procedure of equations (23) to (25).
Time series analysis
analysis
series
Time
was mentioned
as
appropriate for single simulation experiments.
have
may also
X(j)
set of
- of
performance
the
However, it
of a
Using the earlier example,
considered
of real
the time series
compared with
Y(j),
be
would
technique
way of validating outputs
utility as a
multiple replication simulation.
the
a
a
and
time series
world observations,
The
measure.
reason
for
considering such a test is, again, the high probability that
adjacent
Jenkins moving
both
The procedure
autocorrelated.
and Y(j)
of
elements
Fishman was an early
the
(HSU77)
would be
resulting
advocate
of
spectral analysis procedures (IS
recently
these
models
are
series
to fit
autoregressive model to
average,
and examine
of
a Box
&
both X(j)
for differences.
the use of time series and
67).
Hsu and Hunter have
performed such a comparison of actual and
estimated time series
on a model of air traffic
control
communications. They derive an estimator for evaluating the
comparison.
Time series analysis is
a method of examining
simulation outputs.
are a number of difficulties
______·
conceptually very appealing as
with
applying
However,
there
it to the airport
209
problem.
First of all, it does assume the underlying system
is covariance stationary,- i. e.
is any
trend or
removed.
provide
The
one
is
compared.
only 48
length
the
X(j)
performance
any
and'
to
use
in
more serious
time series
a 12
points,
must be
simulation may
A
are
Y(j)
there
-If
it
trend
series.
of
to
be
sampled
as
hour simulation will
insufficient for
Further limitations
methods arise
reliable
on the use of time series
from the fact that data on the overall
f airports
is,
both rare and unreliable.
values of
of the
15 minutes,
data
data,
d'rivingthe
estimate
the short
Even if
estimates.
the original
steady state time
frequently as every
produce
in
demand function
possible
extracting the
problem
cycle
in steady state.
as we
It
will see in chapter IIr
is unusual
performance measures,
let
such measures for an entire day.
undoubtedly applicable
to
enough
to find mean
alone time
series of
So, while the method is
this case,
there
are severe
practical limits on its usefulness.
3 Selection of Simulation Outputs
An important
design
model shculd produce.
issue for FLAPS is wh.at Outputsthe
We need tc consider both what actual
performance measures should be calculated
and also how they
should be aggregrated over time and space.
.*
LL.3--.
I
__
LI
_.
----
·----
----
--
_
-----------
·-.....
_
IL.
I
r
_1_______.
__.
210
3.a -Statistics for capacity and delay
We have often referred to the
capacity and -delay issues.
the
estimates
of
model as one oriented to
At the heart cf the outputs are
delay
to airc-raft
and
the
number
of
movements that take place.
Capacity is assesed by counting
the number of aircraft
movements.
Three measures are often suggested for assessing
de-lay:
-the average delay,
1)
2)
the fraction
delayed more than some value and 3)
of aircraft
the length of the queue
of aircraft waiting to use the runway.
To
enable
analysis
statistic must be
in addition. to
As mentioned
of
transient
conditions,-
each
measured over smaller periods, of the run.
averages being computed for
in the demand
the entire run.
generation section
II.C above,
the model divides the run into a series of equal length time
periods.
Each capacity and delay statistic is measured for
each time period.
Additional breakdowns are needed to assess performance.
Each runway's activities are reported
the entire airport's.
Landings
separately as well as
and takeoffs are tabulated
separately.
Significance of delay statistics
To accurately interpret the outputs, it is important to
understand exactly when
and what is being
measured.
Each
time an aircraft begins a landing or a takeoff movement, the
difference in time between the scheduled and actual start of
_·--II·IY·LIYIY·UI-·
·
.
I--I-I*III
..I------
I~UI~·-·
211
the
movement is
aircraft.
the delay
experienced by
This.measure corresponds to Wq,
the queue
aircraft
counted as
in queueing notation.
is counted
waiting time -in
The period in
is the period
the
which the
in which it completes
the
runway operation.
The meaning of this delay
may be questioned as,
the
approach
measure for landing aircraft
in fact,
gate.
Any
aircraft do not
arrival
delay
ueue up at
encountered
is
probably taken in vectoring or
in holding stacks many miles
from the runway.
The point,
however,
occurs
he limitations
because
of
is that this delay
on the acceptance rate of
the runway. To the extent that FLAPScorrectly models this
process, it correctly measures the delay induced by it.
An
additional
point
about the collection
statisticswill be made below
after
of average delay
the
discussion
of
extreme delay statistics.
Analysts
are
often
interested
in
the
fraction
of
aircraft that experience extreme delay, where the definition
of extreme may be set by the
20 minutes.
user.
One
method would be merely
running count for each period,
the
total
experiencing
is
We must consider carefully the construction of
this statistic.
of
An often used valu
number
of
replicationsthe
ratio
runway and type of operation
operations
extreme delay.
to maintain a
At
of che two
and
of
the
number
the end
cf
the set
of
would be an
estimate
of
the true proportion.
I
I
I_ I-----.
_ · IL---------- _
__
----L-·--·-
_I-
I------ -
_ IL--·IILIII
_
212
The only difficulty with
the
procedure
each
is that
We
numbers of operations.
replication will have different
replications with more operations
will
tend to have a higher proportion with extreme delays.
This,
would
expect that
moreover, might be reversed for operations of low priority in
the model
where high congestion
might actually
mean fewer
The procedure suggested above
operations of low priority.
to
would tend to give greater weight in the overall average
Yet each replication
replications with higher flow rates.
in some sense,
system.
is an equally plausible
Therefore,.
there
seems
no
weight to
each
is
replication.
proportion, p(i)*,
is over, the average
why
each
reason
proposed for
each
For
of aircraft
critical amount is calculated.
of the
in the final average.
replication
shouldcountdifferently
The following measure
realization
assigning equal
replication
more
delayed
than the
after the simulation
Then,
of p(i), standard
deviation
of p(i) and
confidence interval of the average of p(i) is calculated
the same manner
as X, Xs and
Xc are calculated.
difference is that no observation of p(i)
any
replication where
assumption that the
procedure
can
be
distribution of p(i)
t
no
operations
statistic
defended
may
on the
is binomial
and that the binomial distribution
a
only
is collected
took
place.
be
used on
grounds
(with
The
that
a change of
in
for
The
this
the
scale)
converges to the normal
will have other dimensioIs for period, runway and
type of operation, here omitted for clarity.
*p(i)
213
as the'number of observations increases.
The
same. point
replication
about
made in
weight
connection to
applies to average delay.
the same manner.
the
Average
given.
to .each
extreme delay
measures
delays are estimated 'in
After each replication an estimate is made
of average delay by dividing total minutes of delay by
number of operations.
This is then averaged across
replications
to give
the final estimate.As withextreme
delay,thepossibility exists for bias in either direction,
i F each replication
is not given equal weight.
The queue of aircraft
each runway
-waiting
a
"snapshot"
period.
queue
each period.
'Thi
queue length
of ' the queue
This is much easier
length
takeoff on
s measured az tne end o
not an actualaverageof the
but
to lard and
during
the
durin,.
length at
is
the pericd
the end
of eac,
to calculate than the average
eriod.
The "sra:,.shot"
procedure
will have a larger variance thenthe period average measure.
Finding
the
observation
enters
average
ofthe queue
queue length
be taken
or leaves a queue.
requires
every
than
time an
aircraft
However, the "snapshot"
providesan unbiasedestimate'ofthe
true
length
an
procedure
at the end
of the period.
3.b
Landing performance statistics
In the
above,
·I
larnding aircraft
a number of modeling
-
_
performance section,
ssues were raised
II.D.3
regardng
the
__
214
use
aircraft' make of runways-.
assess
the- impact
of
As discussed, we may want to-
new exits
or.-new- aircraft on
distribution' of exits used or on runway occupancy time.
order
t.o do this,
needed.
statistics
Because of
on
landing
pe'rformance
the nature of takeoff
-the.
In
are
operations (see
II.D.4) no statistics on takeoff performance are collected.
Each time an aircraft exits a landing runway the runway
occupancy time and exit used
occupancy
time and
are recorded.
percentage
use
of each
Average runway
exit for
class of aircraft -and each runway are calculated.
each
A runway
used in'both directions has' data bollected se-parately for
each direction.
As the performance of each airc-raft isindependent
of"the
performance
of 'other
aircraft
independent of the amountof delay at the airport,
no need to obtain statistical
replication
basis,
estimates
and
there is
on a replication
by
as was done-withdel ay and extreme delay
215
MODEL VAJIDATION
III
discusses -the question of
This chapter
scale complex
that
validation
the model
is validated.
such as FLAP3
involves
number
a
but not limi.ted to,
including,
of
model
several such
comsparisons of
the results
of other
FLAPS
models.
We will see
tests,
different
of
comparisons between ou-tputs
data.
and observed
large-
how a
presents
This chapter
daEta and
to both oberved
the
However,
scarcity
of
data and the incompleteness of other models means
of FLAPS cannot rest
confidence in the validity
reliable
that
A
THE PROB3LE
OF VALIDATION
This section
the
one
major
"validation"
remaining
statistical,
p.21)
a host
"involves
and even
At its most
has been descr:-Led
methodological
problem
A major reasonfor this
simulation(NAY 67 pB-92).
validation
models can be
how large-scale
discusses
The concept of
validated.
as
on such tests.
or even primarily,
entirely,
of
practical,
in
is that
theoretical,
philosophical complexities." (NAY 71
fundamental level,
unresolved epistemological
questions of
validation involves
how we
can ."kniow'
In the context of complex mdels,. a.
something to be true.
numberof conclusions have come to be generally accepted.
Wereview them here.
__
I_·I___
I
___
I·
216
A consensus seems to be emerging
far
been
loosely called validation
to divide
what has so
into three
stages (NAY
67, LAW80, GAS80):
1) Verification - establishing the extent to
which a computer implementation of the model is
is equal to the description
of it in formulas,
on paper or in the analyst's mind,
2) Validation proper -
establishing the extent to
which a model description, such as chapter II of
this work, is in fact an accurate
of how the real. world functions,
representation
and
3) Certification - establishing that the model is
appropriate to answer the questions being studied.
Speaking colloquially, verification is proving that you
did what you thought you did, validation is proving that the
world operates the way you think it does,
and certification
is proving that you are studying the right thing
to begin
with.
Verification involves techniques such as modular design
of the computer program, detailed walk-throughs of outputs,
deterministic
runs,
runs equivalent
systems, and so forth.
but it is a separate
chapter
and is not described
involves
critical questions about
simple
queueing
Much verification work was done for
FLAPS,
Certification
to
issue from the concern
of this
here.
topics
such
as
identifying
the real world system
and finding
217
future problem areas.
The work that
was done in this area
for FLAPS is contained at various points in Chapter II where
the importance
for
airports
related questions
of analyzing capacity and
is
established.
model's attention
The
to ground
operations at
runway operations,
its schedule
its
model changes
inability
to
criticism
of the
ASM
the expense
of
generation methodology and
in
operating
rules
are
primarily criticisms of its appropriateness as an analytical
tool.
The
development
of
limitations
is an attempt
analytical
to
tool. The results
demonstrate the
FLAPS
overcome
*o
these
create a more appropriate
presented
appropriateness of
in Chapter IV also
the model for studying
airport operations.
We
turn now
to
the
consideration of
validation
as
defined narrowly in point 2 above.
First,
validation is
a question of degree
absolute yes or no decision.
The more tests performed, the
more confidence
one can have in the model,
cost effective
nor possible
(NAY
67
p.B-93,
LAW
79
purpose
knowledge
to building
of
to pursue
p.8).
validation could.be achieved,
but it is neither
complete validation
If complete
and
total
there would in fact be little
a simulation,
the real
and not an
world
as
system
no uncertainty
would remain
to
in
be
investigated with the model (CON 59 p.104).
A number of approaches to validation were identified by
Naylor and Finger in their paper
·s
_
NAY 67.
These were:
1)
218
Rationalism,
set
that views models as built up logically from a
of axioms
that are
themselves not
subject to
proof.
Verification is here seen as "the problem of searching for a
set
of basic
assumptions
underlying
the
system of interest" (NAY 67 p. B-93).
each of
the assumptions
experimental evidence
Economics where
of a
and
ability to
indicator of validity.
by itself sufficient
behavior
The
the
2) Empiricism, where
model must
3)
of
be supported
methods
of
predict correctly
by
Positive
is the
sole
It is claimed that each approachis
to establish a model's validity,
but
Naylor and Finger contend that, when operating as we usually
are,
with a scarcity
verify
a model with
of information,
any one method and must use
three approaches as appropriate
have.
Thus,
we cannot completely
to the
we might empirically
test
any of the
information we do
a
uniform random
number generator to see if it produces well. distributed
numbers, rationally argue that certain
mathematical
transformations
on these uniform numbers will produce random
numberswith other desired probability density functions and
test an entire model
by having it predict
a certain case for
which we do have data.
A
recent
survey
of validation
develops the philosophies identified
possible tests
for validity
techniques
(LAW
80)
by Naylor to catalogue
into three
general techniques
.?
219
(LAW 80 p.10--14):
1) Face validity - how reasonable are the assumptions
2) Tests of assumptions
3) Tests of results
All three methods
The reasonableness
validity of FLAPS.
the degree of
may be used to assess
assumptions
the
of
was defended as they were developed in Chapter II.
were
assumptions
FLAPS
section
model. in
performance
for
performed
II.D.
and/or data
uses methods
important
the
At a
that
number
have gained
Tests of
landing
of points
general
acceptance among airport analysts.
Validation of results poses its own difficulties.
Law point out (NAY
Naylor and
that -the interpretation
rejection
wrong
with
be ambiguous.
will be
taken to
rejection
the model.
is,
of
LAW
80 p.10,15)
of a result of a statistical
can
a simulation
67 p.B-93,
A test
course,
there is
which does not
preferable,
test on
results in a
A test which
mean that
Both
something
result
and' taken
in a
as
confirmation of the accuracy of the model, but of what is it
a confirmation?
the model?
How much does it enhance our confidence in
Obviously answers to these questions will depend
on the difficulty of the test, how much is being tested, and
the possibility
of offsetting
Resolving these questions is a
errors among
other factors.
much more subjective process
than a statistical test.
1
_I
I
r_ _·
11_1_
1
__·_
220
There
are
simulations
a
reliable
collected
and
We have seen
considerable
hypothesis
problems
in general
particular.
pose
other
testing.
data
on .
II.G)
the
of
simulation
in
that simulations
theory
model.
accurate
by a number
of airlines
Such data can
and detailed
Delay data
airlines)
are typically
or by controllers
to
delay as
a secondary
multiples
of 5 or 15 minutes.
task.
and,
be helpful
in
are not
be used to validate a
collected by pilots
(for the FAA).
very busy with other duties and
of
Data on delay are
making general assessments of delay condi-tions but
sufficiently
of
by the scarcity
at airports.
by the FAA.
results
classi c
This is exacerbated
ongoing basis
to some extent,
testing
an airport
(section
strain
on events
on an
of
in
(for
Both groups are
tend to look upon recording
Delays
are ulsually
given in
Most importantly such data
rarely include information on conditions in effect
at the
airport at the time the data are collected.
The result
statistical
sections
of all of these problems
tests
below.
will be
Instead,
performed
we will
and
is that few classic
presented
present
in
a number
comparisons involving a variety of models and airports.
the
of
The
intent is to establish that thle model described in Chapter
II gives reasonable results over a range of conditions,
it provides options and insights
match.
and
that other models cannot
221
B
TEST CASE: LA GUARDIA
La Guardia airport
reported results
other
on
information was assembled
Figure
III-1
comparisons between
a series of
shows
La
as
The
Guardia.
described
the airport
FLAPS and
geometrical
in section
geometry
has
This
of studies in the past.
been the subject of a number
section reports
figure II-1)
in New York (see
II.B.
elements for
La
Guardia used in FLAPS.
I
1 .a
Comparison to FAA capacity analysis
Introduction
A study
estimating
configurations.
by
Peat,
has
been
capacities
by
conducted
for
the
La
four
FAA (FAA77),
Guardia
The study used a capacity
Marwick
and
Mitchell*.
configurations were run on FLAPS,
Two
runway
model developed
of
the
using the same values
four
of
parameters which were reported in the FAA study and assuming
standard values for the parameters
FLAPSwas found to
exhibit slightly
not reported by the FAA.
lower capacities
for
reasons probably related to A/D separations.
*
--- L--
---
Different from the airfield simulation model developed
by P
-----I
which
v
has been reviewed in this wcrk.
--
----·
I
C1--_
It
222
22
(9®
' '~o
to
*-t X
x
Y
0)
0
50
S
I.
(oti09
-,,o
SO
,-
-
JO
('0
,
,, J
-
3-
/
high exit inumbers
b
j.s)
/4
4 9!
4-.
- 1andiTngs owards
low exit numbers
=50
y=j
0
- 0,
Keypoint
x
811
812
37
6
821
90
178
170
221
822
314
43
37
53
77
6
121
32
70
122
123
90
143
I
92
1.24
126
1G8
108
122
179
208
125
126
136
127
145
128
111
112
113
114
115
116
117
118
119
120
92
100
i10
117
124
147
170
FIGURE III-1.
y
Keypoint
x
v
Keypoint
21.2
x
130 155
148
218
103
248
311
153
84
Scale:
28 feet/unit
1406
140
173
221
La Guardia:
y
FLAPS Geometry Representation.
223
1.b
Case description
The
(FAA 77)
study
the
gives
II-1
.
(A/D, D/D) were not
Other separations
Values assumed for FLAPS were those presented in
supplied.
Aircraft performance information
section II.D as typical.
in the
was not specified
mix
four classes and the size
They correspond closely to classes
of each class is given.
in II.D,
as described
the aircraft
however,
study,
percentages are given in terms of
i to 4
and
The values are
arrival/arrival separations that were used.
shown in table
mix
aircraft
the aircraft performance
and
parameters described there were used.
Two configurations
actual use
runways,
in
the
at
as listed
test
of
La Guardia
intersection
located
can be
is an
There are
used:
1)
to
the
arrivals on 13, departures
on 4.
22,
in
runways
two ways in which
arrivals on
single
This case was also used
intersecting
close
three different
presented
normality
2
runway.
of
in the figure.
Configuration
III-2.
single runway which represents
The first configuration is a
the
shown in figure
were used as
II.G.
section
case with
start of
the
the
arrival
such a configuration
departures
on
2)
31;
Each case was run for both
IFR and VFR separations with aircraft mixes varying slightly
under IFR and VFR conditions.
rlllllllYIIIIIIIIII1111*111
-· --
-I I
_
224
__ _
____ _UI_
__
D
Configuration
1
D
Configuration
.a
D
Configuration 2.b
FIGUREIII-2.
__la1__LIIIII^_I___
La Guardia Configrations.
225
Aircraft
mix:
Class:
D
.03
.03
VFH:
IFR:
C
B
A
.72
.76
.15
.16
.0iO
.05
Arrival/Arrival Separations:
(miles at threshold)
IFR:
3
.
A
8.4
3.2
.(0
15.0
4.9
3.2
3.2
6.1
3.5
3.5
Trailing Aircraft CassLeading Aircraft Class- D
D
4.5
C
6.O
C
B
A
3.2
4.2
3.0
Class- D
VFR:
Leading Aircraft
Data
Table III-1:
1.c
5.1
5.6
5.0
3.1
.0
3.9
5.7
B
2.5
2.3
A
2.5
2.3
1.1
1.
0.8
1.5
from FAA 77 p. A-16
La Guardia Validation: Capacity Parameters
Discussion of results
Table II-2
results,
presents the results
as given in FAA77,
three
single
are the
capacities
from a
run
aircraft.
in
which the
among he
between the
two
arrivals.
runways
FLAPS results
were saturated
come
with
Ten replications of four hours each were run. and
are the averages of the
of each replication.
minus
or
The AA
The FAAresults shownin table I1-2
for 50,
the results shown
on the
of the runs.
do not disfinguish
runway situations
intersecting cases.
·------s-·-·__.-8--^"P""CLT
4.1
C
Confidence
FLAPS estimates
intervals
vary among the
last three hours
at the 95% level
cases from
plus or
1 to 2 aircraft.
-·LilDTPYIII-LL"
*T·--·--·-·---L-·l··Lsll^·l-lls*-i
_WL.II_Yr_
226
IFR
A
Configuration
Configuration
T
T
26.2 . 26.2
26.8 26.8
52.5
53.6
28.3
31.0
28.5
28.3
21.9
30.3
56.7
52.9
58.8
34.1
26.8
34. i
30.9
68.2
57.7
26.9
33.6
60.5
37.6
31.2
31.3
31.3
31.8
37.6
33.6
38.5
37.5
42.9
75.2
64..8
69.8
68.6
74.9
from
FAA 77
from run of 10 replications
average of last three hours.
A - Arrivals
D
D
2:
FAA -FLAPS(2.a,Rmt=2.O):
FLAPS(2.a,Rmt= .):
FLAPS(2.b.Rmt=2.O0):
FLAPS(2.b,Rmt=1.0):
FLAPSresults
VFR
A
T
1:
FAA
FLAPS(AP):
FLAPS(Alt):
FAA results
D
for 4 hours,
- Departures
- Total Operations
AP - Arrival Priority
Alt - Alternating Mode
Table III-2:
La Guardia Validation:
The single runway results
models
priority
are very
close
increased.
configuration
for IFR.
scheme reduces
Capacity results
takeoffs
1)
of the two
VFR the
Under
arrival
more than arrivals
are
The alternating mode produces a more equal split
between arrivals and departures and an overall capacity very
close to the FAA results.
FLAPS results
for configuration 2 show
numbers of operations
per hour than the
FAA numbers imply a significantly
than
for
configuration
1.
somewhat lower
FAA figures.
The
higher number of arrivals
However, this appears unrealistic
227
as the same
A/A rules apply to both
capacities,
on the other hand,
as the
(8 in
increment given in
previously,
report
for FLAPS
several
and,
FLAPS arrival
are the same for all cases.
The increment in capacity by going
aircraft/hour
cases.
from IFR to VFR is seven
configuration
2.b),
the FAAresults.
the same
As mentioned
parameters are unspecified in
therefore,
may
not coincide
the FAA
with
the
corresponding parameter values used in the FLAPS runs.
particularly significant
parameter is the
One
minimum distance
to the threshold of an arrival whena departure rolls across
the threshold.
This parameter was termed Rmt in section
II.E.
Twomiles is the standard value for this parameter.
However, La Guardia is noted for its tightly
and this value may well be relaxed.
was discussed in
intersection
it were
FLAPSapplies
when the departure
of the runways.
assumed to apply
if
II.E,
run prccedures,
if
this
crosses
2
miles,
it
to
would raise
as
the
separation
only when the departure begins
less than
Rmt,
were
roll
or
capacity
significantly.
Results are shown in Table 11-2 for the VFR
cases with an Rmt of one mile.
Note that a value of 1.0
mile
applied
in FLAPS,
when the departure crosses the intersection, as
is roughly
equivalent to
an Rmt
applied when the departure begins to roll.
a departure
intersection
1 mile
__
takes approximately
in this case,.
on final in
miles
This is because
seconds to travel
to the
and an arrival will travel
30 seconds.
__C__
30
of 2.0
An arrival that
about
was two
228
miles out on final when the departure begins to roll will be
approximately 1 mile away from the runway threshold when the
departure crosses in front of it.
an additional
5 departures per hour under VFR conditions.
It was mentioned
77
do
This single change allows
not
that the FAA capacity
distinguish between
the
alignments for configuration 2.
higher capacity
cases, while
intersection is closer
2.b
than in
departure
2.a.
for
Additionally,
end of the
a
the difference
intersection
configurations 1, 2a,
for
2.b
in
than
is closer to
in 2a.
in
This means
II.E)
The
departures
well,
that a
net effect of
per hour.
that the
results
).
The only
(Figure Il-
the two cases (2.a,
2.b)
La Guardia
was a
change
in
change
in
2 could be
run on the ASM
The two
model
but the analyst would be required to recalculate
separations
for
for
and 2b were obtained by FLAPS without
once the
configuration
2.a.
between
runway assignment policies to redirect operations.
cases of
a
the departure
(see Section
emphasize
the
the runway in
to program inputs,
geometry was provided
parameters
to
The two
arrival blocks
in 2.b than in 2.a.
is important
runway
identical since
that an
period
is 4 additional
any modifications
are not
means
a shorter gap
arrivals to depart
It
This
runway in 2.b than
departure needs
than for 2.a.
to the arrival end of
shorter
the
possible
As exvected FLAPS produces
estimates for 2.b
very similar,
two
figures in FAA
each blcase.
As discussed
in part
as
the
E.7 in
229
chapter
II,
ASM
applies
threshold crossings.
separations
as a
time
There are no internalized
between
rules (i.e.
"hold arrivals until departure crosses the intersection"')in
ASM, as there are
·
the
in FLAPSe
analyst- would
Thus', to run these cases on ASM
have- to
explicitly
calculate
the
time
required for each class of arrival to cross the intersection
and submit these as inputs.
These se'oarations are different
for the two cases of configuration 2.
2
Comparison
with
ASM and MITASIM
2.a.Background to the comparison
As part
of the validation
process hat
for the ASM model during the period
1977-78,
proposed
a.series of sensitivity runs
Guardia
Airport
suggested using
manual
as
the data
(PMM 77),
those cases
a test
case-
have been run and
developed,
part,as
these cases.
A number
set of
using La
14 runs
PMM users'
4-1.
Several of
simulatior
way of testing
of sensitivity
was
in the
results reported in
The MITASIM airport
a
A
p.2-1 to
and KUL 78b*.
in
M iTRE/Me
trk
to be made,
base supplied
see KUL 78b,
was conducted
KJL 78a
(NOR 79)
the ASM
was
model on
cases were
run on
MITASIM in late 1978.
*
Note that only the cases labeled "revised sensitivity"
runs in the cited documents
-_------
111
---
1-
---
-- ·----- I-·---I
1
are from the 14 cases.
__...
--- r.___
230
In
this
replicate
part
of
the validation
those sensitivity
runs.
we
used
FLAPS
to
Comparisons are' made
among ASM, MITASIM and FLAPS for 3 cases and between MITASIM
and FLAPS for 2 others.
In several cases ASM's performance
was in substantial disagreement with FLAPS and MITASIM, due,
we suspect,
to partially incorrect separations.
MITASIM are
in general agreement.
slightly lower delay estimates,
used
to
define
FLAPS and
MITASIM tends
to give
due to different procedures
separations on
intersecting
runways
and
different D/D separations.
2.b Case description
Each'of
the
'4 sensitivity
Guardia with landings
4.
The
landing
intersection and
and taxi
runway
one exit
has
running La
31 and departures
on runway
two
exits
prior
after it.Arriving
to
spend no time at the
gate,
the
aircraft land
across the deparu-tre runway to a gate.
aircraft
taxi
on runway
cases involves
-Through
but begin an immediate
out to the
departure runway where they queue for
takeoff. Theschedule for all cases uses the base schedule
method
without
any
lateness
distribution
being
before the schedule's use in each replication.
consists of 208
through
aircraft.
corresponding
1
above,
aircraft.
There
Almost all of
are
to those used in
save
that
four
classes of
_
__1_-
aircraft,
studies
speed
of
_·I_
__
The schedule
the aircraft are
the capacity
the approach
applied
in part
the class
4
231
hours
All
arrival process.
an oversaturated
four
As will be seen, all cases have
is set at 110 kts.
aircraft
and
each
of
the
run for
cases are
three
models
used
10
replications.
for the base case has been
As the entire set of inputs
comparing results.
are of special interest in
will report
Table III-3
ive cases chosen for analysis
The
lists these parameters.
we
the cases of interest or
only those inputs that vary acrcss
We follow the numbering of the cases and
are listed below.
for the separations
the names
B),
(KUL 78b Appendix
published elsewhere
given
in KUL 78a and KUL 78b.
trigger
IFR separations, derture
1A) Base Case
at 12 (Q=12)
2A) Group
2 IFR separations,
Q=12
3A) Group
4 IFR separations,
Q=12
7A) IFR separations,
Q=24
8A) IFR separations,
Q=-1
The three
sets
of separations
(IFR,
Group 2
IFR,
Grou
They
IFR) involve changes in both A/A and D/D separations.
are
given
III-3.
in table
departure queue trigger
queue
at
which
a
various values
refer to the size
changeover
alternating operations
effectively always
The
mode is
from
made.
in alternating
4
of
the
of the departure
arrival
priority
to
Thus,
Case 8A
is
operations mode.
This
type of procedure was discussed in section II.F above.
--
-.
---------.--
-·IT·r.
I
___I-------
_
--_____
I
_
____
__
232
The inputs
occupancy
Note,
are defined in KUL
time
to
however,
Replications:
Hours: 4
78b in terms
an exit and -specific
that these inputs
of runway
exit probabilities.
to ASM and MITASIM
are in
10
-Closest arrival allowed when departure crosses
intersection, Rt: 0 miles.
Separations (at threshold, minutes):
A/A
(miles)
D/D
(minutes)
1
2
3
4
1
2
3
1
5
6
7
7
1.5
2
2
2
4
5
5
5
1
4
4
4
4.
I
!
1
1
.3
1
1
4
4
4
4
4
1
1
1
t
1
4
5
6
6
2
3
4
4.5
4.5
1
1
1.5
I
1
1
3
3
3
3
1
1
1
1
3
3
3
1
1
1
1
1
3.5
4
5
5
2
3
3
3
3.5
3.5
1
i
1
1
1
1
1
1
3
3
3
3
3
3
1
1
I
1
1
1
1
1
The
results
IFR:
4
Group 2 IFR:
4
Group
1.5
4 IFR:
3
4
3
Table II-3: Sensitivity runs: Parameters
fact
computed
duplicated
in
as
results in
FLAPS
by
deceleration speeds and other
output of lnding
FLAPS.
adjusting
exit
were
locations,
parameters until the detailed
statistics showed agreement between FLAPS'
performance and the inputs to the other models.
233
2.c Discussion of results
Summarystatistics
for the five
cases are presented in
Graphs of the landing and takeoff delay for
table III-4.
the cases are given
The base case,
In
are much
tnan
the other two
it
the apparent reason
of
II-7
takeoff
each case the AS
available- information,
specification
through
results are very similar among the
1A,
three models.
lower
II-3
in figures
models.
is the opinion
for this
results
Based
on all
of the author that;
diffe ence
A/D separation
delay
is the
improper
and some internal
problems
in the ASMmodel concerning applicat on of the additional
gap in the
alternating
operations mode.
The value of A/D
separations involving a class 4 aircraft as the arrival is
speci:fied
as zero
implies that,
(P,.4 '7 p.
88,KUL 7b
if a departure is
p.
B-22).
ready to take off
Thi
whena
class 4 aircraft is on final, then the departure will not be
held until
means
thne arrival
that ASM
is
runway occupancy
separations
in ASM.
the threshold can
-·II·II-·II---..--.--____II-·----
to A/D
(the
arrival
Similarly
are zero.
may cross
separations,
This
-o the "window"
off.
class 4
of class 4
runway.
seconds
simultaneously with a
Returning
suspect values
30
se for taking
arrival of
an arrival
runway threshold
landing
of a class 4 arrival)
could
with an
implies that
to roll.
adding about
time
that the departure
clears the
D/A
This
the landing
departure beginning
there
are other
An arrival of class 2 or 3 crossing
be followed by a departure of any class
as
I
I
*X·II·IIPL·I-
I.
CI---_
234
O/
!
7n
-Y
age
60
50
40
a)
30
20
10
0
16:00
17:00
19:00
18:00
20:00
Time
FIGURE III-3.
Sensitivity Run
A:
Base Case.
235
70
/
/4
a
Landing
I
/,
!
60-
Dai ly
Average
LAPS -
50
kS IM
40I-
Takeoff
M
1)
:z
30
APS
20ASIPI
10-
a.0.
. .
·,
.
It
.
r~~~~~~~~~~~~r~414
----
TO
16:00
FIGURE III-4.
411111111*'--·a-srr·rra-·--
.
17:00
·
18:00
Senstirvity
----·--I-----·----·--·-rul--rrrrr·----axl---··---
--·
-
19:00
Run 2A:
I
C r olup
---
20:00
2 Separations.
236
-- t
Tal
Daily
40
r,
Average
30 -
- --
M1
,/
rg(
20 r--
10 A·
U
16 :00
7n
18:00
17 : 0 0
20: 00
19 : 0 0
"--'II
I L andi ng
Daily
60
Average
S
50
t
tA
40
3
4j
::I
.
30
/
ad
r-q
©
/
20 -
VI
-1
'
..
AS TM
10
-
/ 9
Ob0
0
16:00
FIGURE 11-5.
17:00
Sensitivity
18:00
19:00
Run 3A: Group
20;00
4 Separations.
237
Daily
Average
60
/
-
I
/'LIanding
FLAPS
/
/
_,~~~~//
/jX I i
'
Landing
/
-
- -
MTAC!IL'A
/
40 .~*.
/
A_If if,
;
/,,
'
/,
30
a,
~/ ,
I
~~~~/
u-4
O
t'
20--
/ ~~~Takeoff
ir,~~~~~
-
· ri
,!/
I~~ ~~~~-
\
FLAPS
----
10-
0,
I
16 :00
.
.
18:00
19:00
,~ .
17:00
20 :00
time
111-6.
FIGURE
-
Sensitivity
I
'-
"
Case 7A:
--
Q = 24
1___11-1
1_1__._
MITASIM
238
r
I
-
7U
-.-. ......----..... ---Daily
--..- X
Average
/
/
60
-
/
FLAPS
/
/
/
50 -
- --- MITASIM
1/
/
40 1
/
0o
,=
30
/
4J
FLAPS
20
/
off
l
-
FLAPS
'\
10
- - - MITASIM
MITASIM
,
o
0 ga*...
0
I
16 :00
17:00
ASM
* * * 0.
o 6· ~e
18:00
19:00
time
FIGURE III-7.
Sensitivity
Case
8A:
Q = 1.
20:00 -
239
Aver.re
Land
Case
Model
1A
Base
2A
2
3A
Group
4
r
FLAPS (2 ) 88.7
88.8
5'7.4
1 4-2 .5
MITAS IM
57.4
ASIM
8*
5-17
-
101 .0
50.
MI TASI
I
84*
FLA PS
108.8
MITASIM
7A
FLAPS
Q = 24
MiTAS
8A
FLAPS
* AM results
1 .3
1
139.8
23.
i0.2
1 5.4
45.8
C
30.5
1 32.0
22.8
1 55.4
141
29.8
1'42.6
105.0
57.
'14
47.7
152.2
88.5
57.3
47.6
1 42.4
1
31 .
i07*
104.9
MITASIM
=-
D e la.v
142.6
1
88.6
IM
cakecffs
126
45.8
10'7 .8
ASM
ASMI
Q
Take off
Dela~
Landin s
FLAPS
Group
iv era.ge
inlg
from KUJL78b
9.6
1 52.4
. C-I for first
i-ours onl T
three
No results have been reported for ASM on cases
7A an
8.
Table III-4: Sensitivity Runs: Summary Statistic
soon as 20 seconds
the arrival will
later,
This s a much smaller ti.r.methan
in fact reauire to cross -the intersectior
or exit the landing runway. The net effect of thesechanges
is to
a
greatly
significant
degree
takeoffs.
This
MITASIM and
until an
I-I--CICII-
C·-IIIQIIII
increase the departure capacity by eliminating
FLAPS
of interaction
problem.was
have
arrival either
-·llCI*l.
.
noted in
internal
logic
clears the
I^-·-t
between arrivals
KUL 78b.
to hold
runway or
__YYL
and
As both
departures
crosses the
240
intersection (whichever comes first), these errors cannot be
to see
duplicated
in
the difference
account for
if they
results.
in the
minor differences
to several
is
probably
due
models treat
way the
analysis to
"worst case"
applies the
FLAPS
separations.
ITASIM
FLAPS and
of
The disagreement
separations (as described in section II.D) more consistently
than
does MITASIM.
The MITASTMrun
separations smaller than the standard
using
once again
the
was also
made with D/D
case.
FLAPSwas run
D/D separationsused by MITASIM and the
result is shown in figure III-3 as FLAPS(2). This is much
closer to the MITASIM
values in the second half of the run.
in level
the disagreement
Despite
agreement between the two in
excellent
there
is
pattern
of
of delay,
the
results.
The set of cases involving
Group
2A:
Base,
3A:
2,
Group
trend toward
delay
as
Differences
in
of the
With all models there is a general
takeoff
increasing
reducing landing delay and
A/A and D/D
considerable
shows
significant fraction
account for a
differences in results.
4)
the models.
in the responseof
differences
separations may
changes in separations (A:
separations are reduced.
For average
landing delay this is 57.4, 50.1,and45.8 minutes for FLAPS
(case 1A,
45.8,
again
and
2A,
22.8
and 3A respectively),
minutes.
The
and for
trend on takeoff
more consistent (12.9, 23.8, 30.5
than for MITASIM (10.3, 10.2,
ITASIM 77.7,
29.8
minutes)
delays is
for FLAPS
minutes).
__·__1·1_11
241
Part
of the
explanation
may
smaller D/D separations used by
instances
of
interarrival
is essentially
case 2A
different,
This allows more
between arrivals
if
The -departure queue length in
unchanged
This is unlike case 3A,
considerably
MITASIM.
2 or more departures
gaps permit.
the
lie in
from case
A
in
ITASIM.
where the departure queue length is
above 12 for almost
the entire
ruri of UITASITM
The gap provided for departures to leave between arrivals
only made long enough for
takeoff must therefore
can takeoff.
later,
for
one departure.
The subsequent
wait for the next landing before it
As this will be on he order
of 1.
minutes
D/D separations will not apply in thi.s cese.
case
delay,
3,
IT7AITMand
despite
difference
FLAPS agree closely
having different
in landing
is
delay
is
D/D
takeof-f
searations.
harder to
MITASIM'sabrupt reduction in landing
on
Thnus,
The
explin
but
delay from case 2A to
3A is harder to explain than FLAPS' more even reduction.
The three
7A:
Q = 24)
The three
delay.
queue
each
trigger
cases
(8A:
Q = 1,
A:
Q = 12,
have the same basic
pattern
of results.
models are in close agreement in regard to landing
Takeoff delay results
vary significantly,
but the
ordering of the models is constant. ASMalways has very low
takeoff delays, while MITASIM
and FLAPSare in reasonable
agreement, with FLAPSshowing the higher values.
Table
III-5 shows the departure queue length results 'oreach half
hour
"IIP·-P··-·nrunP·L*ar-~**pL""
in
FLAPS
and
ITASI. :
s
l.-r·ll·l
inf o rmation
eV
is
not
i·r
· IP-
l-*.t
242
available for
ASM,
but the
very low takeoff
delays imply
that queue lengths were not significant.
The most apparent
point is the small
impact a change
in
Case
Time
16:30
17:00
17:30
18:00
18:30
19:00
19:30
8A(Q = 1 )
FLAPS
MITASIM
10.4
8.0
8.9*
15.7*
13.9*
1A(Q = 12)
7A(Q = 24)
' ITASIM
FLAPS FLAPS(2) MITASII4liFLAPS M
0.4
8.0
7.5
13.4*
11 .4*
7.0 10.10 .
1.3
8.0
2.7
8.7*
11.1*' 14.5*
9.9*1 12.6*
7.2 1 10.5
1.5 ' 7.7
2.7,
8.2*
11.5*' 14.1*
10.2*' 12.3*
11 .5*
6.3
10.4*
8.8*
6.7
0.6
4.3
2.3
3.6
20:00CO
2.0
2.3
17
1.6
C.
1.2
1I.4
1.6
I.
5.5
1.0
7.2
1.5
2.7
1.5*
10.2*
t 10.2*
6.7
4.7
3.6
0.8
1.9
0.8
1.0
1.5
1.2
C.I. - Average half width of 95% confidence interv-alon
half-hour estimate of queue length.
* Maximum observed queue length equaled or exceeded 12 in
one or more replication.
Table
I-5: Average Departure Queue Length Statistics
the value of Q has on the results.
the use of large A/A separations
means that,
most of the time,
already by
the
A/A
departures between
procedure
of
constraint
adding
a,
due to
(4 miles and above)
to
Thus,
MITASIM calculate D/A separations,
any additional
is primarily
which
sufficient space is provided
separation
landings.
This
allow
when both
this
more
FLAPS and
The ASM model
interval
separation, when the departure queue
or
does not result in
on arrivals.
uniform
one
to
each
A/A
is above the critical
243
value,
ordinarily results in more responsiveness to changes
in the trigger value.
However. the suspected mistake in A/D
separations probably
means that the
reach either
12 or 24 to trigger -the changeover
model runs.
This is speculation,
7A and 8A have been repcrted
g
I
1.-----
takeoff queue
I
··I
I
------ ·--
I
since no results
for ASM.
_
._
I
did not
in the ASM
for cases
244
C
TEST CASE: BROMMA AIRPORT
1
Case Description
1.a
Introduction
Bromma
extensive
airport in
analysis of
demands
in 1979
results
in
delays under
(ODOC 79).
ODO 79
was
Stockholm
fcr
the subject
current and
FLAPS.was
3
an
projected
compared
There
cases.
of
was
with
very
the
good
agreement between the two studies.
1.b
Aircraft Separations
Brommae airport
both takeoffs
employ
did
aircraft.
Odoni
operations
used for
Odoni
ODO 79)
did not
separations
use
one
set
(in
between aircraft
which
rules
use the
set of
same
of the two types are
threshold
standards.
VFR separation
separations
set of separations.
intermixed.
all.
and other
All
IFR
and all
VFR
Operations
All separations apply at
and are deterministic,
Table
for
there are instead
use IFR separation standards
use
classes
in this chapter.
o'f operating
Under VFR weather conditione,
operations use a different
the runway
that is
used for various analyses
some aircraft which
aircraft
single runway
and landings.
the standard
which have been
Nor
has a
widths are assumed
zero.
of separations.
which were modeled
i.e., all buffer
III-6 gives the complete
in FLAPS
set
by treating
245
each type of operation
as a
class.
Class I represents
Leading a/c
'
Trailing a/c
Arriving
r Departing
Arriving J Departing
!FR
I
I
I
I
I
I
I
IFR
I
I
I
VFR
I
I
I
I
I
I
I
I
IFR
I
I
I
I
IFFR
I
I
I
I
VFR
I
I
I
I
I
I
I
I
II
i
II
!
VFR
I
I
I
I
I
I
I
I
,
I
IFR
VFR
!
I
!
I
I
120
;
I
I
I
I
i
105
IFR
I
II
II
I
II
,
I
IPR
(sec)
I
i
I
I
I
i
I
I
I
I
VFR
VFR
From ODO 79 p
TFR
VFR
VFR
IFR
Average
separation
I
I
IFR
VFR
45
45
60
60
120
55
45
45
45
45
4.5
i
II
IFR
VFR
6C
I
45
I
I
60
45
Incorporates changes described
C-2.
in text of ODO 79.
Table II1-6: Practical
Separation
Minima
at
Bromma Airport
movements;
class V represents
VFR movements.
were derived from those listed in
table
Separations
III-6 and are given
in table III-7.
To
both classes were given
approach speeds of 120 kts.*
Then the A/A
model A/A
deterministic
separations,
separations, specified as times,
1_111_____
1_·
_ _·
_
can be taken directly from
_ ^____
_1_1_
246
table III-6.
They were
imposed at the approach gaze but,
Arrival/Arriv2l Separations (seconds):
Trailing Class -
-1.
V
Leading Class - I
120
45
V
45
45
Departure/Deoarture Separations (seconds):
Trailing Class -
V
Leading Class - I
V
120
60
55
45
Arrival/Departure Separations (seconds):
Effective Lead Aircraft
Class Arriv.al Runway
Trailing Class -
Occupancy
I
Leading Class -
V
45
60
52.5
45
45
45
im,'
Departure/Arrival Separations (seconds):
Traiing
Class -
V
I
Leading Class - I
V
105
60
OU
45
Converted Derparture/Arrival Separation
I
V
Trailing Arrival(j) Lead Takeoff(k) - I
V
3.5
2
mies):
2
1.75
Table I11-7: FLAPS Equivalent Separations
because approach
same
speeds are the
separation
also
same for each
hold
Departure/Departure separations
at
class,
threshold.
the
can be taken
thle
directly
from
taken from
the
table III-6
Time values for
A/D separations
are
Brommavalues and presented in matrix form in table III-7.
Since the only A/D separation logic in FLAPS is to hold
* However,
used.
any other approacr speed could also
have been
247
departures
until
separations
the
were
arrival clears
simulated
(a.r.o.t.).
runway
deterministic
performance
a
parameters
was
runway,
these
adjusting
arrival
runway
One exit
was defined
on the
set
landing
by
occupancy times
and
the
chosen
a.r.o.t. for class V aircraft.
a 52.5 second
values.*
a.r.o.t.,
is
is
This
of
to result in
a 45 second
Class I aircraft were given
midway between the
he only
aircraft
two separation
approximation to
the published
separations needed to prepare inputs for FLAPS.
Departure/Arrival separations are given
in table
Given the 12Okt.
1I-7.
be converted
directly
into
in matrix form
approach speed, these can
iles and used as
the values
of
Rm(k,j), pre:ersed at the bottom of the table.
1. c
Demand
A number
reported
for
of daily demand
Bromma
in ODO
function was chosen for the
profile is given
profiles were
79.
The
comparison.
tabulated and
"weekday"
demand
A separate demand
for landings and for takeoffs
for each of
the following: 1) Linjeflyg (LIN) Airline IFR operations; 2)
general aviation flights under IFR operations;and 3) general
aviation flights under VFR rules.
These were converted to
meet FLAPS' requirements by the following procedure.
III-8 gives a schematic of the
IFR flights
The cases
*
were LIN
process.
flights,
as
Fifty per cent of
used in
ODO 79.
I
CIll---
-
I
_
The
we examine have a 50;' VFR, 50% IFR mix, see
below.
-
Figure
I-U
-·.
-···
-_
___.l-·--LIIIIIIII____
248
LIN IFR Profile
GA
averagi
r)uP-rAI1
IFR profile
J
/1
T.TP-n--r f i1 -
aver
r
V
nrnf
.L-
-
i- I-
io
I
i
ratefuncion
I
I
rate function
FIGURE III-8.
Bromma Demand Profile.
mix percentage
as
function of period
249
average
of (1 )
IFR profile
nd (2)
above was taken to obtain
for bcth landings
delays
for a
example
used 50 ^ IFH flights.
(3)
number of
different
HI.C)
with
(i.e.,
These rate
aircraft).
IT1 profile
and
rate
'
function
were
functions
or departures
Interaircraft times
For
were
both arrivals and
percentage was created as
a mix
This
rocedure (see secton
either arrivals
distributed negative exponentially.
departures,
arriv
schedule
all aircraft as
no through
splits.
The overall
rate function.
used to control a generated
ODO 79 reports
IR/VFR
obtain ai
above were averaged to
and a departure
and takeoffs.
an overall
a function
of
the period of time involved.
The mix percentage for class V
was taken
o ' VFR operations
froi
the
ratio
to
total
operations for each period.
The resulting demand ro.files
are given in figure
The rates
II-9.
given as !'fraction of landings (takeoffs)
i- the
figure
per hour".
fraction is multiplied by total landings (takeoffs)
over the entire run to obtain arrival
hour.
Three cases were run,
landings,
landings,
200
300
at
and
landings, 400 takeoffs).
iiiCI'-l------·--·-------·----·-mu^··· I
_...,
___
This
desired
rates per
at 400 operations/day (200
takeoffs),
takeoffs),
(departure)
re
___
600
at
00
operations/day
operations/day
(500
(400
250
i
t t
I~Lr'
0
I
i;)
X
i
\\
N
'
,,')
H
i
'
;r0
-
"
,
"I-
q
I.H
rrl
0
IjI ao
I
Zs
I
c
lct
ilD
I
..
I. i
t
o m i~~~~~~~~~~
iiio
I
W7sr-T ,T
Lf
+j
u0
0
l
·1
C
i
r-4
mC1
0
+j
c(
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IT
C-
Lfl Z
h:1~
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i
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F
1 0
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ed
S-4
Cd
0
4-)
*,
25
2
Discussion
f results
The delay estimates
a simulation.
that
the runway as
equations for this
demand rate.
(delay),
each time interval
an M/G/1 queue.
an estimate
day.
The
statistics,
for
Exrlanation of
the
DO 79
Fraction of aircraft
Delay
(minutes)
95
on Ercmmaare given in
C.
I.
Delayed
> 20 nminutes
400 Operations/day:
0.1
0.0 0
600 Operations/day:
FLAPS
2.6
DELAYS 2.3
0.6
0.01
800 Operations/day:
FLAPS
15.0
O
DELAYS 14.7
2.8
0.27
DELAYS
time
HEEN 75.
mean
FLAPS
state
of the waiting
for this model can be found in
Results for the three cases run
Model
DELAYS,
a time-dependent
and other queueing
during the
background
C ad
model,
queue are solved using
This produces
in the queue
Appendix
79 are not produced through
They come from an analytical
treats
theoretical
in ODO
r7
O.6
O.
DELAY results from
ODO 79, Appendix
0. 000
0.012
0.315
E
Table IIT-8: Bromma: Summary Comparison of Results
252
table III-8.
Comparisons of the
during the day are given in
models seem to be in
pattern of delay produced
figures III-10 to III-12.
good agreement.
The
This is particularly
significant in-view of the fundamentally different nature of
One difference is the timing
the two models.
The FLAPS
delay.
particularly
probably
due
on
to
aircraft complete
peak delay
the
occurs
later than
800 operations/day
FLAPS collecting
delay
landings or takeoffs..
of the peak
case.
DELAYS,
This
statistics
is
when
DELAYS estimates
are for delay expected as of the moment an aircraft arrives.
Thus,
delays.
the difference is more
significant at higher average
253
r.
ct
C)
r
I rv
>1 t
--IH
.0
j
cc
r4-
Lr
,
od
II=
A
r"
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(s ;J00o',Iv
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254
1
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255
,~~~~~-<I
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256
D
CONCLUSIONS
Several
general points
can be made abo-ut the
presented in this chapter.
both
capacities
estimates in
to
FLAPS?
has been used to estimate
delays and
all situations.
using data from
models.
and
has
produced
two airports and against
questions
of
FLAPS can
interest
to
with the
presented
here establish considerable
of FLAPS, although further
material
in
several different
e used successfully
airport
chapter II,
Together
validity
reasonable
Comparisons have been made
We have shown that
analyze
tests
definitely
be conducted in the future.
the
confidence
tests
analysts.
esults
in the
shol d mcst
257
IV
A
EXAMPLE OF MODEL APPLICATION
INTRODUCTION
This chapter* will demonstrate the capability of FLAPS
to
analyze
operations.
significant
questions
This will be done
capacity and delay analyses
Massachusetts.
by performing a
for Logan Airport
The process
FLAPSwill be described.
concerning
airport
number of
in
Boston,
of assembling input data for
Capacity estimates
for two runway
configurations under several weather conditions will
presented.
a
third
A demand rate function will by hypothesized for
configuration.
Delay es timates
for this
configuration
demonstrate
be
will
the
be obtained for several runs that
dynamic
capabilities
demonstrating that FLAPScan analyze
of
FLAPS.
the questions
By
that
arise in performing a comprehensive analysis,
this chapter
contributes to the certification of the model.
A second objective of this
number
of
issues connected
Several definitions
analysis.
We
of
with
capacity
the
are
is to discuss
of the model
to
a
use of the model.
used
will discuss the appropriate
obtaining these estimates with
sensitivity
chapter
in
airport
techniques for
a simulation.
The relative
certain parameters,
its
input
The author wishes to thank William Hoffman and Steven
Aschkenase of Flight Transporation Associates,
Canbridge, Massachusetts, for assistance
this particular case study,
in preparing
258
requirements and
its computational efficiency will
also be
discussed briefly,
It should
also
be emphasized
that this
chapter
is not
intended as a comprehensive analysis of operations at Logan.
Performing a full analysis would be a major undertaking.
It
would
of
involve
identification
configurations as
runs
of the
Rather,
of
a
well as collection
model,
all
beyond
complete
of data
the scope
set
and numerous
of this
the intent here is to establish that FLAPS could be
used for such a comprehensive analysis.
This chapter is not
offered as further evidence of the model's validity,
comparisons
capacity
work.
to
existing
and delay
models
data were
are
made.
not available
and no
Sufficient
for Logan
to
perform a meaningful validation.
B
THE AIRPORT
Boston's Logan
United States.
Airport is
one of
the busiest
in the
In 1979 more than 15 million passengers and
226,000 metric tons of cargo were served by 319,000 aircraft
movements (landings and takeoffs) (ATA 80 p.5).
The airport
has been the
subject of
several capacity
and delay studies.
Many of the specific assumptions used in
this analysis come
from OSE 78,
a report by
Systems Engineering Management of the FAA.
be referred
to as the OSEM study.
the Office of
The report will
259
II
t
A.
FIGURE IV-1.
i----
-----s_-__._r__.^..__
*------
-·-
Boston
-------------
Logan Airport.
L
r----------_x_·_---·---·--------_
_.
260
Figure IV-1
airport
is a
map of
is surrounded
on
Boston Logan
three
sides by
making physical expansion difficult.
under the flight
33L,
making
Runways
4R,
reduction a
15L,
22L,
27
Residential areas are
major
and
The
Bostcrn Harbor,
paths of all runways save
noise
Airport.
the approach to
area
33L
of
concern.
are equipped
with
instrument landing systems.
The geometry information was
collected as described in
section
II.B.
An arbitrary origin due south of the southern
end
runway
4L was
of
chosen
positive coordinatevalues.
the scale of the grid used to
so that all
The scale
use,
sufficient to
feet
a map
unit.
of the
values.
scale of figure
Modules
for runways
in this case study and
The keypoints
and
IV-I was
to within 50
Runways 13R/33L
4R/22L and 9/27 were defined.
were not analyzed
map used
It was found that,
define geometry features
of published
in the model.
of the
overlay the map resulted in a
scale of 42.5 feet per coordinate
with careful
keypoints assumed
to 75
4L/22R,
and 1 3L/33R
were not included
and coordinates
are listed
in
table IV-1.
A number
of Logan
runways have
displaced thresholds.
The split runway technique (see part E.6 of chapter II)
used to
model this
feature for
runway 4R/22L.
was
When the
runway is used in the 4R direction, the landing threshold is
at
the
however,
point
may
marked "L4R"
in
begin farther back
figure
IV-1.
at point "T4R".
Takeoffs,
In the
261
Key o i nt
V
coordi nate
0
99
21 6
110
0
80
30
42
58
113
114
100
18
217
822
124
189
121
12
38
38
122
123
124
125
126
127
128
48
58
81
64
76
1 23
98
1 54
200
75
54
1 71
131
65
132
133
65
61
97
59
134
56
135
150
171
223
31
54
63
Table IV-1: Logan Airport:
threshold.
point
point
exit
exit
exit
exit
exit
exit
exit
exit
runway end point
exit
exit
exit
exit
exit
exit
intersection
'74
87
98
108
opposite direction,
runway end
runway end
exit
exit
exit
exit
exit
exit
exit
47
134
7
832
point
point
1 59
1 9go
115
116
821
831
runway end
runway end
88
120
138
6
12
keypoin
80
81 2
81 1
Purpose of
Y
ccordinate
number
Geometry Elements
this runway, 22L, also has a displaced
The landing threshold for 22L is designated
1
"L22L" and the takeoff threshold "T22L'!.
Two rinway modules
were defined for the physical
the two
is used for
L22L.
The second
runway 4R/22L.
landing only
module is
The first
and extends from
used for
of
L4R to
takeoffs only
and
extends fom T4R
~ tc1iT22Lt. The runway modules have the same
*----^--.Llllr.
_1
_·L-----_-_.
262
centerline,
with the takeoff
runway module overlapping the
ends of the landing runway module.
All actual runway exits
on
on the
4R/22L
module;
these
were defined
as
being
the takeoff runway module needs no exits.
modules
operation of
they are
intersect
with
the split runway
9/27.
To
modules as a
landing runway (L4R/L22L)
must
for this
runway
Both of
insure
proper
single runway,
specified as dependent parallels.
the takeoff "runway" (T4R/T22L)
course,
landing
Departures on
clear
arrivals on the
split runway case.
Of
the two modules must always be operated in the same
direction.
Table
keypoint
IV-2 lists
nmbers
intersection
the keypoint
the
and
three run-ways in
distances
fTr
use and the
each
exit
and
These distances are derived by the .cdel front
coordinates
giveli in
Table IV-I
Values in
parentheses are the corresponding publiched values of these
runway features
when available.
A final approach path of 6 nautical miles (6.9 statu'e
miles) was used (OSE 78 p. 11).
from visual examination of the
map of keypoints
C
Exit speeds were estimated
airportmap.
and modules is shown in figure
The resulting
IV-2.
DESCRIPTION OF OPERATING POLICIES
We will
describe the analysis
runway configuration
of the capacity
under a variety of
of one
weather conditions
263
4L/22R
Runway:
Runway Module Numbers:1
Length:
7149 (7032)
Length of common
6
approach path:
Direction
is
4L
Direction
2
22R
is
Runway
4R/22L
9/27
2 and 4
3
7531 (7494)
6986 (7000)
6
6
4R
22L
27
9
Exit paramete
Keypo int
Direction
Length
4L/22R
110
111
112
113
114
115
0
(
)) N. U.
N. U.
425
2125
3043
4165
5806
0
0
7209
4R/22L
9/27
Direction
1
Velocity
Length
7149 (7032)
6724
0
0
5025
4106
0
0
0 +2
2984
15
15
0
1344
60
O+2
N. U.
0+2
121
-460
N. U.
7990
122
123
124
125
126
127
128
223
1428
2125
2755
0 + 2
0 + 2
6103
5406
0
4778
15
4284
131
0
2471
132
133
134
135
223
3247
4063
N. U.
3468
5678
15
1853
8160
15
876
( o)
(2500)
3833
6090
6986
1024
2
Velccity
30
0
N. TJ.
15
-632
N. U.
N.,
A.
6656
N. A.
N.
U.
6986 (700Qo)
451 5 (450)()
30
,152
10
0+2
0+2
0+2
(7000)
897
0
N.
0
A.
(
0)
5962
5
10
.
N.
U.
A.
Numbers in parentheses are published distances.
N. U. -
Exit not used for traffic in that direction.
Exit velocity in knots.
Number after plus sign is number of seconds aircraft
needs to clear runway after coming to complete stop.
N. A. - Not applicable.
Table IV-2: Logan Airport: unway Modules
---
_I
__·__l__l_·I_·
14111111111111.111
264
Runway module 1
116
x
O
115
812
//
128
822
y = 200
114
Runway modul es 2
/
127
/1
/
/12125
I/
124
111/
123/
110,811
122/
831 -
132
133
135
131
/821
/121
832
kRunway module 3
x=0
y = 0
See Table IV-1 for cordinates of keypoints.
See Table IV-2 for exit distances and velocities.
FIGURE IV-2.
Logan Airport:
FLAPS Geomretry Representation.
4
265
and of a second runway
condition.
The two configurations chosen are among the most
complicated
describe
configuration under a single weather
in use
them
at
Logan
here.
In
Airport.
following
We
will
sections
briefly
additional
details for each configuration will be presented.
The
first
configuration is
shown
schematically
in
figure IV-3, parts a, b, and c.
Case a
This
is used
ceiling 2500 feet
under
conditions
or higher,
labeled VFR-1
visibility 5
(cloud
miles or more).
Aircraft land on 4R and 4L, takeoff on 4R, 4L and 9.
Case b
This
(ceiling
is
800
used
under
to 2500
Landings approach
conditions
feet,
in a single
labeled
visibility
in
aircraft
to land on
for
modeling
this
"sidestep"
procedure
2 to
queue headed for
below the cloud ceiling (i.e.
execute a
VFR-2/IFR-1
5
miles).
4R.
Once
view of the runway)
will
be
4L.
some
The process
discussed
below.
Takeoffs use 4R, 4L and 9.
Case
c
This
is
visibility
1/2
used
in
IFR-2 (ceiling
to 2 miles).
Landings
200
to
800
are limited
feet,
to 4R.
Takeoffs can use 4R, 4L and 9.
Case d
Case
d uses
the
same runways
different aircraft mix.
1
I
I_____I
I·___I
__
as case
c
but has
a
Case d is used in IFR-3 conditions
_
__
I
_·_
_
_
266
D
D
4
D
!
,
D
i
/
/
I
/
/ ~
D
D
/1
/
A
sidestep
At
A
a) Case a
b)
b
Case
i
Dy
Dt
/
/
/
/
I
hold
/
/
/
/
4
D
A
c) Case
c
FIGURE IV-3.
D
d
d) Case e
Logan Configurations.
A
~/ short
/
f
1/
A
"Ai
267
when the
ceiling is
less then
200 feet
or visibility
is
below 1/2 mile.
The
second
configuration,
case
e,
is
shown
schematically in part d of the figure.
Here the runways are
operated in
the opposite direction.
Case e is
under VFR-1
conditions.
Landings on
22R must be
Landings
able to
process will be discussed below.
Each of the five cases
separation rules.
use 22L,
used only
22R and
27.
27.
This
hold short of
Takeoffs use 22R and 22L.
has different aircraft mixes and
These are discussed under the appropriate
section below.
D
CHARACTERISTICS
OF DEMAND
1 Aircraft classes
Four
report.
aircraft
classes
This
diversity in
Class A
was
propeller
done
aircraft
because
of
into three sub-
the
considerable
the performance characteristics of
of airplanes.
Class
identified in the OSEM
For this analysis this mix was altered by breaking
the class for twin-engine
classes.
are
this class
The resulting 6 classes are:
-
B1 -
Single-engine piston, Gross Takeoff
Weight (GTW) less than 12,500 lb.
Twin-engine piston, GTW less than
12,500 lb.
Class
B2 -
Twin-engine turbo prop,
GTWless
Class
·I
I__
B3 -
han 12,500 lb.
Twin-engine turbo jets,
_
_
I
__
II____
_
268
GTW less than 20,000 3.b.
2
Class C
-
Four-engine propeller and non-heavy jet
between 12,500 lbs. and 300,000 lbs.
Class D
-
Heavy jet capable of 300,000 lbs. or
greater takeoff weight.
Aircraft Performance
IV-3
Table
the
lists
characteristics for Logan.
come directly from the OSEM
assumed
performance
aircraft
The starred entries in the table
The remaining entries
report.
have the same values as discussed in the landing performance
were
Approach speeds
chapter.
by
supplied
78 provides data
Transportation Associates (PTA).
OSE
arrival runway occupancy
After the outputs
times.
model were examined with an
deceleration rate
values shown
the
OSEM
and coasting speed
on arrival
runway
This process
match with
The
time.
still within the reasonable
resulting parameters values are
range.
occupancy
the
to the
were adjusted
produce a closer
for
of the
initial set of parameters,
in table IV-3 to
data
Plight
is discussed
further
in section
F
below.
3
Aircraft
M.ix
The five cases use four different aircraft mixes.
overall percentage of each class
aircraft
cannot
fly
during
The
changes because most small
bad
weather,
··
due
to
_L__·
the
269
Attribute
Aircraft Class
Approach speed (knots):
mean, Va
st. dev.,
p. d. f.
Vas
B1
B2
B3
80
100
1 5
130
6
4
4
4
D
C
140
4
4
8
8
Triangle
In-air
14
12
700
250
1000
300
1200 1400
1500
400
450
450
Uniform
1500
Deceleration rate (f/s/s):
mean
5.75
st. dev.
.75
5.75
5.75
5.75
5.75
5.75
.75
.75
.75
.75
.75
39.
79.
deceleration
(knots):
Float distance (feet):
mean
st. dev.
p. d. f.
10
8
450
Normal
p. d. f.
25
Runway coasting speed (knots):
Departure runway
occupancy time (seconds):
mean*
29.
st. dev.
5.
p.
32.
34.
5.
d. f.
39.
,
Nor m al
Starred attributes
st. dev.
p. d. f.
36.
No. r.
are from OSE 78.
- standard deviation
- probability density function
Table IV-3: Assumed Aircraft Performance Parameters
requirement
of instrument
ratings
for
the pilot
and
sophisticated navigational equipment for the aircraft.
of
The
OSEM study assigns aircraft to runways on basis of the class
of
aircraft
assignment
by class
capacity runs.
C-·l
-q·rrllll-
-·llrrrrl--ul·r-·r·s·r----·llll··
(OSE 78
pp. 14-17).
The
procedure in- FLAPS was
corresponding
used for
the
As the set of active runways varies over the
·- r--rrrr-^-·---
^--·------
^·I_PPe*BIIIIIIIgYIIIPI-IX
IL·-----a
*r
-__._- .-r;--·-EDI-mu.r·mq·*IL-·-11
270
five cases, we need aircraft
case.
assignments
These are also available
Since
1978,
conditions
at
when
Logan
Transportation
in the OSEM report.
the
OSEM
have
Associates
was
prepared,
somewhat.
made
Flight
available
revised
the 6 classes used here.
IV-4 presents these percentages.
provided by FTA.
report
changed
has
aircraft mix percentages fr
to runways for each
The
Table
overall mix was also
The runway assignment percentages -(tothe
left of the vertical lines)
come
from OSE 78.
As will be
seen in the section on "discussion of results", these runway
assignments create
analysis.
traffic
This
problems
is because
assignment
capacity.
that
they
performing
a
capacity
do not correspond
results in
the
highest
to the
airport
We will also run the "shortest queue" assignment
procedure for
these cases
shortest queue assignment
any runway where the
zero.
in
and compare
was used
the results.
The
to allow aircraft to use
OSEM assignment
percentage was
non-
The assignment for any particular aircraft is made to
the shortest queue at the time
the aircraft
is ready to use
the runway.
E
AIR TRAFFIC CONTROL RULES
A
number of
specified.
are used
air traffic
control
parameters must
IFR rules are used for cases c and d.
for cases
a and
e.
An intermediate
be
VFR rules
type
of A/A
271
Departures
Arrivals
Class
4R
Case a:
A
BI
D
1.00
.17
.83
.83
B2
B3
C
4L
.17
.83
1.00
.00
1.00
.00
I Mix
.00
1
.06
.22
.00
4R
. OO
00
9 : Mix
4L
1.00
1.00
.00
.06
.00 " .22
1.00
.O0
1 15
1.,00
.00
.03
.00
.34
1 .10
.00 ! .15
.00
.03
00
.44
.00 I .10
.00
.00
.00
1.00
.00
O00
1 .00
.00
.59 · .44
.00
.41
.66
Cas e
A
.00
1 . 00
B1
.17
B2
.83
.17
.83
B3
.17
.83
C
D
Case
·CO
.21
.00
.00
.16
.03
.46
.00
.00
i .11
C:
.00
none
A
31
.00
1. 00
1 .00
07
.00
.00
I .00
.00
.15
B2
1.00
B3
1 CO0
.00
.00
.17
.00 I .04
C
1. 00
·.00
. 00
.00
.00
D
A
31
B2
B,
D
i.00
.00
none
. C
1.00
1.00
.00
1.00
.00
.00
.00
.00
22L
22R
Case
.O
.00
. 00
.00
.00
. 12
.02
.t04
.04
)70
.20
27
. 00
.00
.06
.00
31
B2
B3
.10
.78
.12 '
.10
.10
.78
.78
.12
.12
. 15
.03
.60
.00
.40
.44
.75
.00
. 25
.10
44
1.00
, 00
.00
· 41
.00
.16
.00
.03
.34
none
80
.00
.00
.59
.00
.66
.20
.*46
:
1t
I
..oo00
.15
.80
.00
.20
47
.80
. 00
53
.85
.00
A
C
D
1.00
.00
I .52
.00
.03
1 .21
.· 5
00U
.04
52
.12
.CO
r.c.ce
.47
.47
.02
.04
.47
.04
.58
.70
.00
. 8
.20
22L
22R
27
.00
1.00
.00
.06
.CO
.15
C03
1 .44
.00
.00
.42
.53
. 53
.00
.82
.00
.00
.OQ
.17
.83
1.
.00I .22
00
1.00
1.00
.O0
.83
.00
.00
.1
.10
Runway assignment percentages (to left of vertical
lines, from 0SE 78 p. 14-17.
Aircraft mix percentages (to right of vertical
lines)
provided by FTA.
Mix
Aircralt
Table IV-4: Logan Air port:
and Runway Assignment
ri·--·-------^-·---"···------·---I--
-----·-----"---·----I"UY··P"--l"·
I^·IYI·L_
272
separation
all cases
is used in case.
are from OSE 78 and are shown in table IV-5.
values used
are very
II-8 and II-9
are
given
A/A and D/D separations for
b.
earlier.
in
similar
to the
study,
so
2 miles
Departure/De
for
arture
(miles
(cases c and d):
Trailing class - - D
Leading
no separations
we assume
Arrival/Arrival
(miles)
IFR rules
onesgiven in tables
For mixed operations,
the OSEM
, The
class:
D
4
C
3
B
A
3
3
C
5
3
3
B
A
D
C
B
A
6
4
3
6
4
90
CO
120
6C
120
120
60
3
60
60
3
60
60
60
60
A
D
,
60
60
60
Intermediate rules (case b):
Trailing class - - D
Leading class:
VFR rules
T
3.2
C
2.5
B
A
2.5
2.5
(cases
class:
2.5
B
5.2
3.2
2.5
C
B
A
90
1 20
60
60
120
2.5
60
60
120
60
2.
60
60
5.2
-. 2
D
C
C
1.9
3.6
1.9
B
A
1.9
1.9
1.9
1.9
D
2.7
B
4.5
A
4.5
represents
60
60
60
2.7 2.7
1.9 1.9
1.9
1.9
C
B
A
90
60
120
60
120
120
45
50
45
40
45
35
50
40
30
D
Data from OSE 78 p. 12.
B -
60
60
a and e):
Trailing class - Leading
C
4.3
2.5
2.5
classes B1, B2 and B3
Table IV-5: Logan Airport: Separation Parameters
Rm(k,j) and Rmt(k,j).
30
273
For
interdependent varies over the 5 cases.
runway,
runways are
which operations on various
The extent to
in the example runs
the separation procedures used
application
are a straightforward
each individual
of the procedures
given in
section D of chapter II and will not be described here.
The
following discussion concerns only separation procedures for
Table IV-6
dependent runways.
summarizes these procedures
applied for the-various
and indicates which separations are
cases.
1)
Arrival/Arrival separations are applied
and 4R
only
conditional
in
the
VFR-2/IFR-i
case
b,
hold short case e, between 2
in case b use a "side-step"
one line to 4R.
Near the runway certain
landings execute
a side-step
Class D aircraft
and 2)
and 22L.
Aircraft
procedure.
approach in
use runway 4L
This procedure
noise considerations.)
to both 4L and 4R,
is modeled by assigning landing aircraft
in accordance with the mix percentages indicated
IV-4.
The values
A/A separations
of
Arrials
(Class C and
to
at Logan are not allowed
for landings due to
in the
class A and class B
on 4.
and land
between 4L
imposed
in Table
between
landings on the two different runways are the same as those
used
on
between landings
runways 27 and 22L operate
(The example of
the same
runway.
in a conditional
In case
hold short mode.
this "hold short" procedure,
discussed
part 6 of section
II.E, was, in fact, the situation
in case e.)
situation
This
_
I
is modeled,
I
__·_
e,
in
at Logan
as was suggested, by
_·_·_I ___·_
_1___1_
LI·
274
Case
Separation
a
A/A
2/1
1 /2
3/2
2/3
d
b
e
No
No
N.A.
N.A.
Yes
Yes
N.A.
N.A.
N.A.
N.A.
No
N.A.
N.A.
N.A.
N.A.
No
Yes(a)
Yes(a)
No
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
N.A.
N.A.
D/D
1/4
2/1
3/4
4/3
No
N. A.
Yes
Yes
Yes
A/D
1/4
No
No
Yes
N.A.
Yes
2/1
2/3
3/4
2/4
Yes
Yes
"
Yes
Yes
Yes
Yes
N.A.
Yes
N.A.
Yes
"
Yes
Yes
''
- Movements on the indicated
Yes
Yes
Yes
No
No
N. A.
Yes
Yes
Yes
N.A.
I
.
4
runways are ceced Tor
.
nonviolation of the given separation requirements.
Yes(a) - Conditional hold short separation, see text.
No
- The movements are independent.
N.A.
x/y
- Not Applicable.
- Runway modules of leading, x, and following, y,
operation. Note that modules 2 and 4 both
refer to runway 4R/22L.
Table IV-6: Air Traffic Control Dependencies
holding
all
landings
on
heavy aircraft (class
runway 27 for
D)
90 seconds
has begun landing
after a
on runway 22L,
and by preventing a heavy from landing on runway 22L for the
first 90
seconds after
a landing has
Other separation values, i.e.,
for:
following
and
all
landings
on 27,
begun on
1)
2)
runway 27.
a non-heavy on 22L
all landings
following a non-heavy on 22L, are set to zero.
on 27
Note that
275
these separations
apply to the module.used for
22L, not the runway module used for takeoffs
landing on
on 22L.
Departure/Departure separations are applied between the
parallel
runways in the two VFR cases
VFR-2/IFR-1 case b.
D/D separations
As runways
(a and e)
and in the
9/27 and 4R/22L intersect,
between these
intersecting
runways are
always applied.
Departures
for arrivals
only.
on one of the
to
parallel
runways must be held
clear on the other runway in
Departures
on either
9/27 or
the IFR cases
4R/22L must be held
until arrivals on the other runwayclear the intersection.
The line
of A/D separations in
table IV-6 marked "2,/4" is
included to make the two runway modules
as a single
F
for
R/2,2L operate
runway.
INPUT REQUIREMENTS
1 Summary of Input Requirements
This
necessary
copy of
section summarizes
for
preparing
the various
a case for FLAPS.
the entire input file
For each item below we refer,
inut
?1_
___11__1__·__1____1_PIII^L·^II_IIIII
an item
of the input.
below refer to
·--.^11I_-_I__I
inputs
IV-4 is a
capacity cases.
where appropriate,
file in Figure IV-4 where te
-·--1_-
Figure
for the VFR
that present the specific values
brackets after
kinds of
to tables
Letters in
the portion
of the
same item is defined
--Llii_..-
·I
----·IIIIIPI)IY·L.IUII^-I-·.
--
A
1111
111--·
.
276
number
of
parameters
with
internal
defaults
were
not
respecified in the input file.
A complete input file for
FLAPS contains the following
categories of data:
1) Simulation control parameters
number of
length of run, length of periods,
replications,
starting
2)
Output control
3)
Geometry parameters
time, etc.
parameters
{AI
iBI
Figure IV-2,Table IV-2, C}
a. Module definitions
Table IV-1, D}
b. Keypoint definitions
Table IV-4, El
4)
Aircraft attributes
5)
Demand generation parameters
6)
Aircraft separations
{Table IV-4, Fl
-
a. Types of dependencies
ITable IV-6,
b. Values of separations
{Table IV-5, HI
7)
Randomnumber seeds
{default values used!
8)
Runway assignment parameters
9)
Dynamic operating rule parameters
I
IJI
Controls changes in operating rules
during a run.
2
Comparison of Input Requirements
Some indication of the performance of FLAPS with regard
277
PARM: IMPER- i,XEP=I 3, P.RLN=60.
{A}
{B}
STTI'4=.O,
Ia,3R !t ( )-1, IR3?:oa?
(2=
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3
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(
ATC. IA2A1 (232,)=,
ATC.IA2A1 (3,2)=3,
A2C. A2D! (3,2)=1,
IDCNTR1 )=2, ID` r2R( )
(,
ATC. I2D
AIf: TnA
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LC
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ATC. ID2D1 (4, 3 )=1 TAC.ID2D ( 3,4)=1 ,
A ' I M1(2,4)=2,
ATC IA2D1 (,29)=1
ATC.IDIROP(3)=1
. IDIROP(1 )=1 , AT ,,.IDLRDOP(2 )=I
,AT. DIR3OP(4 -l=
AT C . XDLV(
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CAPAC'ITY
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r ( 1 )=
;
ORDER: 1:50 ID!,N,
Gln
1 ( )=$ ,ATC. MDA3' ( 2)=1;
ORDER: 3:00 ATC.
E ID
Logan VFR Capacity Input File.
(continued.on next page)
__
*
0 3 )
IDCNR(1 )=9;
( 1 )=2 ,AC. DA.3 (2 )= ;
>..
ORDER: O:00 AC.DA
FIGURE IV-4.
1)
*
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1
0
0)
.
{J}
278
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PT:
AIRIR
4
50334
150
100
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13.
13.
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FIGURE IV-4, continued.
6(1 5
'50*3
6*1 .
0 0)
*
Logan VFR Capacity input File.
(continued
nr!
next page)
279
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9)
I'%1TD
FIGUE IV-4 1 continued.
Logan VFRCapacity Input File.
280
to the workload that it imposes on its users can be obtained
by comparing the
ASM.
at
input requirements of FLAPS
with those of
Unfortunately, such a comparison is made difficult by
least
two
factors.
First,
equivalent
capabilities.
movements,
and
this is
the
FLAPS
a major
capabilities in
specification
specification
of
does
do not
model
of the
the area
of demand
have
ground
ASM input
On the other hand,
dependent runway
of changes
not
portion
requirements (see section II.B).
has added
models
FLAPS
generation,
separations,
and
in operating
rules, all of which
require additional inputs.
Second,
we do not
have input
files for the two models for identical cases.
Despite these cautionary points,
that setting
up a case for
analysis
it is rather obvious
using FLAPS is
simpler task than setting up a case for ASM.
a muich
We saw earlier
(section II.C) that several hundred or even several thousand
lines
could
be required
to prepare
a case for ASM.
The 100
line file of FLAPS for a moderately complex airport compares
very favorable with that.
G
CAPACITY ANALYSIS
1
VFR Results
Table
the
V-7
VFR cases.
presents the capacity analysis
Results
are
reported for
results for
arrivals
and
281
departures
seperately.
listedfor
each active
results are
two cases,
The values reported
rurnway.
rates produced
from averaging flow
obtained
estimates
In
FLAPSwith the various streams of aircraft
per hour.
The size of
is the reason r.esults
are reported
rate was plus or minus one altrcraft
the confidence interval
IV-7 using
Table
at
figures.
most two significant
are
Arrivals"
"Percent
heading
Results under the
Ten
on a flow
interval
95% confidence
A typical
last two hours.
by
are averaged over the
and results
used as a warmur period,
are
hour is
The first
of 3 hours each were used.
replications
in
saturated.
also
the
capacity estimate for case a for the entire onfiguration
under sustained operation at the given arrival-departure
ratio.
The method used to
The results
described below.
obtain
some
of
in
the difficulties
analysis
capacity
performing
estimates
the
next
that
can
with
is
(and to a
for the VPR cases
lesser extent t'ne IFR results
illustrate
these
section)
aT ise
in
complicated
configurations.
in fact,
There are,
on how
depending
discusses
the
capacity in the
at least three different "capacities",
the problem
proper modeling
is
This
defined.
technique
context of discussing the
for
section
each type
of
reported results
for case a.
Capacity estimates using FLAPS were reported in chapter
III.
ilPIII·-·IIIIPr^X-·I
X
In those cases,
·- *LgUII···I·IP1*PIIllsllllllDsliT-^l-X
only one
1III---_----_II·II__--LIL_-I_--
-
runway was in use for each
282
Ass ignment
Method
Runway
Arrivals
Departures
To
Percent
Arriv9ls
al
40%/50%/60%
Case a:
Arrival Priority
OSEM
4L
30
22
52
4R
34
52
9
O
18
20
Total
64
60
20
124
4L
4R
34
5
49
34
38
9
O
4
32
51
119
68
66
123
26
22
17
65
32
58
.,0
40
105
26
32
21
21
16
0
58
3,
68
48
SQ
68
Total
Case
a:
32
Alternating Operations
OSEM
Total
55
SQ
Total
56
Case e:
1 24/1 20/1 13
122
Alternating Operations
OSEM
22R
22L
27
Total
SQ
22R
22L
27
Total
21
11 6
OSEM - Runway assignment using OSE 78
SQ - Shortest queue assignment
Table IV-7: Logan VFR Results
type of operation.
how to assign
typically,
operation,
must be
Thus there
aircraft
multiple
so
to runways.
runways
a policy for
provided.
was no question of deciding
The OSEM
in
The
use
Logan cases have,
for
each
assigning aircraft
report provides
type
of
to runways
one rossible
method - a certain percentage of each aircraft class must go
283
to a given
runway.
this method
IV-7.
The capacity estimates
of assignment are
resulting from
reported as "OSEM"
in table
This represents the first of three possible capacity
estimates,
or given
capacity when runway .assignment is constrained,
in advance.
When the
airport is
assignment policy
simulated under
in case a,
runway 4R
with landings at a significantly
than does 4L,
If the
this constrained
becomes saturated
lower overall arrival rate
as more traffic is assigned to 4R than to 4L.
flow rates
are increased
further,
then,
at some
higher value, both runways will operate at saturation.
queue of aircraft waiting to land
4R than on
a short
L.
The
will be growing faster. on
At the end of the simulation, there will be
queue on 4L and a very long queue c
runways saturated,
the arrival capacity
4R.
With both
will then be close
to equal on the two runways, as the same A/A separations are
used and the runways differ only in aircraft mix.
if
flow rates
saturated,
were
the
increased so
mix percentage of
that
However,
both runways
actual landings
were
in this
situation will be slightly different than the mix percentage
of arrivals.
The reason for this is that arrivals assigned
to 4L will have a better chance of having actually landed by
the end of the simulation run than aircraft on 4R.
If, then, the objective is to determine the capacity of
the
I·I
__
_
I
airport,
while
assignments,
then
_· _II
___
maintaining
the proper
__I
the
constraint
technique is
_I_
_
to raise
on
flow
I
_
284
rates until
one of the runways
saturated.
This
IV-7.
Using
was done to
this
(in this case
becomes
derive the entries
procedure
will
mean
additional time available for operations
utilized.
4R)
However this additional
that
in Table
there
is
which is not being
time cannot be utilized
without violating the assignment constraint.
The second of the three
methods of assignment
termed a flexible, or shortest queue,
SQ,
can be
assignment.
In
this method, it is assumed that some classes of aircraft may
be limited to operating on certain runways,
preordained
constraint on
will be assigned to the
how aircraft
but there is no
within each
class
runways which that particular class
is eligible to use.
With the shortest queue assignment,
the mix percentage
for actual landings will always be the same as the given mix
percentage
for
aircraft to
course
arrivals.
runways is
of the
may exist
aircraft classes).
assignments.
(subject,
on the use
the
assignment
the computer
of course,
of runways
of
in the
to
any
by some
Thus, the runway assignment percentages
for arriving aircraft
turn out to be
determined by
sumulation
constraints that
However,
of classes A and
B in case a
the same under the SQ procedure
do not
as the OSEM
As one might expect, the SQ procedure leads to
both arrival runways being used about equally for case a.
Consequently a larger fraction of class A and class B
aircraft are assigned to runway 4L under SQ than under the
285
The equal capacities, 34 aircraft
original OSEM assignment.
for 4R and 4L may seem surprising since all heavy
per hour,
jets (with the longer separations they require) are assigned
to 4R.
the
However,
fact
approach
this effect is apparently counteracted by
that the
speeds
aircraft
differ from OSEM assignments
runways 4R and 9
with SQ,
than
(80 tol30 kts.)
(130 to140 ks.).
assigned to 4L
to 4R
assigned
do
have
the
slower
aircraft
SQ assignments also
The
However,
for takeoffs.
even
are saturated with departures at
The
flow levels higher than those at which 4L is saturated.
reason
for
in case
this is that,
little flexibility allowed in
Classes
a for Logan,
and D can be assigned only to 4R or to 9.
either 4L or to the 4R/9 set of runways.
runway to saturate at flow
required to saturate
4R and 9.
Classes
C
This means that,
assigned to
The heavy load on
rates below those
Increasing
departures will eventually saturate 4R
again,
to 4L.
each aircraft is deterministically
4L causes the
is
the assignment of departures.
A, B1, B2, and B3 must be assigned
in effect,
there
flow rates for
and 9 as well,
but,
only at the cost of causing the mix of aircraft that
actually takeoff to deviate from the given mix of aircraft.
The allocation of
departures between 4R and
from nearly half
and half in the OSEM
entirely
runway 9
all to
occurs because arrivals
considerably
longer
under the
than they
intersecting runway 9.
*
II___
II
_________I_
assignment to almost
_i______
This
SQ procedure.
on 4R block departures on
time
9 changes
block
4R for a
departures
on
286
The third type of capacity estimate often computed is a
when the entire airport
capacity for cases
period with a given ratio of
Typical ratios used are 40:60
a sustained
to departures.
operate
for
arrivals
(A:D), 50:50 and 60:40.
to
is restriced
Ratios more extreme than these are
The ratio of arrivals
not commonly observed at peak hours.
to departures at which a configuration operates will vary in
response to changes in separations and runway operating mode
(arrival priority, alternating operations).
There
first
for given
simple
and
The second is
method which
time-consuming trial-and-error
exact results.
A:D ratios.
extrapolation
and gives approximate results,.
interpolation,
a more
uses
method
of
obtaining estimates
with a simulation
aircraft capacity
The
techniques for
are two
yields
be described
These methods will
briefly
below.
Bothmethods,
A/A and
nowever, are subject to a limitation.
D/D separations
there is
an
ultimate
ultimate
maximum
example,
the
in this case,
even with maximum arrivals,
to 40%
capacity is 68/.6
case
a,
capacity
of the
= 113 aircraft
This
for
is
68
runways
of the total.
then found simply
total.
an
departures under
are more than 40%
arrival capacity is
departures
arrival
In
so
and
capacity
Since there are three departure
some saturation conditions
The 60%
capacity.
possible
values,
minimum
arrival
maximum
departure
maximum
aircraft per hour.
have certain
by reducing
means that
total
per hour at 60% arrivals.
287
Simple interpolation-extrapolation
an
approximate estimate
arrival and 40%
of airport
arrival situations.
was used to
capacity
Case a
obtain
for the
was run
50%
using
the alternating operations mode and the results are as given
in table IV-7.
The simple method assumes that the tradeoff
between arrival and
departure
capacity can be adequately
approximated as linear over the range 40:60 to 60:40*.
Figure IV-5 shows how the technique is used for case a.
The
arrival
priority
result
68/119*100 = 57% arrivals.
The
gives
capacity
alternating
at
operations
result gives capacity at 56/122*100 = 46% arrivals.
The
arrival and departure capacities for these two
plotted
at their respective A:D ratios.
the arrival capacities and the
The lines
cross
at
of each type at this
capacity
Lines are drawn connecting
two departure
the point
arrivals and departures.
are
of
a
capacities.
50:50 ratio between
The number of operations per hour
point
is
60.
Thus a 50% arrival
of 60 + 60 = 120 operations
per hour
is found.
To
find the 40% arrival capacity figure the lines are projected
from the alternating operations point towards
arrival
ratio
capacity of 50
operations
(to
the left
of the figure).
arrivals plus
per hour.
The
74
departures
projection
in this case since the ultimate
departure
can
a
lower
A 40% arrival
equals
124
be justified
capacity
is
very
high, perhaps 100 opeartions per hour or more.
*
Subject to the ultimate capacity constraint for arrivals
only and for dpartures
_
_ _I
only.
I_____
288
78
74-
Alternating
operations
Arrival Prioritv
70
.r
Ultimate
Arrival
Capacity
66
T4
0
62 4o
58
_
cO
PO
a)
54
To
4-J
Cd
$_4
O:
P-
50
_
,_
I
0 c'
7
.I---·----r----.
-
40:60
50:00
.
60:40
Ratio of Arrivals to Departures
FIGURE IV-5.
Interpolation-Extrapolation Method for
"Percentage Arrival" Capacity Estimation.
289
The estimation process described above was used here in
a simple approximate estimate
order to obtain
A
capacity estimation
detailed
more
investigate
exact
the
slowly increasing A/A
between
tradeoff
A trial-and-error
departures.
study
of capacity.
could
arrivals
could
method
easily
separations from the VFR
be used
and
by
minimum and
The capability of FLAPS
observing the resulting flow rates.
to modify operating rules would facilitate combining several
of these experiments into each run.
for
The results
also
in
included
operations
case e for alternating
IV-7.
Table
The
and SQ)
assignment policies (OSEM
difference in arrival capacities is
results
are very
for the
similar.
are
two
The
primarily due to random
Additional departure
variations in the simulation runs.
capacity is provided by the SQprocedure, as compared to the
capacity achievable by strictly adhering to the OSEMrunway
by reassigning aircraft from 22R to 22L.
assignments,
The
resulting capacity estimate (68 + 48 = 116) is very close to
60:40 arrivals
of
estimate
to departures
This
To obtain
the
arrivals would require larger A/A
estimates for 40% and 50%
separations.
and so may be used as an
this situation.
for
capacity
ratio,
could be
done directly,
as described
above.
The
complexities
for a
estimate
of
complicated
just discussed illustrate
i
-LC
--
I
ill
obtaining
a
configuration
simple
case that
the fact that care
-11-·----·111111-----11·-·-··11·1·
capacity
we have
must be taken
290
in
of what
the specification
exactly has been
the airport is,
of total
is
in fact,
constrained
analyses.
If
in certain ways (i.e.
or arrivals
cannot use 4R or 9,
-then any capacity
operations),
what
desired or
estimated in such capacity
small aircraft really
60%
exactly
are
estimation
procedure should reflect this fact by recognizing that there
will be
if
the maximum
capacity for this
should not
without
the purpose
of the analysis
other hand,
constraints
find
to
then
case,
what
is to estimate
the constraints
The model
at all.
be applied
On the
to the constraint.
due
unused capacity,
should be
the optimal
run
assigrnment
policy is.
2
IFR Results
Table IV-8
cases.
It
uses the
same format as
involves the side-step procedure
aircraft mix.
similar
under
in detail.
three IFR
table IV-7.
Case b
described above.
Cases c
only in
terms of
and differ
The results for
issues as
discussed
on 4R
all landings
and d have
for the
gives capacity estimates
these three
VFR results
and,
Cases b and c as
cases involve
so,
are
constrained
by the
OSEM assignment, have large, unused departure capacity.
SQ
method
results
in
significantly
larger
not
The
departure
capacities. Regardless of assignment method, all cases have
departure
capacities
large
enough that,
even
when
the
291
Assignment
Runway
Method
Arrivals
Departures
Total
Percent
Arrivals
40%/50%/60o
Case b:
4L
OSEM
SQ
42
27
13
14
0
29
Total
27
65
23
92
4L
4R
9
Total
15
15
27
42
0
40
4L
4R
9
Total
o
21
13
27
40
27
27
O
61
81
27O
Total
27
32
8
36
32
4R
Total
Total
28
60
88
28
23
62
90
4R
9
13
27
29
40
14
1I11
81
75/60/50
Case c:
OSEM
SQ
4.l
Case d:
OSEM
SQ
35
36
68/54/45
76
70/56/47
All capacities in aircraft per hourr.
All cases are arrival priority mode.
Table IV-8: IFR Capacity Estimates
configuration
is operated
at the
ultimate
flow rate
for
arrivals (full arrival priority), arrivals do not constitute
40%
of total
operations.
Hence,
all of
the "per
cent
arrival" capacity figures can be obtained directly using the
s-
·--
l-g----···t·ri···Y·l--i·rrmr·rP.·a
-
292
arrival flow rate.
H
DELAY ANALYSIS
The cases
this
chapter
estimations.
sensitivity
presented in the
validation chapter
have
been
so
The only
runs,
far
delay cases
Bromma)
operating rules remained
run.
This is
existing
have
operating rules.
capac ity
examined (La
have been
cases
Guardia
where
constant over the duration
partially a
models
primarily
and in
consequence of
very
little
FLAPS has
of the
the fact
capability
to
such capabilities,
the
that
alter
and this
section discusses three hypothetical cases that illustrate a
practical use of this capability.
I
Case description
We continue
example.
to use Logan
Airport as
our illustrative
For this demonstation we limit aircraft to the use
of just two runways: 9 and 4L/22R.
for 4L/22R
is retained in
The geometry information
the input specification
case, but as no aircraft are assigned to 4L/22R,
a factor
in these
confined to
runs.
a single
As all landings
runway at any
-it was not
(takeoffs)
one time,
is run,
for the
9AM to 5PM period.
are
the runway
assignment problems discussed above do not arise.
hour case
of this
An eight
During
this
293
figure
IV-6 for configurations and
changes of
specific
times of change.
These
not reflect
actual
configuration may
one runway
that this results in
Note
operating practice.
See
twice.
use changes
in
configuration
time,. the runway
being used in both directions at various times in the run.
demand
A
arrivals
and
is shown in figure
IV-7.
for
rate
hypothesized and
times
inter-aircraft
using
negative
distributed
of the
the stochasticity
to reduce
exponentially,
as
This was done, rather
second order Erlang random variables.
than
Inter-aircraft
were distributed
and takeoffs
both landings
times for
is
departures
input
This permitted the use of fewer replications to
The
narrow confidence intervals.
achieve acceptably
process.
aircraftmix used
B2,
B3 were
performance
was that of cases
collapsed
into a
single
of the B2
attributes
a and
e.
Classes
B1,
class
B with
the
to permit
class in order
the addition of more classes as described below for case 3.
All other parameters
the Logan capacity
are the same as in
cases a to e, above.
For the base case (case
VFR-1 rules all day.
from 9AM to 9:30,
remainder of the
these changes.
aircraft
conditions
·
_I
I·I_·____ II
·__
Case
performance
to
simulate
the airport operates under
conditions
Case 2 operates under VR-1
FR-3
day.
1)
from 9:30 to 12:30
See figure IV-8,
for
same as case 2,
3 is the
parameters
the slower
·
and VFR-I for the
__
are
changed
a summary of
except that
during
IFR
movementof aircraft
on
__
_
_I
294
A
/
L
D
9
a)
L.
a,
Configuration
9 AM to
11AM
D
9
/
A
_/
b)
b,
Configuratio
11 AM to
1 PM
9
A -
4R
c)
Configuration
FIGURE IV-6.
c,
1 PM to -5 PM
Logan Delay Configurations.
295
40
Arrivals
35
;.
0
30
O
25
.H
1-0
20
0
04
15
c
a)
10
5
0
9
10
11
12
13
14
15
16 17
Time
Logan Delay Cases:
FIGURE IV-7.
~I
---
1~
·
Q II(·IIIL·-
-
_
l
·
·
Demand Function.
(
-
296
ATC Rules:
Cases
2&3
VFR
t
IFR -
-
VFR
Case
1
1-1---
----
--- ·--------,.c,
IFR
Runway Configurations:
aAll Cases
b
c-
--
.
-I
~--------·I
i
I
9
10
I I
f1
.
I
1i2
_
13
i ·
14
Time
FIGURE IV-8.
Logan Delay Cases:
Summary of Parameter
Changes.
15
16
17
297
the
runway in
bad
weather.
weather were assumed
respect
to
distances
performance
20% for classes
is 2kts.
3)
compared
1)
to
float
15% for classes
coasting speed for all classes
rather than 25kts.;
increases by
2
4) takeoff runway occupancy
seconds for
all
classes;
5)
standard deviation of approach speed increases by lkt.;
the
bad
changes with
IV-3):
C and D,
in
2) deceleration.rate for all classes decreases to
5 f/s/s from 5.75 f/s/s;
time
parameters
weather (See also table
increase
A and B;
to undergo the following
aircraft
aircraft in VFR
Aircraft operating
standard deviation
increases by
These
of
takeoff
runway occupancy
the
6)
time
kt.
changes were
implemented by
aircraft classes, AI, BI, CI, and DI.
defining four
new
These classes are the
bad weather equivalents of classes A,
B,
C,
and D.
The
aircraft mix was set so that during good (VFR) weather, only
classes A, B,
C,
and D would use the airport.
During bad
(IFR) weather, a changeover is made to classes AI,
and DI.
The mix of the
"bad weather classes"
as
BI,
C,
he same
as the mix of the "good weather classes".
2 Discussion of results
Average delay for the threecasesis graphed in figures
IV-9 (landing)
16
and IY-10 (takeoffs).
replications.
Selected
95%
Each case was run for
confidence intervals
are
shown in the figures.
n
I
_I ___
____
II__
_____
298
50'
40
Cases
2
3
a0 30
-,,
Case
o
20-
d0
H4
< 10'
0
,
r
9
10
11
12
13
14
,
15
16
17
Time
FIGUREIV-9.
Logan Delay Cases:
Landing Delay.
1
299
la _
ase
1
12 -
10 -
8 -
+t
9
i
6 - II
M
I-
c)
4I
i
2
s
i
II
I- -r
0
9
10
11
y- i-
12
13
14
15
16
17
Time
FIGURE IV-10. .
---
-r~~----
-~
s
r
Logan Delay Cases:
w~l--
Takeoff Dela-v.
-l~l~l·i-~---D I-XI
~
.
~
----
300
As might
be expected, in case 2,
landing delays
than in
capacity
IFR operations.
during
case 1,
due
are imposed.
This occurs for
backlog caused
by IFR conditions
weather.
Second,
o'clock.
already in
the
lower airport.
also be noted
in
to grow after VFR rules
two reasons.
-First,
takes time
The aircraft that land immediately
were
to the
It should
case 2 that arrival delays continue
reimposed)
there are much larger
the
to dissipate.
after 12:30 (when VFR is
the landing
demand rate
queue during
increases
IFR
after
12
This illustrates the potential usefulness of being
able to model operations during the entire day with a single
run
of
the
simulation.
Even
interested in
the period after
conditions at
12:00 can
if
the
analyst
12 o'clock,
greatly influence
delays
This is as expected,
priority
mode
and
in case 3
delay estimates
Note, as well,
were unchanged
since all
only
the "initial"
for a considerable period of time afterward.
that landing
is
from
case 2.
cases are run in an arrival
A/A separations
are
not
affected
by
changes in runway occupancy time.
Takeoff delays
decline from case
occurs because the larger D/D
1 to case
2.
separations in use during
This
FR
weather are more than offset by the additional opportunities
to depart
provided by
the larger
The increase of delay from case
significant.
can have on
arrival/arrival spacing.
2 to case 3 is particularly
It illustrates the impact aircraft performance
airport delay.
Thic impact was
made clear by
301
the
caused by
occupancy time
estimate
to first
not necessary
bad weather,
aircraft
changing
requirements.
not separation
performance characteristics,
It was
from
resulted directly
and
model
in runway
changes
estimate
and then
revised separations for use in the model.
I
MODEL PROPERTIES
1
Sensitivity Analysis
An extensive
would
an
be
develop
part
integral
a
of
using
the
model
for
a
As the primary purpose of this work is
particular airport.
to
analysis of modelparameters
sensitivity
model
than
rather
to
an
perform
actual
analysis, we have nct performed such a sensitivity analysis.
in
However,
the course of
runs and for the
examples of
general conclusions
model
using the model
this chapter, a number of
relative sensitivity
about the
results to changes
for validation
in the values of certain
of the
parameters
were made and are reported here.
Landing Performance Model
As
reported
in
range of uncertainty
the model.
This
section
II.D
there
is a
this part of
in several parameters of
means that,
where runway
significant
occupancy time
data exist, it can be useful to adjust parameters within the
reasonable
_
range to
approximate more closely
I_______
the
data.
302
Arrival
runway
reported in
conditions
occupancy
OSE 78:
under
times (r.o.t.)
though
which
was apparent
they
r.o.t.
than
were
obtained.
OSE 78.
with the
selection.
To bring
OSE data,
parameter exists,
it was
adjusted from 30kts.
both r.o.t.
As
to
No
chosen to
the value
of this
.'It
be revised.
so
combination
seconds to
and exit selection probabilities.
r.o.t.
used for
5.75
its
value
was changed
to
of
these
two changes
added
average r.o.t.
This
below OSE 78 results.
still
Since
The initial
The
impact on
capacity of
f/s/s.
will occur
eft
FLAPS arrival
the latter tend to be
The impact on departure capacity
extent to which arrivals
we did not
LAPS and OSE 78.
changing runway
in arrival
arrival capacity is controlled
The
-approximately 2
times will vary depending on several factors.
arrival capacity
This
the validation
longer than -those reported in SWE 72 and KOE 78,
pursue closer agreement between
was
Dec eleration.rate affects
highest deceleration rate
runs,
were
it does not
value of this parameter used for Logan was 6.00 f/s/s.
was the
exit
results into
two parameters
no data on
25kts.
of the
shorter arrival
Coasting speed affects only-r.o.t.,
affect exit
are
When FLAPS was first
it was producing
reported in
closer agreement
adjusted.
that
Logan
without any indication
selection probabilities are reported.
run it
for
occupancy
No change in
priority cases
as
entirely by A/A separations.
will vary depending on the
block departures.
If departure
303
capacity is affected then this, in turn,
capacity in
a case that
example of the
can affect arrival
uses alternating
operations.
potential interaction of shifts
performance with
capacity and delay estimates
An
in aircraft
was provided
by the delay cases run in the previous section.
Aircraft Separations
Aircraft separations have a
capacity.
They must
accurate results.
case
that
case
provided
specified
As has been
airport
separations used
be
very significant impact on
mentioned,
analysts
report
in their work.
an
example of
with care
to
obtain
it is often the
only
A/A
and
D/D
The La. Guardia capacity
the
importance
of
carefully
specifying the A/D and D/A separations as well (Rmt in FLAPS
notation).
Demand Generation
In a delay case,
can
greatly
the methods used to generate aircraft
influence
not only
the
results but the mean values as well.
section II.C.
airport
variability
of
the
This was discussed in
For capacity cases, due to the fact that the
is saturated
and the
stochasticity
of the demand
is
not a factor.
2
Computational Efficiency
FLAPS
is written
4000 lines of code.
in PL/1
It is
and contains
approximately
currently operated from the CMS
304
interactive system on an IBM 370/168 machine using a virtual
operating
system.
storage to run.
(cases a to e)
The
program requires
The 6 hour,
required
720k
bytes
of
10 replication capacity cases
between
35 to 45 c.p.u.
(central
processor unit) seconds to produce all the results (OSEM and
SQ assignments) reported for each particular case.
the three 16 replication,
required 44 to 46 cp.u.
in effect
minute
at the
8 hour delay cases
seconds.
time these
Each of
(cases 1 to 3)
Under the rate structure
cases were
run,
one
c.p.u.
costs $6.00.
Only
efficiency
limited
information
of ASM is available
that a five hour runrof
about
to
the
computationalit is known
the author.
a simple 2 runway,
system airport cost $63.00- (BAL 76 p. 4).
minimum taxiway
A three hour, ten
replication, run of O'tare (a very complicated system)
$76.00 (BAL 76 p.
7).
cost
No indication of the cost structure
or computer used is given.
A three
hour, ten replication,
run of a LaGuardia example under congested
conditions took
18 c.p.u. seconds on a CDC CYBER 70 and cost $18.00 (PMM 77
p.
44).
A
operating is
two
hour run
said to cost
not seem to be directly
of
O'Hare
with five
$100.00.* These cost
correlated with the
the situation being simulated,
runways
figures do
complexity of
but they give an idea of the
execution costs of the model.
*
Personal communication to Prof. Odoni by PMM staff, 1978.
305
of inrut requirements in section
As with the comparison
a detailed comparison of
F above,
not possible.
not
Information on the cost of identical
available.
The
models
and ASIM are also
FLAPS
different rate
FLAPS run
structures.
ASM
capabilities
have different
run on
reported cost
inexpensive
run,
of
FLAPS
result
one third
it
seem
would
average
cost of
feasible to
a FLAPS
run,
the
demand
to $6,
and operationg
added
more extensive
do
to use extensively.
$ 3
most
generation,
performance)
not
The low
means that
perform many more experiments
airport configurations
of the
that
replications,
of aircraft
using
most expensive
less than
in a model too expensive
cases is
different computers
(internal
calculation
thus,
capabilities.
However as the
essentially unlimited maximum
statistics,
ASM ard FLAPS is,
it is
with alternative
conditions than
has
heretofore been possible.
3
CONCLUSIONS
This
cnapter
flexibility
Airport is
numerous
and
"special case"
arrivals,
side-step
changes
usefulness in
a challenging
parallel runways,
short
further
demonstrates
airport
airport to
arrivals,
in use
frequent weather
in the runway configurations
Logan
model because
situations (intersecting
runways
model 's
analysis.
displaced thresholds,
multiple
the
of its
runways,
conditional hold
simultaneously,
changes,
in use, among
frequent
others).
306
The
cases described
in
this
chapter illustrate
model's flexibility. adaptability and efficiency.
be emphasized
again that this chapter
comprehensive analysis
Such an
effort is
of the
a major
scope of this work
is capable of performing such
major airport.
estimation.
environments.
situations.
can
It
The
be
can
is beyond
the
we establish here that FLAPS
a comprehensive analysis of a
FLAPS can be
It
as a
Logan Airport.
undertaking and
Instead,
It should
is not offered
operation of
the
used for capacity
used
model a
combination
capabilities is unique to FLAPS.
for
analysis
number
of
o-
all
of
and delay
of
dynamic
special
of
the
case
above
307
V
3SJMIARYA
A
REVI E
'31TLiOJIr 3
to contribte to the analysis
tas3
The aim of tnis work
modelin
a unifi
of ai r port
ope r at ion3 b levelopig
franmeworkthat can analyza the performance of
a wiidevariety
contribition3s
numnbe-of secific
been made to -nodeling
hlve
wich
tool
si nificantly
expandsthe scope of
issues that can be analyzed.
method of
efficient
A simple,
existing
usability
for
a prer3qUriite
7met.iods
a
geometry was leveloped.
Q nie
lefinition
of
patns
airport.
Wie foun
flexible
sufficiently
methol for
A related
aircraft
level
of detail
reor esea3 in
and
that
current
the
over tha
rmethods were neither
nor economical.
whi le
issuea is
in taxiing
tke
described a new approach which approimates
an economical fashion
with the15
It oermits rapid scification
of airport geometry.
alteration
'Je 3a tt
model.
sable
ai rpo rt
sosecifin
are so cumbersome as to interfere
the models.
of
of
n a 3inglne moel is the construction
these contriba:t.ons
geormetry is
task Ai
The cumulative ffectof incorporatin
airport operations.
an analytical
2o accomplish thiis
ondiions.
of
unler
irports
allowing
,Je proposed
and
taxiing
elay in
flexibility
in the
are
modeled.
at rwhich roulnd operations
This appro3ih, however, fnsnot been implementei anl renains
area for further
a potential
..
I
-PL-_··__-_IX
.Lb--
ork (see saction B).
L-·-lll·ll
308
specifying the number and
Existin. methods of
These
about aircraft
considerable amount of uncertainty
It ws establisni.
that
demandi.
current Iem-anl gnerration raethols
lan1, and
in
to catuur-e certain types of unertinty
failel
to
a
to situations involvina
apliel
mislealing resul3 if
may lead
souna,
coneptlally
-hile
aethods,
of
were reviewel. critically.
which use the airport
aircraft
type
that this results in significantly unlerestimatin, .rielay. A
new enand
m3ethodwas levelopel
neartion
this problem.
everal contributions
modeling of rw-.y
aircraft
wer-emade in ths
The lanlin
operticn3.
of
work to
the'
perforance
of
phVysia].
to; tahe unde-lyin;
accorling
is modeled
whnichis fre
process, ratlher than by soecifyia taersul, tin behavior -s
o
Islanlingr,
do exist'ng mnodels. Th'rasonabens3 s .f
It wa3 fo;uni that
data sets.
for
The rules
in
differently
appropriste,
by testing
was verified
performancemoel
rthe
aircraft
xistin n models.
on
the
Was demonstrated
that
Derformance.
It
model a class
of situations
approx imat.
Th,=
arcraft
oerforiani
in
i:?
FLAPS, where
basis
was
of
average
the new methods can
,hdtich existing
ire t connection
=
moleled
Existing models usually
of indlividual aircraft.
performance
solely
were
based explicitly on t'he
uses separation rules
-3
3pecify spar ations
two
model gave good results.
separatiang
LAP3 tha;n in
it a.g'inst
between
sh on
models -an only
separations
to
and
facil.itate
309
mod.elin
impact
of the
aircraft
for -lanings
aircraft.
.ss
as in the
-rll
eather ndu.ced)
( .g..
to model time trigered
apability
event trigge re
odel
to
FLAPSis specifically
changes.
congestion induced)
have lmost no
odes
Existinz
changes and a limited
designed to facilitate analysis of both of tese
The most significant
can
into one
be placed
of the
contr'ibutiors
of two
cate
intera.cion
hal to
were
capabilities
be
Interactions modeled were:
above,
1)
the several aircraft
t.tributes
the
of
characteristics
simulation;
runway
2)
exit
performance,
and se par t
the
the
interaction
iilCp-p·p--nrr·rrinnrrrrr-x--;ra-rql
ly.
r
and
aircraft
the
dyna'>ni .
The
II.F.
in section
which, in turn,
anon
determine
generated
by
the
of aircraft attributes with
to
the interaction
rules to
previously
the interrelationships
chara teristics
and 3)
on
external
moi eled
iscussed
work'
iheyeit
ries.
where
omponents,
airfield
of tis
or they moleL interactions
case,
was limlit'e to the static
situations.
w1here reviou3sly theanalysis
provile a ynamic capability,
between
emrani
and takeoffs and in the performance of
hn.,,es
Tho occurrence of '-oncestion can triar
operating policies.
capability
oper lt i ng
of changes in
and runway configurations
policies
:ranges in
in ia ynamic environment.
oerate
weather induce a complex set
(e.g.,
in
oer orane.
Airport
in
by changs=
produced
on delay
deterine
determine
of aircraft
aircraft
performanlce
wheonoperations
may
be
-^usrs·-r---rrr··-----rrr-i·
---I-..---(·9·-
310
comnitted to mTOZ;. 'he not-ential sin
these int.-ar tions3
-33 est'.ablist.fi
nhapter£T.
The oumulative effet
in
betwd
een Par
a'e er
capabilit,y is to greatly
can be aire:3sel
in
capacity
n 'lelay
course of
lay's
.here
ooeratinc
ised to
relate,
l.esiyn
I
folloa1In
I M IV.
Y3
in
airess
of t
Furthr
results obtainel
ost
cas. s.
analysi
diemonstration
irpoort.
a coplet3
n one 'odel
'
ru1.
numloer of
airport
[,stio
g,-cmetry anI fL
explor.
.ere
exarnoles
ill
be -iven
The
of its
nodel
by testi-n
.:reementwiith
A
DroblemdefinLtion.
airport
-
-the
iurin
Lin
majority
of
wias
ble to
the
Las
signif
ant
to minor lisorcrnie3
v of th
i3
e tstablishe
applicability
tio
the other ressults
The utili
s
its r esltt s
fro-a fo-ur other mo eleis .f
li3agree:nen's3 ncoull be attributel
the
change
conlitions
.as3p rtly v,-i:late
iEfffer-at airports.
gool
rules
iste above
section.
The nolei
against
to stairlari
3Son of these possibilities
fr lees
in chaptrs
Ln aliition
This allows --.
n an-alysi,3 of
optial
noiiel ing
FLAPS
? ari be used to directly
operationundler realistic
Op3 r ating
ic
involvin- the interactions
a ,iay.
to
a 1 lyn
xoani the3scope of 'llenstions 'Ahilh
Tb're nodel c;an be
-,"'
rovilin
estimates,
and siLtuations
a9 they. were introluel
simnle .nolel.
an.lyze siti:-itions
each of
of incorpo-atin:I interactions
of
as
of
o
nmolel for
trough
the
reoLi Ite
in
case of
aensive
Login
any,
tha :If
311
special situIations in .ffet
model ch'anes.
i.
at Lo.ni.
a-rting rules
The c3lpability to
..
was also
.lernonstrate
in
that environmnent.
The a.Ivancesan
capabili ties- t ha-t ;. e have
jus,3t
outlinel,have not rsulte
i-n a olel wi.cn is difficult t'o
useorcomputationilly in-affriient.
Inout rqlirema-t3 f.or
runn:ing
the
modelare
relativilLy little
very inexpensive.
coull be
f
ani
haefact that,
ani run
ork
t'this
ca.n be
preparel
wiith
Lndividualruns of the odelare
ffort.
evelopel
constraints
simple
models of three airport3
within the
testif
to
ies
time and :aonet'ry
="
ffiCi a,,
the
anI
ease of uaie of the oiel.
13
W I.R IR
Nee3ie
' OR-
R.search
that
Des.3ite the fact
traffic control system
minute
our
basis
sat3
valilating
there
aircraft,
re closely
are surprisingly
of kniwlelge
airport
when
performanc
study, a number of topics
it
airports
and
tha air
onitored on a ainute-bymaany iaport'nt
comes to
models.
As
:gapsin
Ie'elopino
an.d
a result of this
hnave been identified
as iportant
for future resaarch.
Performance of landirni aircraft
A.s
I
_
__
iScU3sl
-iin
_
Sct
i on ID
develonment of . lann-in.'
·
312
performance
odel was hindered
by a lack of consensus
values of a number of basic
parameters
Research in thi3 area has specialized
related to somes
particular
In order
aspect
to fievelop better
of
research
understood
can
this research
to be
there is
fforts.
- It may
a need 'for
Only with this kind
between
performed in
Some specific
pilots.
of the landing proceaiure.
interactions
and quantifieL.
of the process.
on measuringparameters
models,
comprehensive data collection
on th
par ameters
be possible
for some of
cockpit simulators
issass for investigation
be
are:
with
1 ) the
timing and rate of deceleration
from approach to touchdot3,;
2)
apprc ch
the
correla tion
distance;
3)
decaleration
between
h3 ralue,
rate;
variance,
speed
and fl't
and functional
4) the 'ialue, variarnce,
for-.n of
an:i1fnationa2'
form of coasting speel and exit sp:-efs as a function of exit
type;
5) interactions
between somneor all of the above.
Performance of departing aircraft
We were not
performance
data
on
i.
this
this
able
-work,
procedure.
significantly less
to
develop
due to
As
the
a
model of
an almost
takeoff
complex than the landing
total
takeoff
lack of
procedure
process,
is
less
effort should be required to obtainlata that. would provide
the background for
developing a credible model of this
process.
Delav statistics
The
motivation
for
this
work has
been
the need
to
313
airport
predict
:neasure
primary
of service and performance,
level
is average
of which
interest of many
parties in this
reliable systenm
for
first,
Such a syste. is needel to,
of models
-andr-porting
second,
data, rather than solely against other models.
be strongly
delay
is
statistics
are not
operating
greatly
accompanied
rules and
b
diminish.ed
a full
lemands
set of
if
permit
It must also
value of accurate
that the
emphasized
to
"real-world"
F-LAPSaainst
as
such
ielays.
assess the main problem
and
area3s under current conditions,
val idati on
not yet exist
theoro ?oes
measuring
the
and the extensive
easure
monitoring of aircraft movements,
any
Despite
delay.
the
these
:ata or,
St atisticS
informatio n on
for service whinh
produced
the
the
recordel delays.
Communication
of results
Research in the field of airport operations is hiniered
by a lack
of communication
of the res&lts of work performed.
Mach orkon airport analysis
is pblished
as consultarnts'
reports
hich receive very limited distribution,
papers,
as
unpublished
memoranda
and
the lile.
as working
This is
particularly true of data collection and of more practically
oriented activities, a: theaccompanying bibliography to this
work
attests.
An
effort should
be made
to collate
and
abstract this literature.
the
The perceptions
-nd experience
airport
lay
on a
to
_ _ _ _ _ I Y ( ·^ -____I · _l __ IYIDIL_~~~~~~~~~~~~~~~~~II_~~~II_
of people
day basis
have
who operate
not
been
--_ l_l
_--Xm_-_l~~~~~~~-----
314
systematically incorporated
The decision making
exits)
oroc3sa of 'oilot3 (e.g.,
and controllers
not been
into t;he theoretical analysis.
(e.g., judgaeent
documentei in
such a
usable in an analytical
of separations)
way as
framework sch
selection of
has
to make it rea ily
as FLAPS.
2 Potential uses for FLAP3
At several
Dointsin
made concerning
performel
briefly
this ork 3sgestions
significant
using FLAP3.
experiments
These sugge3tions
have
which
been
can
be
are collected
and
smmarized here.
Capacity analysis
Significant analytical work
of predicting
the capacity
either arrivals
only or
of a single
more than
to
While some
analytical
simulation,
systematic
changes
experiments
in
specific
more
intersectinc runways, cases
of these
methods,
fewer
sitations
aay
it may be eatier
use a simulation to obtain capacity estimates
adaptable
For
two runway3 simultaneously)
studies are available.
prove aenable
the area
runway used for
for mixed operations.
complicated situations (e.g.,
involving
has been ione in
or them.
to
An
such as FLAPS, can be use3 to conduct
which
aircraft
investigate
the
pararameters or
effects
of
operationg
procedures on overall capacity for complex configurations.
315
A' practical
example may be citel.
Examination of the
feasibility of shorter A/A3eparation3 currently
of intens.
stdLly (KJE 73. SWE 79).
intersects
or is coincilent with an arrival
A/A aseparation-swill
between
intersetions
nar
of shorter
For
For
the beginning
other configurations
runway)
interesting
impact
to
analyze
of
intersection
aircraft
far
would be
departure
capacity
Analysis of
on
tie
runway
from the
related
.w
hich
also used for
beainning
the
and the
of th5
mix or D/D 3eprations
small.
of
the
It would be
reduction
in
to the position of tne
tepar ture
thn sen-itivity
the impact
wonuld be
a
way in
to roll
involving
runway,
epartures
runway
shorter
departures
ore signifi'ca.nt.
the
is
the
of
(departures
intersections
the
runway,
some 'configurations
A-/A separations
arrivals,
'.non a departure
mean less time for
arr iv-als.
a subject
arrival
results
runway.
to co-anes in
could be one.
Management of aiport operations
Most airport
nature.
Tneir
capacities for
Little
analyses
to
d.ate
concern
primary
a given situation
nave been
has
been
static
to
in
estimate
and runway onfiguration.
td.y has been made of how to manag, the airport
in a
dynamic sense.
This is presrmably because, until now, there
were no models capable of analyzing changes in operating
rules.
The capabilities
of
LAPS in this area make feasible
a 3tudy of this topic.
I
_
_
_
_ *__
II__·
___
_________
316
period.
The nature, duration and effects of this transition
It may be that certain transitions
are largely unexplored.
result
a transition
runway configurations involve
Changes in
disruptions to
in major
a transition between
significance of
Knowing
operations.
the.
configurations is
two
of making the
important in- determiningin the desirability
change. For example, if the airport were operating in
in wind or noise
"a" and
a change
would make
possible
a- shift
configuration
"b", the decision to shift
configuration
not always
things,
to.
be the correct one.
capacity
a higher
from "a" to "b" may
It depends,
amonI other
conditions which
of how Iona the
on an estimate
curfews
"costs" of
permit the use of "b" wil persist,the transition
and the transition
"costs" of
cianging from "b" to some other configuration.
It is likely
changing from "a" to
understanding
air port
developed
have
controllers
that
"b",
of which transitions
With a simulation
changes it may be possible
a
intuitive
.ood
work for
their
capable of analyzing
own
these
to quantify the process involved
or even to suggest better operating policies.
Sensitivity studies
As indicated
in
the
performance model in sections
done to explore
the sensitivity
discussion
of
II.Dani IV.I,
the
landing
work should be
of this model to the value
of a numberof different variables.
Somework in this area
prior to further collection of data on landing operations
317
help focus
could ident-.if the most important variables an.
the3data ollection process.
study
3systematic
a
how
of
of
a2ffoet tie capacity
perfornance
ouli involve, for ex ample,
This
ca-sn-s
perforance
used to estimat
=
be -ppropris.te to
in
changes
varsous
land ing
_onfiuLIatLons.
the magnitude of
assessing
could be
Ti:en FAP3
i-In bad weataer.
c:apicity
and formn
values
ould
of the lanlin- oerfornanca model, it
make
the
est.ablisra.d in
onOlV.ience is
Once
u:line- these circinustances
chane,
for a nmber of airport configuration.
Statisical tsts
Ir
to te
c tlonII I.
a number
interpretaticn
of s i mIlat on
of simniattion resnult3,anid t;he iesign
experiments
:i3-3use- .Tuch furt1her
were
theoretial. ork should be done on thlse
these statisticalproblems
Nonetheless,
3simrlation.
persons interste-l, in uing
lt-as
to :generate
FLAPS to
use
an i to
forms
for
are
FLAP3S may
issues .
ut.ni ue
not
onci3se
to
airport
for
a complex system
The
work.
probability
Most of
a testbe
provide
a simulation of
this type of
variety of
produce
r1late,
of -3ttitical
.U. iS
abilit
of
ernsity functional
replication
by
replication
outputs wouli facilitate 3suh an experiment.
Interaction
with other models
Even thou.h the
airside of airports is
relatively "isolatable" entity,
ways
ground
Sp-·-----·-·--·--·lII
ith
the entire air network
network
C.rU*i-nlw;U
).-.I....--
on the
a distinct and
it interacts in significant
on one hand
ther.
_-I
and
with
the
318
As
of
sequencing
the
at a
is 'actallyaccomplished
the airport
to
arrivals
section - II.D,
in
discussed
The acceptance rate
distancefrom the airport.
significant
of the
departures
ATC sector may limit
the number of
aircraft
'the airport can allow to takeoff.
Certain runway
modeling
Thus
constraints.
airspace
the
of
terminal
work.
area of
and important
airspace.is- another distinct
due to
times
certain
may not be u.sable' at
configurations
Were a good terminal airspace model available, it would then
be possible
to combine it with FLA-PS in order to study a set
of airports
in an urban area (e.g.,
jointly with
Such a study :would crtainly
airspace.
the commonterminal
New York)
provide important insights into the operation of the entire
terinal area system.
interactions between
The understanding of significant
the airside and groundside of airports would also benefit by
apron areas
and
Patterns
effort.
a joint modeling
ani taxiing
gates,
that cansometimes
terminal building.
the
influence
1-1--·-- -·II·II-·-.I-11·1--i-·--···-··I*-I·--
passenger
cars,-
load
unloading
and boarding of passengers,
ticketing
are factors
congestion
in
can all
of baggage,
influence
movements.
X-
ths
Conversely, the ability of the terminal
to accomodate. the parking of
aircraft
of arrival, choiceof
· ·.
·.
·-
l
·-----
·
I
---
L-^·
vY-·-U
--1-·----31111-·1-----
319
35 xtensions
to ?FAP
be ale - to enhance
boill
lto ?TJP3
Several extensions
its U3sfulnes3 for airport analys-is.
Groundopert ions
The
most
significant
implementation of
section
taxlway
This
would
be
all ow analysis
an of the interactions,
sstem
woua
th:
the grouni operations model levelope
iI.3.
ccn gestion,
extension
andl the
of
if any,
in
ground
betwee
t-
runways.
Runwayassignment rules
A.n xtension
LA.PS
. coul d be develel o el
to
first-come-firs-t-servedt
pairs of aircraft
shufflin:
in which aircraft
the
to use
occurrence of
increase capacity.
considerable
This is
attention
certain to re-eive
recently
are
norn
Certain
require large A/A ani D/D separati.ons.
the order
miniize
diel
(PCF3) runway assignmernts.
q.a3ue of tho3se waitin.
to
to
3y
removedfromnthe
the ru-nway it may be possibLe
long
separations
a subject
(DEA
anri th'r.3
that has
76,
receivel
PSA 73)
and
is
more in the fture.
mch
Antithetic variates
As
mentioned
antithetic
ariate
and
r esult
might
in
the
statistics
capability
in
section,
ould be easily
3sionificant
--
an
added to FLP?3
reduction
0-
II.G,
in
the
320
variability
of the outputs.
Validation tests
The
validation tests
sufficient
to establish
Additional
validation
various
performed
the
aspects of the model.
of
several
characteristics of
days.
chapter. III
mod.el'sgeneral
tests.- would be
to have data on actual delays
period
in
wre
credibility.
desirable
The ideal situation
to
test
woul
be
collected at an airport for a
Naturally,
the aircraft that
used the
all
major
airport and
the operating rles
in. effect would need to be recorded. If
such tests were performed carefully,
it would allow testing
of several features of the model.which, of necessity,.
remained unvalidated to date.
detailed
Of particular
interest
have
is
the
handling of changes in operating rules and in
runway assignment policies.
321
B IB
I 3JRA P-IY
ATA 3O3
ir Transport
ssoci9t-ion of Aerica,
1980:
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ts
J.
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e o Indu3stry7",Ju-ne 930.
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S3titi
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ratic
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IllCIIQII
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BIOGRAPHICAL
NOCTE
John Nordin was born January 9,. 1954 in Toronto, Canada.
He attended Kansas Sate University, majoring in Computer
Science.
He received
from Michigan State
a B.S. degree in Systems Science
University
degree in. Transportation
Institute
in July
1976 and a S..M.
Systems from the Massachusetts
of Technology in August 1978.
He is a member of
Tau Beta Pi Engineering Honorary Society and The Operations
Research Society of America.
After graduation he will be
employed by Systems Applications
Rafael, California.
_
I
________
Incorporated
of San