Estimating Delay and Capacity
Impacts of Airport Infrastructure
Investments
Mark Hansen
May 2003
1
Systems Analysis in Aviation
R&D and
Deployment
Decisions
Models
Realized
Benefits and
Impacts of
New
Systems
Introduction
of New
Systems
Post-deployment
Analysis
2
Post-Deployment Analysis
q Study actual effects of infrastructure and
technology deployments on NAS behavior
and performance
q Close the systems analysis loop and allow
learning from experience
q Two schools of thought on PDA
qCounting school—how deployments effect
capacity and throughtput
qTiming school—how deployments effect delays
and times-in-system
3
This Study
q Achieve “best of both worlds” from
counting school and timing school
q Overcome methodological problems in
both schools
q Use censorer regression to estimate
capacity impacts
q Extract delay directy from capacity
impacts
4
Background
q Runway 4L/22R Came
On-line 12/11/01
q Simultaneous Arrival
and Departure
Streams Under IFR
and VFR
q 4R/22L Dedicated to
Departures Instead of
Mixed Ops
5
Expected Impacts
q Benchmark Study: VFR and IFR
capacity increases of 25% and 17%
respectively (assuming “full use of
runway”)
q Press Release
qOverall capacity increase of 25%
q50% capacity increase during peak times
q3000 hrs of delay reduction
6
Motivation
q Initial Free Flight Office analysis found
little impact
q Implications for ability to measure
impact of more incremental changes
q Confounding effects of 9/11
7
Data
q ASPM quarter-hour data for first six months
of 2001 (before) and 2002 (after)
q Four metrics
qArrival counts and departure counts
qArrival demand and departure demand
q Flight counted toward demand beginning in the quarter hour
when it is expected to arrive/depart based on last filed flight
plan before departure/time of gate departure
q If arrival/departure occurs earlier than planned then flight
counted toward demand in the earlier period
q Demand never exceeds count
q Different between count and demand is queue length at end of
period
8
Relationship between Demand (D),
Count (Q), and New Demand (N)
N o (t − 1)
N o (t )
N o (t + 1)
Do (t − 1)
Do (t )
Do ( t + 1)
Qo (t − 1)
Qo (t )
Qo (t + 1)
9
Change in VMC Distribution of Arrival and Departure
Counts, Jan-June 2001-2002
(purple is increase; light is decrease)
35
30
25
Arrivals
20
15
10
5
0
-10
-5
-5
0
5
10
15
Departures
20
25
30
35
40
10
Change in IMC Distribution of Arrival and Departure
Counts, Jan-June 2001-2002
(purple is increase; light is decrease)
35
30
25
Arrivals
20
15
10
5
0
-5
-5
0
5
10
15
Departures
20
25
30
35
11
FIGURE 9
Mean Departure Count vs Departure Demand Jan-Jun 2001 & 2002 VFR Conditions.
30
25
Dep Count/Qtr Hr
20
2001
2002
15
10
5
0
0
5
10
15
20
25
Dep Demand/Qtr Hr
30
35
40
45
50
12
FIGURE 10
Mean Departure Count vs Departure Demand Jan-Jun 2001 & 2002 IFR Conditions.
20
18
16
Dep Count/Qtr Hr
14
12
2001
10
2002
8
6
4
2
0
0
10
20
30
Dep Demand/Qtr Hr
40
50
60
13
FIGURE 11
Mean Arrival Count vs Arrival Demand Jan-Jun 2001 & 2002 IFR Conditions.
25
Arrival Counts/Qtr Hr
20
15
2001
2002
10
5
0
0
10
20
30
Arrival Demand/Qtr Hr
40
50
60
14
FIGURE 12
Mean Arrival Count vs Arrival Demand Jan-Jun 2001 & 2002 IFR Conditions.
25
Arrival Counts/Qtr Hr
20
15
2001
2002
10
5
0
0
10
20
30
40
Arrival Demand/Qtr Hr
50
60
70
15
Censored Regression Analysis
q Data “saturates” measurement device
q Example: speedometer
60
0
60
120
Speed=60 mph
0
120
Speed>=120 mph
16
Application to Airport Capacity
q Actual Speed⇔Capacity
q Maximum Speed Measurement⇔Demand
10
0
10
20(=Demand)
Capacity=10 FPQH
0
20(=Demand)
Capacity≥20 FPQH
17
Censored Regression Model 1
COUNTop ,t = min(CAPop ,t , DMDop ,t )
2
CAPop ,t ~ NORM ( µop ,m( t ), a ( t ) , σ op
,m(t ) )
COUNTop ,t
ASPM count of operation op(arrs/deps) and 15-min
time period t
CAPop,t
Capacity for op in time period t
DMDop,t
ASPM demand for op in time period t
µ op ,m (t ),a (t )
Mean capacity for op, meteorlogical condition m
(VMC/IMC), before (a=0) and after (a=1) new runway
σ
Capacity variance for op, meteorlogical condition m
(VMC/IMC)
2
op , m ( t )
18
Problems with Model 1
q Flights counted toward demand may be
unable to land/depart for reasons other than
capacity constraint (“anomalously delayed”
(AD) flights
q These can greatly distort capacity inferences
q Example
qDemand=5
qCapacity=20
qNo AD Flights⇒Capacity≥5
q1 AD Flight⇒Capacity=5
19
Censored Regression Model 2
*
COUNTop,t = min(CAPop ,t , DMDop
,t )
2
CAPop ,t ~ NORM ( µ op ,m ( t ),a ( t ) , σ op
,m (t ) )
*
op ,t
DMD
~ BINOM ( DMDop ,t , PNADop,m ( t ) )
Where PNAD op,m(t ) is the probability that a
flight counted toward the demand for op is not
anomalously delayed under meteorlogical
condition m. It is calculated using count/demand
ratios for under low demand conditions.
20
Rates of Anomalous Delays
based on Count/Demand
Ratios for Demand<5 FPQH
Meteorological
Condition
VMC
IMC
Operation
Type
Arrivals
Departures
Arrivals
Departures
Predeployment
0.0132
0.0285
0.0245
0.0662
Postdeployment
0.0153
0.0300
0.0214
0.0603
Overall
0.0142
0.0293
0.0230
0.0634
Table 2—Observed Rates of Anomalous Delays
21
Likelihood Function
LL(α o,V , β o,V , σ o,V , α o,I , β o,I , σ o,I | Qo (1)...Qo (T ), Po,V , Po, I ) =
 Do (t )! PoD, mo (( tt )) −Qo ( t ) (1 − Po,m (t ) )Qo (t )   α o,m( t ) + β o, m( t ) A(t ) − Qo (t ) 





⋅ Φ
+




Qo (t )!( Do (t ) − Qo (t ))!
σ o ,m



 
log
D ( t ) −Q ( t )−1

∑
n
Do (t ) −n
o
o
Qo (t )< Do ( t )
 Do (t )!Po,m (t ) (1 − Po,m (t ) )
φ ((Qo (t ) − α o,m( t ) − β o,m (t ) A(t )) σ o ,m ) 

Qo (t )> 0


⋅
 ∑ 

n
!
(
D
(
t
)
−
n
)
!
σ
n
=
1
o
o
,
m



 D ( t ) Do (t ) −1  Do (t )! Pon, m( t ) (1 − Po ,m( t ) ) Do ( t ) − n  − (α o,m( t ) + β o, m( t ) A(t ))  
 
+ ∑ log Po, mo ( t ) + ∑ 
⋅ Φ


n!( Do (t ) − n )!
σ o, m
Do (t )> 0
n =1 


 
Qo (t ) =0

 α o,m (t ) + β o,m (t ) A(t ) − Qo (t )  
Do (t )


+ ∑ log (1 − Po, m(t ) )
⋅ Φ 


σ o, m
Qo (t ) = Do (t )



22
Meteorological
Condition
VMC
Coefficient
α o,v
β o,v
σ o, v
IMC
α o,i
β o,i
σ o,i
Operation Type
Arrivals
Departures
24.578
(0.263)*
-0.611
(0.254)
6.535
(0.142)
18.524
(0.228)
0.403
(0.293)
5.584
(0.140)
Capacity
change
after new
runway
20.667
(0.167)
1.569
(0.194)
6.039
(0.092)
18.129
(0.245)
-0.274
(0.309)
7.196
(0.160)
*Standard errors in parentheses.
Table 3—Estimation Results, Truncated Capacity Models with Anomalous Delays
23
Key Estimation Results
q Significant increase in VMC arrival
capacity after new runway
q Small but significant decrease in VMC
departure capacity after new runway
q No significant changes in IMC capacity
q Large variability in capacities
24
Delay Impact of Capacity
Increase
q How much more delay would there
have been if 2002 demand had been
served by DTW without the new
runway?
q How much less delay would there have
been in 2001 demand had been served
by DTW with the new runway.
q Deterministic queuing analysis.
25
Delay Impact Calculations
E(t)
Difference between
demand and count in
time period t.
26
Delay Impact Calculations
~
1. Set t=1 and initiate the demand using Do (1) = N o (1).
~
A
2. Draw the number of anomalously delayed flights in time period t, o (t ) , from the
~
binomial distribution with success probability Po,m(t ) and number of trials Do (t ) .
~
3. Draw the capacity in time period t, C o (t ) , from the normal distribution for the
appropriate deployment scenario, operation type, and meteorological condition.
~
~
~
~
4. Calculate the throughput in time period t as Qo (t ) = nint (min( Co (t ), Do (t ) − Ao (t ))) where
the nint (⋅) function rounds its argument
to the nearest
integer.
~
~
~
D
(
t
+
1
)
=
N
(
t
+
1
)
+
(
D
(
t
)
−
Q
o
o
o
o (t )) , t=t+1, and go to step
5. If t=T, go to 6. Otherwise set
2.
6. Calculate delay by summing unsatisfied demand at end of each time period.
27
Departures
Arrivals
Jan.-June 2001
Mean
Std. Dev
Observed
1.92
Simulated Baseline
2.00
0.060
Simulated Counterfactual
1.77
0.052
Difference
0.23
Observed
1.01
Simulated Baseline
0.89
0.026
Simulated Counterfactual
0.92
0.027
Difference
-0.03
Jan.-June 2002
Mean
Std. Dev
1.93
1.92
0.032
2.26
0.070
-0.34
0.95
0.93
0.029
0.90
0.041
0.03
Table 5—Delay Comparisons, Simulated vs Observed, and Baseline vs Counterfactual
28
Key Delay Analysis Results
q Average departure delays decreased
15-20 seconds per flight as result of
new runway
q This translates into 1000-1300 hrs of
annual delay savings for departures
q Arrival delay impact neglible (2 second
increase)
29
Caveats
q Delays that are incorporated into flight
plan gate departure time ignored
q Demand impact ignored
q Assume that before/after change is
consequence of new runway
q Analysis based on early postdeployment experience when
procedures not fully adjusted
30
Conclusions
q New post-deployment analysis method
that should please both the counters
and the timers
q Also useful for many other applications
(e.g. capacity impact of facility outages)
q Further refinements to consider serial
autocorrelation in capacities and
explain throughput loss in high demand
conditions
31