Models for Estimating Monthly Delays and
Cancellations in the NAS
Avijit Mukherjee
Michael Ball
Bargava Subramanian
University of Maryland
Introduction
• Objectives
– Develop a metric that indicates the level of congestion faced by a
each operation (arrivals/departures) at an airport.
– Estimate various percentiles of the distribution of the congestion
metric across all operations in the NAS.
– Model NAS average flight delay and cancellation probability as a
function of the congestion level (i.e. the percentiles of the
distribution of the congestion metric).
• Application in NAS Strategy Simulator
– Estimating flight delays and cancellation under various demand
growth or capacity increase scenarios in the NAS
– Estimating passenger delay
Measure of Congestion
The demand/capacity ratio is a good measure of congestion. Each
operation at an airport faces a congestion level depending on the
capacity and demand at the airport in a time window at which the
operation takes place.
Percentiles of Rho
Concept of Rho
h1
O
100%
h2
Time window I
ρ=
Y = % of
operations
with ρ ≤ X
# operations during I at O' s airport
airport capacity during I at O' s airport
ρ50
ρ95
ρ99 X
Estimating Rho at an Airport
Input
•
•
%
– Hourly scheduled demand
– GA demand
– VMC / IMC capacities
ORD
Associate demand/capacity in
an hour as the Rho value for
each operation during that hour
Estimate the monthly
distribution (or percentiles) of
Rho at an airport
100
90
80
70
60
50
40
30
20
10
0
Average Delay:29 min
Cnx Prob. 5.53%
0
0.5
1
Rho
1.5
2
2.5
MSP
%
•
100
90
80
70
60
50
40
30
20
10
0
Average Delay:10 min
Cnx Prob. 1.77%
0
0.5
1
Rho
1.5
2
2.5
NAS Rho Percentiles
0.8
•
0.7
Rho50
Estimate Rho50 (50th
percentile) and Rho95 (95th
percentile) for all airports
Rho50
•
2000
2001
2002
2003
2004
2005
0.6
0.5
NAS Rho50 and Rho95 are
weighted average of
corresponding airport Rho’s
0.4
1
2
3
4
5
6
7
8
9
10
11
12
Month
1.3
1.1
Rho95
Weights are proportional to
the fraction of NAS operations
at each airport
Rho95
•
1.2
2000
2001
2002
2003
2004
2005
1
0.9
0.8
0.7
0.6
1
2
3
4
5
6
7
Month
8
9
10
11
12
Average Delay
Prob. Of Cancellation
Impact of Rho50 on Delays and Cancellation
Rho50
Rho50
Average Delay
Prob. Of Cancellation
Impact of Rho95 on Delays and Cancellation
Rho95
Rho95
Estimating Flight Delays and Cancellation
Probability
•
Hourly scheduled demand and
capacity at 35 major airports
obtained from ASPM database
Rho50
Cancellation
Probability
Load factor
•
Monthly load factor data
obtained from Database
Products Inc.
Rho95
Average Delay
•
Average flight delay and
proportion of flights cancelled
obtained from ASPM
Cancellation
Probability
Monthly Cancellation Model
-1
-0.75
-0.7
-0.65
-0.6
-0.55
-0.5
-0.45
-0.4
-1.2
Log (P_Canc)
y = -3.3432x - 3.746
R2 = 0.6132
-1.4
-1.6
-1.8
-2
-2.2
-2.4
Log (Load Factor * ( 1 - Rho50 ) )
September 2001 considered outlier, hence excluded
Monthly Delay Model
21
y = 38.62x - 23.84
R2 = 0.6862
19
Avg Delay
17
15
13
11
9
7
5
0.8
0.85
0.9
0.95
1
1.05
Rho95 * (1-P_Canc)
1.1
1.15
1.2
Functional Relationships
Canc. Probability = e-3.75 * [ Loadfactor * ( 1 – Rho50) ] -3.34
Rho50
Cancellation
Probability
Load factor
Rho95
Average Delay
Average Delay = 38.62 * [ Rho95 ( 1 – Canc. Prob.) ] – 23.84
Predicted vs. Observed Prob. Of Cancellation
in 2005
3.5
% of Cancellations
3
2.5
2
Model Cnx
Actual Cnx
1.5
1
0.5
0
Jan
Feb Mar
Apr May Jun
Jul
Month
Aug Sep
Oct
Nov Dec
Predicted vs. Observed Delay in 2005
20
Model Del
Actual Del
18
Average Delay (minutes)
16
14
12
10
8
6
4
2
0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug Sep
Oct
Nov Dec
Applications
NAS Performance Model
NAS Performance Models
VMC capacity of
airport of type j
IMC capacity of
airport of type j
Scheduled demand
for airport of type j
ρS for airport of type j
% time w IMC for
airport of type j
airport ρs for NAS
% demand covered
by airports of type j
airline robustness
factor
Load factor
Non-scheduled demand
for airport of type j
(GA Traffic)
Average Flight
delay (F_DELAY)
Flight Cancel
probability
Airspace ρA for
NAS
Scheduling Padding factor
Passenger
performance
metric
Airport Categorization Based on Rho
Objective : To cluster airports using monthly Rho 50, Rho 95, Average
Delays, Probability of Cancellation.
Method used : Clustering is carried out using K-Means clustering
procedure. This is an iterative procedure wherein airports are assigned to
various clusters so as to minimize the distance from the clusters’ centroids.
Result : The airports can be divided into four categories :
Category 1 : Low Rho50,Low Delay, Low Cancellation probability
Category 2 : Rho50, Delay, Cancellation probability similar to NAS average
Category 3 : “Constrained” airport-set – delay similar to NAS average but
cancellations increase beyond a particular Rho50.
Category 4 : High Rho, High Delay, High Cancellation Probability
Airport Categories
7
6
% of Cancellations
5
4
Category 1
Category 2
Category 3
Category 4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
Rho 50
0.6
0.7
0.8
0.9
1
Airport Categories continued…
25
20
15
Avg Delay
Category 1
Category 2
Category 3
Category 4
10
5
0
0
0.1
0.2
0.3
0.4
0.5
Rho 50
0.6
0.7
0.8
0.9
1
Airport Categories continued
Category 1
Category 2
Category 3
Category 4
TPA
PIT
DEN
PHL
MCO
MIA
IAD
BOS
SLC
CLT
DFW
EWR
BWI
FLL
DTW
ATL
PDX
LAS
DCA
ORD
MDW
SFO
LGA
CVG
JFK
SAN
LAX
PHX
SEA
IAH
MSP
STL
Application: Estimating Passenger Delay
Avg. Flight Delay
Decision Tree
Flight Cancellation
Disrupted passenger
f1 canceled
Passenger delay = flight
delay
Probability of flight
delay > 15 min
direct
trip:
Passenger
Delay
f1 not
canceled
f1 delay
> thresh
f1 not
canceled
f1 delay ≤
thresh
2-leg
trip
Probability of Passenger
missing a connecting
flight: P_miss
f1canceled
P_miss = Prob{delay > layover time | delay > 15 minutes}
f2 canceled
f2 not
canceled
Flight Delay Distribution of Delayed Flights
50
From Individual flight data,
construct histograms of
delayed flights in each time
interval for each month.
Need to determine
distribution of flight delays
45
40
% o f f li g h t s
35
30
25
20
15
10
5
0
1 5 -3 0
3 0 -4 5
4 5 -6 0
6 0 -7 5
7 5 -9 0
Two approaches to achieve the objective
T im e in t e r v a l
1)
Fit one family of distribution for each
month
2)
Regress shape parameters to obtain
distribution of flight delays as a
functional form of average delay and
cancellation probability
1)
Regress each time interval to have a
functional form in terms of average delay
and cancellation probability.
2)
Fit a smoothing spline to the time interval.
3)
Normalize it to obtain distribution of flight
delays
Comparison of two methods
Jul ’03 Delay : 11.62min
•Data calibrated over 48 months
ranging from Jan’00 to Dec ’04
Cnx: 1.3%
50
A c tual
B i-weibull
•10 months used for validation –
5/00,10/00,7/01,4/02, 10/02,
12/03, 7/03, 3/04, 8/04,11/04
% o f flig h ts d el
40
S pline
30
20
10
0
15-30
30-45
45-60
•Both the curves fit well.
50
75-90
90-105
tim e in te r val
Oct ’00 Delay : 13.06min
105-120
120-135
135-150
Cnx : 2.5%
Actual
% of flights delay
•But Bi-weibull distribution is
marginally better than bezier
curve because the rate of descent
initially(15-30 and 30-45 min) in
bi-weibull matches more closely
to the actual than bezier curve.
60-75
Bi-weibull
40
Spline
30
20
10
0
15-30
30-45
45-60
60-75 tim75-90
90-105 105-120
e inte rval
120-135
135-150
Work in Progress
• Introducing a metric (similar to Rho) for enroute
congestion
• Evaluate the impact of demand growth at various
airport categories on NAS Rho Î Delays and
Cancellation