NAS Strategy Simulator–
Fleet Mix Module
Chieh-Yu Hsiao
Mark Hansen
10/20/03
1
Outline
‰ The Problem
‰ Approaches
¾Framework
¾Four models
9 Equilibrium Flow Model
9 Load Factor Model
9 Aircraft Size Model
9 Fleet Mix Model
‰ Future Research
2
Problem
OD Demand
Information
Fleet Mix Module
‰ Given the OD
demand, predict
¾ Segment traffic
¾ Fleet mix
Origin
‰ Scope: 31
Benchmark Airports
Fleet Mix
Hub 1
Segment 1
Hub 2
Direct
:
Segment 2
Destination
Hub n
3
Framework
OD
Traffic
Hub
Choice
Segment
Traffic
Load
Factor
Model
Segment
Seats
A/C
Size
Model
Segment
Flights
Fleet Mix
Model
Segment
Flights
By A/C
Category
Equilibrium Flow Model
Hub 1
Segment 1
Origin
Hub 2
Direct
:
Segment 2
Destination
Hub n
4
Equilibrium Flow Model
OD Pax
Hub Choice Model
Distance
SegPaxn
HHI
Delayn
Choice
Probabilities
SegPaxn+1
Initial Values
n=0
Distance
SegPax0=OD Pax
HHI
Delay0
n=n+1
System Update
Converge?
SegPaxn+1
SegPaxn
No
SegPaxn+1
Delayn+1=f (Airport Pax n+1,
Fixed effects)
Yes
Equilibrium
SegPax
Equilibrium
Airport Pax
5
Hub Choice Model
‰ Allocates OD Traffic to Segment Traffic—
Route (hub) Choice
‰ Nested Logit Model
¾ Direct or one-stop connecting
¾ Conditioned on connecting, choose the
connecting airport(hub)
Direct
Connecting
Hub1 …
Hub n
6
Model Specification
Pod ( Direct ) =
exp(Vod ,i )
exp(Vdirect )
;
P
(
Hub
:
i
|
Connect
)
=
od
exp(Vdirect ) + (∑ exp( βVod ,i ))1/ β
∑ exp(Vod ,i )
i
i
Vdirect = c0 + b01 ln(distDod ) + b02 ln( paxDod ) + b03 ln( HHI od )
Vod ,i = b1 ln(distCo −i − d ) + b2 ln(max paxoi / di ) + b3 ln(min paxoi / di ) + b4 ln( Delayi )
‰
‰
‰
‰
‰
‰
distD/ distC : direct /connecting (O-hub-D) distance between OD
paxD: # of pax of the direct segment
maxpax: # of pax of the higher traffic segment
minpax: # of pax of the lower traffic segment
HHI: Herfindahl-Hirschman Index (0 to 1) of the direct segment od
delay: the delay (the number of delayed operations per 1000
operations) of connecting airport i
7
Model Estimation
Estimate
Parameter
Standard
Error
(*10-4)
P-value
ln( Dist. of Connect)
-2.929
0.984
[.000]
ln( Max Pax of Connect)
0.226
0.179
[.000]
ln(Min Pax of Connect)
0.665
0.201
[.000]
ln(Delay of Connect)
-0.073
0.063
[.000]
β , 1/(inclusive value)
1.453
0.399
[.000]
Constant of Direct
2.386
2.295
[.000]
ln(Dist. of Direct)
-3.027
0.847
[.000]
ln(Seg. Pax of Direct)
0.986
0.127
[.000]
ln(HHI of Direct)
-0.272
0.294
[.000]
Associated Factor
ρˆ 2 = 0 . 5555
N=39,298,503 (100,951 routes)
8
Equilibrium Flow Example
‰
Segment and OD density, and delay effects (segment pax are endogenous)
Delay1=30
Background
Pax=105
O
Dist1=1800
Hub 1
Equilibrium
(After 7
iterations)
Background
Pax=105
1,000 OD pax
Dist=1500
Initial Pax=OD pax, HHI=0.9
Background
Pax=105
Background
Pax=105
Hub 2
Dist2=2000
Delay2=30
D
Assigned
Pax=611
Background
Pax=105
O
Assigned Pax=0
Background
Pax=105
10,000 OD pax
Background
Pax=105
Equilibrium
(After 10
iterations)
O
Background
Pax=105
Assigned
Pax=389
Assigned
Pax=2350
D
Background
Pax=105
Background
Pax=105
Assigned Pax=6165
Background
Pax=105
Assigned
Pax=1485
D
Background
Pax=105
9
NAS Equilibrium- Segment Level
10
NAS Equilibrium- Airport Level
7
Actual EQ pax (millions)
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
Predicted EQ pax (millions)
11
Equilibrium Prediction
‰ Possible situations:
¾Multiple Equilibria
¾May depend on the initial values and
convergence criteria
¾Some equilibria may differ from the
current status
12
Equilibria- initial values
Segment Level
Airport Level
13
Equilibria- Convergence Rules
Segment Level
Airport Level
14
Policy Experiment—
ORD Delay Improvement
‰ Delay:
30
ln( Delay it ) = α 0 + ∑ α i * C i + β 1 * Pax it + ε it
i =1
‰ Airport fixed delay effect improved:
α ORD = 1.70542
Current
α ORD ' = α DEN = 0.42284
Delay (ops/1000 ops)
Improved
Airport Yearly (10%) Pax (m illions)
15
Policy Experiment—
New Equilibrium Results
‰ ORD:
+1,164,665
‰ Other hubs:
-876,506
‰ Net effect on
the system:
+288,159
‰ ORD attracts:
1200
800
600
400
200
0
AT
BOL
S
BW
C I
L
C T
VG
D
C
D A
E
D N
FW
D
T
EWW
H R
N
L
IA
D
IA
H
JF
LA K
S
LA
LGX
M A
C
M O
E
M
M
IA
M
S
O P
R
PHD
PH L
X
P
SAIT
SEN
SF A
SL O
C
ST
TP L
A
Changed Pax (*1000)
1000
-200
Connecting Airports
¾ ¾ from
competing hubs
¾ ¼ from “direct”
routes
16
Conclusions—Hub Choice Model
‰ Conclusions
¾The equilibrium model reflects the
economics of the route choice
¾Conserves OD traffic at airport level while
allowing connecting traffic to vary
¾A tool for policy analysis
17
Future works (1/2)
‰ Model Structure (Better Equilibrium
Estimation)
¾Positive Feedback system
¾Dynamics of the system
¾Travelers’ behavior: flexible model form &
Endogeneity
¾Computation efficiency
18
Future works (2/2)
‰ Affecting Factors Modeling
¾Delay
¾Market Concentration (HHI)
¾Other factors, for example, airport
capacity
‰ System-wide Effects Estimation
¾Better Policy Analysis Tool
19
Questions?
20