Airport Taxi Operations Modeling:
GreenSim
John Shortle, Rajesh Ganesan, Liya Wang,
Lance Sherry,Terry Thompson, C.H. Chen
September 28, 2007
CENTER FOR AIR TRANSPORTATION SYSTEMS RESEARCH
Outline
• Queueing 101
• GreenSim: Modeling and Analysis
• Tool Demonstration & Case Study
2
CATSR
Motivation
• GreenSim
• Airport as a “black-box”
– 5 stage queueing model
• Schedule and configuration dependent
– Queueing models configured based on historic data
• Stochastic behavior (i.e. Monte Carlo)
– Behavior determined by distributions
• Comparison of procedures (e.g. RNP procedures) and
technologies (e.g. surface management)
– Adjust distributions to reflect changes
• Rapid (< 1 week)
– Fast set-up and run
CATSR
Typical Queueing Process
Customers
Arrive
Common Notation
λ:
Arrival Rate (e.g., customer arrivals per hour)
μ:
Service Rate (e.g., service completions per hour)
1/μ: Expected time to complete service for one customer
ρ:
Utilization: ρ = λ / μ
CATSR
A Simple Deterministic Queue
λ
CATSR
μ
• Customers arrive at 1 min, 2 min, 3 min, etc.
• Service times are exactly 1 minute.
• What happens?
Customers
in system
1
Arrival
Departure
2
3
4
Time (min)
5
6
7
A Stochastic Queue
•
•
•
•
•
CATSR
Times between arrivals are ½ min. or 1½ min. (50% each)
Service times are ½ min. or 1½ min. (50% each)
Average inter-arrival time = 1 minute
Average service time
= 1 minute
What happens?
Arrival
Departure
Customers
in system
1
2
3
4
Time (min)
Service
Times
5
6
7
Stochastic Queue in the Limit
100
90
80
Wait in
Queue
(min)
70
60
50
40
30
20
10
0
0
500
1000
1500
2000
2500
3000
3500
4000
Customer #
• Two queues with same average arrival and service rates
• Deterministic queue: zero wait in queue for every customer
• Stochastic queue: wait in queue grows without bound
7
• Variance is an enemy of queueing systems
CATSR
The M/M/1 Queue
CATSR
0.018
A single server
L=
Avg. # in
System
1− ρ
Normal
0.012
0.01
Service times follow an
exponential distribution
0.008
0.006
0.004
Exponential
0.002
0
40
60
80
100
120
140
x
50
45
40
35
L
ρ
0.014
f(x)
Inter-arrival times
follow an
exponential
distribution
(or arrival process
is Poisson)
Gamma
0.016
30
25
20
15
10
5
0
0
0.2
0.4
0.6
ρ
0.8
1
1.2
160
180
200
220
240
The M/M/1 Queue
CATSR
• Observations
– 100% utilization is not desired
• Limitations
– Model assumes steady-state. Solution does not exist when ρ > 1 (arrival
rate exceed service rate).
– Poisson arrivals can be a reasonable assumption
– Exponential service distribution is usually a bad assumption.
50
45
40
L=
ρ
1− ρ
35
30
L
25
20
15
10
5
0
0
0.2
0.4
0.6
ρ
0.8
1
1.2
The M/G/1 Queue
CATSR
Service times follow a
general distribution
Required inputs:
• λ:
arrival rate
• 1/μ: expected service time
• σ:
std. dev. of service time
35
30
L
25
20
15
10
5
0
0
2
2
ρ +λ σ
L=ρ+
2(1 − ρ )
Avg. # in
System
2
0.2
0.4
0.6
ρ
0.8
1
1.2
μ = 1, σ = 0.5
M/G/1: Effect of Variance
CATSR
18
16
14
12
L
Deterministic
Service
Exponential
Service
10
8
Arrival Rate
Service Rate
Held
Constant
6
4
2
0
0
ρ 2 + λ2σ 2
L=ρ+
2(1 − ρ )
0.5
1
1.5
σ
2
2.5
λ = 0.8, μ = 1 (ρ = 0.8)
3
Other Queues
CATSR
• G/G/1
– No simple analytical formulas
– Approximations exist
• G/G/∞
– Infinite number of servers – no wait in queue
– Time in system = time in service
• M(t)/M(t)/1
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– Arrival rate and service rate vary in time
– Arrival rate can be temporarily bigger than service
rate
Queueing Theory Summary
CATSR
• Strengths
– Demonstrates basic relationships between delay and
statistical properties of arrival and service processes
– Quantifies cost of variability in the process
– Analytical models easy to compute
• Potential abuses
–
–
–
–
Only simple models are analytically tractable
Analytical formulas generally assume steady-state
Theoretical models can predict exceptionally high delays
Correlation in arrival process often ignored
• Simulation can be used to overcome limitations
13
GreenSim
14
CATSR
GreenSim Input/Output Model
15
CATSR
GreenSim Architecture
16
CATSR
Data Analysis Process
17
CATSR
Queueing Simulation Model
CATSR
NAS
λA
Runway
G / G / ∞ / ∞ / FCFS Runway
μ
μ DR
AR
Taxiway Taxi-in
G / G / ∞ / ∞ / FCFS
μ AT times
Turn
around
18
G / G / 1 / ∞ / FCFS
Taxi-out
Taxiway G / G / ∞ / ∞ / FCFS
times
μ DT
Ready to
depart
reservoir
λD
Service Times Settings
19
CATSR
Segment Name
Settings
Arrival Runway
S1~Exponential(1/AAR)
Arrival Taxiway
S2~NOMTI + DLATI- S1
DLATI~Normal (u1 ,σ 1 )
Departure
Taxiway
Departure
Runway
S3~NOMTO + DLATO- S4
DLATO~Normal (u2 ,σ 2 )
S4~Exponential(1/ADR)
Notation
Performance Analysis
CATSR
• Delays (individual, quarterly average, hourly
average, daily average)
• Fuel Fuel = ∑ (TIM ) × ( FF / 1000) × ( NE )
• Emission (HC, CO, NOx, SOx)
j
j
j
j
Emission i = ∑ (TIM j ) × ( FF j / 1000) × ( NE j ) × EI ij
j
TIMj
FFj
NEj
EIij
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= taxi time for type-j aircraft
= fuel flow per time per engine for type-j aircraft
= number of engines used for type-j aircraft
= emissions of pollutant i per unit fuel consumed
for type-j aircraft
EWR Hourly Average Delays
21
CATSR