# Airport Taxi Operations Modeling GreenSim by syz14012

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```									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                              CATSR

• Queueing 101
• GreenSim: Modeling and Analysis
• Tool Demonstration & Case Study

2
Motivation                                                 CATSR

• 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
Typical Queueing Process                                  CATSR

Customers
Arrive

Common Notation
l:   Arrival Rate (e.g., customer arrivals per hour)
m:   Service Rate (e.g., service completions per hour)
1/m: Expected time to complete service for one customer
r:   Utilization: r = l / m
A Simple Deterministic Queue                       CATSR

l                   m

• Customers arrive at 1 min, 2 min, 3 min, etc.
• Service times are exactly 1 minute.
• What happens?

Customers
in system

1   2    3         4       5   6   7
Arrival                   Time (min)
Departure
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       5   6    7
Time (min)
Service
Times
Stochastic Queue in the Limit                                                    CATSR

100

90

80

Wait in    70

60
Queue      50

(min)      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
The M/M/1 Queue                                                                                             CATSR
0.018

0.016        Gamma
A single server               0.014

0.012                              Normal
0.01

f(x)
Inter-arrival times   Service times follow an
0.008

0.006

0.004

follow an        exponential distribution                  0.002

0
Exponential
exponential              50
40   60   80   100   120   140
x
160   180   200   220   240

distribution             45

(or arrival process          40

is Poisson)              35

30
L   25

20

r            15

L=                    10

1 r            5

0
0   0.2   0.4   0.6   0.8                       1                1.2

Avg. # in                                         r
System
The M/M/1 Queue                                                         CATSR

• Observations
– 100% utilization is not desired
• Limitations
– Model assumes steady-state. Solution does not exist when r > 1 (arrival
rate exceed service rate).
– Poisson arrivals can be a reasonable assumption
– Exponential service distribution is usually a bad assumption.
50

45

40

r
35

L=
30

L   25

1 r                20

15

10

5

0
0   0.2   0.4   0.6   0.8   1   1.2

r
The M/G/1 Queue                                                             CATSR

Service times follow a
general distribution
35
Required inputs:                   30

• l:   arrival rate                25       L
• 1/m: expected service time       20

• :
15
std. dev. of service time   10

5

0
0       0.2   0.4   0.6   0.8      1       1.2

r           m = 1,  = 0.5
r l 2     2   2
L=r
2(1  r )
Avg. # in
System
M/G/1: Effect of Variance                                                   CATSR

18

16

14

12

L   10
Exponential
8
Service
Deterministic       6
Arrival Rate
Service                                                                 Service Rate
4
Held
2
Constant
0
0       0.5   1      1.5     2       2.5     3


r 2  l2 2
L=r                                      l = 0.8, m = 1 (r = 0.8)
2(1  r )
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
– Arrival rate and service rate vary in time
– Arrival rate can be temporarily bigger than service
12       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   CATSR

14
GreenSim Input/Output Model                                      CATSR

Outputs:
User adjustable input:                    · Delays (taxi-in, taxi-out)
· Flights Schedule
GreenSim Airport   · ADOC
· Aircraft type
Operations      · Emission
· Capacity (AAR, ADR)
Simulation      · Departure Runway
Queue Size
· Gate Utilization

15
GreenSim Architecture                                                                                      CATSR

Airport Performance
Data Analysis                                               Simulation                   Analysis
Error
Actual taxi-in and     report    Simulation taxi-in
taxi-out times                  and taxi-out times
-

ASPM
Databases

Airport
Service Times Settings
Data                                                                                performance
Individual                                                                                              enhancement
processing
Taxi-in, taxi-out      model
Airport
Capacity Settings        Airport
Data                                              simulation
Airport
processing                           Settings        Queueing
model                          Environmental
analysis
Arrival and Departure                    External                        Emission             model
Schedules                          demands                         Database

16
Data Analysis Process   CATSR

17
Queueing Simulation Model                                                           CATSR

NAS

lA

G / G /  /  / FCFS Runway                             Runway    G / G / 1 /  / FCFS
m                                 m DR
AR

Taxiway G / G /  /  / FCFS
Taxi-out
G / G /  /  / FCFS
Taxiway Taxi-in         times     m DT
m AT times
Turn     depart
around   reservoir

18
Service Times Settings                                      CATSR

Segment Name      Settings                    Notation

Arrival Runway    S1~Exponential(1/AAR)

Arrival Taxiway   S2~NOMTI + DLATI- S1    DLATI~Normal (u1 , 1 )

Departure         S3~NOMTO + DLATO- S4    DLATO~Normal (u 2 , 2 )
Taxiway
Runway

19
Performance Analysis                                            CATSR

• Delays (individual, quarterly average, hourly
average, daily average)
• Fuel Fuel =  (TIM j )  ( FFj /1000)  ( NE j )
j

• Emission (HC, CO, NOx, SOx)
Emissioni =  (TIM j )  ( FFj /1000)  ( NE j )  EI ij
j

TIMj     = taxi time for type-j aircraft
FFj      = fuel flow per time per engine for type-j aircraft
NEj      = number of engines used for type-j aircraft
EIij     = emissions of pollutant i per unit fuel consumed
20                      for type-j aircraft
EWR Hourly Average Delays   CATSR

21
CATSR
EWR Quarterly-Hour Average Delays   CATSR

23
EWR Daily Average Delays   CATSR

24
CATSR



You cannot always replace a random variable with
its average value.
25
The M/M/1 Queue                                                                           CATSR

A single server
Service times follow an
Inter-arrival times   exponential distribution
exponential                0.016        Gamma
distribution               0.014
(or arrival process
0.012
is Poisson)                                                    Normal
0.01
f(x)

0.008

0.006

0.004

0.002
Exponential
0
40    60   80   100   120   140   160   180   200   220   240
x
Poisson Process                                           CATSR

• For many queueing systems, the arrival process is
assumed to be a Poisson process.
• There are good reasons for assuming a Poisson process
– Roughly, the superposition of a large number of independent
(and stationary) processes is a Poisson process.

• However, the assumption is over-used.
• For a Poisson process, inter-arrival times follow an
exponential distribution.
27
Notation for Queues                                                 CATSR

A/B/C/D/E
M for Markovian
A=interarrival time distribution
(exponential) distribution
B=service time distribution               G for General
C= Number of servers                      (arbitrary) distribution

D=Queueing Size Limit

.
E=Service Discipline(FCFS, LCFS, Priority, etc.)

Examples
M/M/1          M/G/1
M/G/1/K        M/G/1/Infinity/Priority
Poisson Distribution                                                                               CATSR

• Ladislaus Bortkiewicz, 1898
• Data
– 10 Prussian army corps units observed over 20 years (200 data points)
– A count of men killed by a horse kick each year by unit
– Total observed deaths: 122
• Number of deaths (per unit per year) is a Poisson RV with
mean 122 / 200 = 0.61.
120

100
Number   Theoretical   Observed
0           108.67         109
Occurrences

80
1            66.29          65
Theoretical     2            20.22          22
60
Observed        3             4.11            3
4             0.63            1
40
5             0.08            0
6             0.01            0
20

0
0     1    2   3    4   5      6

Deaths per Unit per Year
Performance Analysis                                                          CATSR

• Delays (individual, quarterly average, hourly
average, daily average)
• Fuel Fuel =  (TIM )  (FF /1000)  ( NE )
j
j         j                  j

• Emission (HC, CO, NOx, SOx)
Emissioni =  (TIM j )  ( FFj /1000)  ( NE j )  EI ij
j

• Cost (Directing Operation Cost and Delay
Cost)
Total DOC = Fuel Cost  Operationa l Cost
= Fuel Cost  Taxi - in Operation Cost  Taxi - out Operation Cost
= Fuel  Fuel Price  (Taxi - in  Taxi - out times)  DOCPrice
30
Where   DOCPrice = (Labor  Maintenanc e  Owership  Other) = 38.24\$/min
Some Common Distributions                                                                            CATSR

Form of Probability
0.018
Density Function (PDF)
0.016        Gamma
Normal
1
e  ( x  m ) /(2 )
0.014
f ( x) =
2    2

0.012                                                                                 2
Normal
0.01                                                                   Gamma
f(x)

1
0.008                                                                     f ( x) =           x 1e x / 
( )
0.006

0.004                                                                   Exponential
f ( x) = l e  l x
0.002
Exponential
0
40    60   80   100   120   140   160   180   200   220   240
x

Mean = 106
Std. Dev. = 26.9 (normal and gamma)
Some Common Distributions                                                                                      CATSR

Form of Probability
Density Function (PDF)
Normal
1
f ( x) =        e  ( x  m ) /(2 )
2    2

0.018

0.016        Gamma                                                                   2
0.014

0.012                              Normal
0.01                                                                  Gamma
f(x)

0.008
1
0.006
f ( x) =           x 1e x / 
0.004
( )
0.002

0
Exponential
40   60   80   100   120   140   160   180   200   220   240
x
Exponential
f ( x) = l e  l x

Mean = 106
Std. Dev. = 26.9 (normal and gamma)
Queueing Theory                                        CATSR

Queueing Theory: The theoretical study of
waiting lines, expressed in mathematical terms
• How long does a customer wait in line?
• How many customers are typically waiting in
line?
• What is the probability of waiting longer than x
seconds in line?

33
Queueing 101                 CATSR

Queue   Teller

Customers
Need vs. Capability                                                       CATSR

• Mismatch between demand for analysis and
capability of existing tools
• Analysis Capability:
• Airport as Single Queue (Odoni)
– Not enough resolution
• Airport as discrete event simulation (TAAM, Simmod)
– Too much resolution requires:
• Time-consuming detailed rules for individual flight behavior
• Long run times
The M/G/1 Queue                                                             CATSR

Service times follow a
general distribution
35
Required inputs:                   30

• l:   arrival rate                25       L
• 1/m: expected service time       20

• :
15
std. dev. of service time   10

5

0
0       0.2   0.4   0.6   0.8      1       1.2

r           m = 1,  = 0.5
r l 2     2   2
L=r
2(1  r )
Avg. # in
System
M/G/1: Effect of Variance                                                   CATSR

18

16

14

12

L   10
Exponential
8
Service
Deterministic       6
Arrival Rate
Service                                                                 Service Rate
4
Held
2
Constant
0
0       0.5   1      1.5     2       2.5     3


r 2  l2 2
L=r                                      l = 0.8, m = 1 (r = 0.8)
2(1  r )

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