Airport%20Taxi%20Operations%20Modeling:%20GreenSim

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Airport Taxi Operations ModelingGreenSim

• John Shortle, Rajesh Ganesan, Liya Wang,
• Lance Sherry,Terry Thompson, C.H. Chen
• September 28, 2007

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Outline

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

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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 (lt 1 week)
• Fast set-up and run

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Typical Queueing Process
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 Utilizatio
n r l / m
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A Simple Deterministic Queue
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
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Time (min)
Arrival Departure
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A Stochastic Queue

• 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?

Customers in system
1
2
3
4
5
6
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Time (min)
Service Times
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Stochastic Queue in the Limit
Wait in Queue (min)
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
• Variance is an enemy of queueing systems

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The M/M/1 Queue
A single server
Inter-arrival times follow an exponential
distribution (or arrival process is Poisson)
Service times follow an exponential distribution
L
Avg. in System
r
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The M/M/1 Queue

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

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The M/G/1 Queue
Service times follow a general distribution

• Required inputs
• l arrival rate
• 1/m expected service time
• s std. dev. of service time

L
r
m 1, s 0.5
Avg. in System
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M/G/1 Effect of Variance
Exponential Service
L
Deterministic Service
Arrival Rate Service Rate Held Constant
s
l 0.8, m 1 (r 0.8)
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Other Queues

• G/G/1
• No simple analytical formulas
• Approximations exist
• G/G/8
• 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 rate

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Queueing Theory Summary

• 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

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GreenSim
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GreenSim Input/Output Model
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GreenSim Architecture
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Data Analysis Process
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Queueing Simulation Model
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Service Times Settings
Segment Name Settings Notation
Arrival Runway S1Exponential(1/AAR)
Arrival Taxiway S2NOMTI DLATI- S1 DLATINormal
Departure Taxiway S3NOMTO DLATO- S4 DLATONormal
Departure Runway S4Exponential(1/ADR)
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Performance Analysis

• Delays (individual, quarterly average, hourly
  average, daily average)
• Fuel
• Emission (HC, CO, NOx, SOx)

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 for type-j aircraft
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EWR Hourly Average Delays
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(No Transcript)
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EWR Quarterly-Hour Average Delays
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EWR Daily Average Delays
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You cannot always replace a random variable with
its average value.
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The M/M/1 Queue
A single server
Service times follow an exponential distribution
Inter-arrival times follow an exponential
distribution (or arrival process is Poisson)
Gamma
Normal
Exponential
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Poisson Process

• 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.

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Notation for Queues
A/B/C/D/E
M for Markovian (exponential) distribution
A

interarrival time distribution
G for General (arbitrary) distribution
B

service time distribution
C

Number of servers
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/Prior
ity
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Poisson Distribution

• 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.

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Performance Analysis

• Delays (individual, quarterly average, hourly
  average, daily average)
• Fuel
• Emission (HC, CO, NOx, SOx)
• Cost (Directing Operation Cost and Delay Cost)
• Where

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Some Common Distributions
Form of Probability Density Function (PDF)
Normal
Gamma
Exponential
Mean 106 Std. Dev. 26.9 (normal and gamma)
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Some Common Distributions
Form of Probability Density Function (PDF)
Normal
Gamma
Exponential
Mean 106 Std. Dev. 26.9 (normal and gamma)
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Queueing Theory

• 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?

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Queueing 101
Queue
Teller
Customers
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Need vs. Capability

• 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

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The M/G/1 Queue
Service times follow a general distribution

• Required inputs
• l arrival rate
• 1/m expected service time
• s std. dev. of service time

L
r
m 1, s 0.5
Avg. in System
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M/G/1 Effect of Variance
Exponential Service
L
Deterministic Service
Arrival Rate Service Rate Held Constant
s
l 0.8, m 1 (r 0.8)