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
                                      AAR, ADR                                                times
                                                                              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
                                                 Ready to    lD
                                         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
     Departure         S4~Exponential(1/ADR)
     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
     follow an                 0.018
    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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