Airport Taxi Operations Modeling Green Sim John Shortle

Airport Taxi Operations Modeling: Green. Sim 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 • Green. Sim: Modeling and Analysis • Tool Demonstration & Case Study 2 CAT SR

Motivation • Green. Sim • 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 CAT SR

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: Utilization: r = l / m CAT SR

A Simple Deterministic Queue l CAT SR m • 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 • • • CAT SR 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 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 7 • Variance is an enemy of queueing systems CAT SR

The M/M/1 Queue CAT SR 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 Gamma Normal Exponential

The M/M/1 Queue CAT SR • 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. L r

The M/G/1 Queue CAT SR Service times follow a general distribution Required inputs: • l: arrival rate • 1/m: expected service time • s: std. dev. of service time L r Avg. # in System m = 1, s = 0. 5

M/G/1: Effect of Variance L Deterministic Service CAT SR Exponential Service Arrival Rate Service Rate Held Constant s l = 0. 8, m = 1 (r = 0. 8)

Other Queues CAT SR • 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)/1 12 – Arrival rate and service rate vary in time – Arrival rate can be temporarily bigger than service rate

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 13 CAT SR

Green. Sim 14 CAT SR

Green. Sim Input/Output Model 15 CAT SR

Green. Sim Architecture 16 CAT SR

Data Analysis Process 17 CAT SR

Queueing Simulation Model 18 CAT SR

Service Times Settings 19 CAT SR Segment Name Settings Arrival Runway S 1~Exponential(1/AAR) Arrival Taxiway S 2~NOMTI + DLATI- S 1 DLATI~Normal Departure Taxiway Departure Runway S 3~NOMTO + DLATO- S 4 DLATO~Normal S 4~Exponential(1/ADR) Notation

Performance Analysis CAT SR • Delays (individual, quarterly average, hourly average, daily average) • Fuel • Emission (HC, CO, NOx, SOx) TIMj FFj NEj EIij 20 = 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 CAT SR

CAT SR

EWR Quarterly-Hour Average Delays 23 CAT SR

EWR Daily Average Delays 24 CAT SR

CAT SR You cannot always replace a random variable with its average value. 25

The M/M/1 Queue CAT SR A single server Inter-arrival times follow an exponential distribution (or arrival process is Poisson) Service times follow an exponential distribution Gamma Normal Exponential

Poisson Process CAT SR • 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 CAT SR A/B/C/D/E A=interarrival time distribution B=service time distribution C= Number of servers M for Markovian (exponential) distribution G for General (arbitrary) distribution D=Queueing Size Limit E=Service Discipline(FCFS, LCFS, Priority, etc. ). Examples M/M/1 M/G/1/K M/G/1/Infinity/Priority

Poisson Distribution CAT SR • 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.

Performance Analysis CAT SR • Delays (individual, quarterly average, hourly average, daily average) • Fuel • Emission (HC, CO, NOx, SOx) • Cost (Directing Operation Cost and Delay Cost) 30 Where

Some Common Distributions CAT SR Form of Probability Density Function (PDF) Gamma Normal Gamma Exponential Mean = 106 Std. Dev. = 26. 9 (normal and gamma)

Some Common Distributions CAT SR Form of Probability Density Function (PDF) Normal Gamma Exponential Mean = 106 Std. Dev. = 26. 9 (normal and gamma)

Queueing Theory CAT SR 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 Queue Customers CAT SR Teller

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 CAT SR

The M/G/1 Queue CAT SR Service times follow a general distribution Required inputs: • l: arrival rate • 1/m: expected service time • s: std. dev. of service time L r Avg. # in System m = 1, s = 0. 5

M/G/1: Effect of Variance L Deterministic Service CAT SR Exponential Service Arrival Rate Service Rate Held Constant s l = 0. 8, m = 1 (r = 0. 8)