Analysing queueing at toll plazas using a coupled, multiple-queue, queueing system model: application to toll plaza design

ABSTRACT A vehicle approaching a toll plaza observes the queues at each of the available toll-lanes before choosing which to join. This choice process, the arrival process of vehicles and the service characteristics of the toll-booths, affect the queues and delay the drivers. In this paper, queueing at a toll plaza is modelled as a multiple-queue queueing system where the arrival process to a queue (toll-lane) is dependent on the state of all the queues. In the past, such systems have been modelled mathematically only for two queues and are not applicable for toll plazas with three or more toll-lanes. The proposed model determines the steady-state probability density function (pdf) for the queues at large toll plazas. This study is used to determine the number of toll-lanes or the length of the upstream queueing area required to achieve certain user-specified levels-of-service. Expected delay and maximum queue length are used as level-of-service measures. Indicative design charts are also provided.

[1]  Kaan Ozbay,et al.  Microscopic Modeling of Lane Selection and Lane Changing at Toll Plazas , 2009 .

[2]  Partha Chakroborty,et al.  Modeling Automobile Drivers' Toll-Lane Choice Behavior at a Toll Plaza , 2012 .

[3]  Benjamin L. Schwartz,et al.  Queuing Models with Lane Selection: A New Class of Problems , 1974, Oper. Res..

[4]  Rami Harb,et al.  Calibration and Verification of SHAKER, a Deterministic Toll Plaza Simulation Model , 2009 .

[5]  Christiane Metzner,et al.  TollSim: Simulation and evaluation of toll stations , 2004 .

[6]  J. P. C. Blanc.  The Power-Series Algorithm Applied to the Shortest-Queue Model , 1992, Oper. Res..

[7]  Seongmoon Kim,et al.  The Toll Plaza Optimization Problem: Design, Operations, and Strategies , 2009 .

[8]  Kenneth Dixon,et al.  Introduction to Stochastic Modeling , 2011 .

[9]  Leslie C. Edie,et al.  Traffic Delays at Toll Booths , 1954, Oper. Res..

[10]  Moshe Ben-Akiva,et al.  Discrete Choice Analysis: Theory and Application to Travel Demand , 1985 .

[11]  Partha Chakroborty,et al.  Modelling Automobile Driver’s Toll-Lane Choice Behaviour at a Toll Plaza , 2012 .

[12]  John Danko,et al.  SIMULATION-BASED APPROACH TO EVALUATING OPTIMAL LANE STAFFING REQUIREMENTS FOR TOLL PLAZAS , 1995 .

[13]  J. Blanc.  On a numerical method for calculating state probabilities for queueing systems with more than one waiting line , 1987 .

[14]  L. Thurstone.  A law of comparative judgment. , 1994 .

[15]  Andrew J. Junga,et al.  TPASS: dynamic, discrete-event simulation and animation of a Toll Plaza , 1992, WSC '92.

[16]  J. P. C. Blanc,et al.  Performance Analysis and Optimization with the Power-Series Algorithm , 1993, Performance/SIGMETRICS Tutorials.

[17]  J. Hunter.  Two Queues in Parallel , 1969 .

[18]  B. W. Conolly,et al.  THE AUTOSTRADA QUEUEING PROBLEM , 1984 .

[19]  Essam Radwan,et al.  New Model for Evaluation of Traffic Operations at Electronic Toll Collection Plazas , 2000 .

[20]  Gerard Hooghiemstra,et al.  Power series for stationary distributions of coupled processor models , 1988 .