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

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  • Partha Chakroborty
  • Rahul Gill
  • Pranamesh Chakraborty

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.

Suggested Citation

  • Partha Chakroborty & Rahul Gill & Pranamesh Chakraborty, 2016. "Analysing queueing at toll plazas using a coupled, multiple-queue, queueing system model: application to toll plaza design," Transportation Planning and Technology, Taylor & Francis Journals, vol. 39(7), pages 675-692, October.
    • Handle: RePEc:taf:transp:v:39:y:2016:i:7:p:675-692
    DOI: 10.1080/03081060.2016.1204090
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    References listed on IDEAS

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    1. Leslie C. Edie, 1954. "Traffic Delays at Toll Booths," Operations Research, INFORMS, vol. 2(2), pages 107-138, May.
    2. J. P. C. Blanc, 1992. "The Power-Series Algorithm Applied to the Shortest-Queue Model," Operations Research, INFORMS, vol. 40(1), pages 157-167, February.
    3. Benjamin L. Schwartz, 1974. "Queuing Models with Lane Selection: A New Class of Problems," Operations Research, INFORMS, vol. 22(2), pages 331-339, April.
    4. Kim, Seongmoon, 2009. "The toll plaza optimization problem: Design, operations, and strategies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(1), pages 125-137, January.
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