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Queuing Models with Lane Selection: A New Class of Problems

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  • Benjamin L. Schwartz

    (Informatics, Rockville, Maryland)

Abstract

This paper presents a new class of queuing models. There are n distinct types of customers and n distinct types of service facilities. Some customers can be processed at any service facility, but other customer types can only use selected ones among the service-facility types. This class of model is named “lane selection,” abbreviated LS, since the arriving customers with some freedom of choice must select the queue, or lane, in which they are to be processed through the system. It is shown by example that many physical situations are represented more accurately by this model than by more conventional ones. However, in analysis, the LS concept raises many theoretical difficulties. For a number of special cases, this paper obtains in explicit form as functions of the model parameters the mean queue lengths and waiting times for the different classes of customers.

Suggested Citation

  • Benjamin L. Schwartz, 1974. "Queuing Models with Lane Selection: A New Class of Problems," Operations Research, INFORMS, vol. 22(2), pages 331-339, April.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:2:p:331-339
    DOI: 10.1287/opre.22.2.331
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    Cited by:

    1. 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.
    2. P S Ansell & K D Glazebrook & C Kirkbride, 2003. "Generalised ‘join the shortest queue’ policies for the dynamic routing of jobs to multi-class queues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(4), pages 379-389, April.
    3. Boronico, Jess S. & Siegel, Philip H., 1998. "Capacity planning for toll roadways incorporating consumer wait time costs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(4), pages 297-310, May.
    4. Li, Yongli & Gao, Xin & Xu, Zhiwei & Zhou, Xuanrui, 2018. "Network-based queuing model for simulating passenger throughput at an airport security checkpoint," Journal of Air Transport Management, Elsevier, vol. 66(C), pages 13-24.
    5. Marina Milenković & Miloš Nikolić & Draženko Glavić, 2022. "Optimization of toll road lane operation: Serbian case study," Operational Research, Springer, vol. 22(5), pages 5297-5322, November.
    6. Lee, Adrian J. & Jacobson, Sheldon H., 2011. "The impact of aviation checkpoint queues on optimizing security screening effectiveness," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 900-911.

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