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Analysis of Tollbooth Systems with Two Tandem Skill-Based Servers and Two Vehicle Types

Author

Listed:
  • Baoxian Chang

    (Nanjing University of Science and Technology)

  • Tao Jiang

    (Shandong University of Science and Technology)

  • Qingqing Ye

    (Nanjing University of Information Science and Technology)

  • Xudong Chai

    (Nanjing University of Science and Technology)

  • Liwei Liu

    (Nanjing University of Science and Technology)

Abstract

The existing tollbooth systems with multi-type vehicles in transportation literature typically assume the servers are either dedicated for each vehicle type or generic for all vehicle types. Conversely, in this paper, we focus on studying two similar systems both with skill-based servers, i.e., each tollbooth can handle a given subset of vehicle types. Meanwhile, we assume that vehicles queue together in a single lane, thus they get served by global First-Come-First-Served discipline. The slight difference between these two systems is the number of exits: one with a single exit (model 1) and the other with two exits (model 2). Nevertheless, it creates large difference in the resolving process. By spectral expansion technique, we obtain a closed-form solution for the system’s steady-state probabilities in the former model and the explicit solution without closed-form expressions in the latter model. By numerical results, we demonstrate how the parameters selection influences system’s performance, along with some intriguing managerial insights. We also use the system of the same structure but with dedicated servers as the baseline for comparisons to show the benefits of skill-based servers.

Suggested Citation

  • Baoxian Chang & Tao Jiang & Qingqing Ye & Xudong Chai & Liwei Liu, 2020. "Analysis of Tollbooth Systems with Two Tandem Skill-Based Servers and Two Vehicle Types," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1145-1167, September.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09758-w
    DOI: 10.1007/s11009-019-09758-w
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    References listed on IDEAS

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    1. Bruneel, Herwig & Mélange, Willem & Steyaert, Bart & Claeys, Dieter & Walraevens, Joris, 2012. "A two-class discrete-time queueing model with two dedicated servers and global FCFS service discipline," European Journal of Operational Research, Elsevier, vol. 223(1), pages 123-132.
    2. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.
    3. He, Qi-Ming & Chao, Xiuli, 2014. "A tollbooth tandem queue with heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 236(1), pages 177-189.
    4. Herwig Bruneel & Willem Mélange & Dieter Claeys & Joris Walraevens, 2017. "A two-class global FCFS discrete-time queueing model with arbitrary-length constant service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 164-178, April.
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