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A tollbooth tandem queue with heterogeneous servers

Author

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  • He, Qi-Ming
  • Chao, Xiuli

Abstract

We study a tandem queueing system with K servers and no waiting space in between. A customer needs service from one server but can leave the system only if all down-stream servers are unoccupied. Such a system is often observed in toll collection during rush hours in transportation networks, and we call it a tollbooth tandem queue. We apply matrix-analytic methods to study this queueing system, and obtain explicit results for various performance measures. Using these results, we can efficiently compute the mean and variance of the queue lengths, waiting time, sojourn time, and departure delays. Numerical examples are presented to gain insights into the performance and design of the tollbooth tandem queue. In particular, it reveals that the intuitive result of arranging servers in decreasing order of service speed (i.e., arrange faster servers at downstream stations) is not always optimal for minimizing the mean queue length or mean waiting time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:177-189
    DOI: 10.1016/j.ejor.2014.01.049
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    References listed on IDEAS

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    1. Benjamin Melamed, 1986. "Note---A Note on the Reversibility and Duality of Some Tandem Blocking Queueing Systems," Management Science, INFORMS, vol. 32(12), pages 1648-1650, December.
    2. Gu, Weihua & Cassidy, Michael J. & Li, Yuwei, 2012. "On the capacity of highway checkpoints: Models for unconventional configurations," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1308-1321.
    3. Papadopoulos, H. T. & O'Kelly, M. E. J., 1993. "Exact analysis of production lines with no intermediate buffers," European Journal of Operational Research, Elsevier, vol. 65(1), pages 118-137, February.
    4. Yiqiang Zhao & Winfried K. Grassmann, 1995. "Queueing Analysis of a Jockeying Model," Operations Research, INFORMS, vol. 43(3), pages 520-529, June.
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    Cited by:

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    2. 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.
    3. Baoxian Chang & Qingqing Ye & Jun Lv & Tao Jiang, 2019. "Mathematical modelling of a tollbooth system with two parallel skill-based servers and two vehicle types," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 479-501, October.

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