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Letter to the Editor---A Doubled-Ended Queuing Problem of Kendall

Author

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  • James M. Dobbie

    (Applied Science Division, Operations Evaluation Group, Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

The distribution of the difference between two independent Poisson variables has been obtained by Irwin (Irwin, J. O. 1937. The frequency-distribution of the difference between two independent variates following the same Poisson distribution. J. Roy. Stat. Soc. 100 (Part 3) 415--416.), when the means are equal, and by Skellam (Skellam, J. G. 1946. The frequency-distribution of the difference between two Poisson variates belonging to different populations. J. Roy. Stat. Soc. 109 (Part 3) 296.), when the means are unequal. The purpose of this note is to point out that the Irwin-Skellam distribution still applies when (alpha) and (beta) are time-dependent.

Suggested Citation

  • James M. Dobbie, 1961. "Letter to the Editor---A Doubled-Ended Queuing Problem of Kendall," Operations Research, INFORMS, vol. 9(5), pages 755-757, October.
    • Handle: RePEc:inm:oropre:v:9:y:1961:i:5:p:755-757
    DOI: 10.1287/opre.9.5.755
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    Cited by:

    1. Giorno, Virginia & Nobile, Amelia G., 2020. "On a class of birth-death processes with time-varying intensity functions," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    2. Philipp Afèche & Adam Diamant & Joseph Milner, 2014. "Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks," Operations Research, INFORMS, vol. 62(5), pages 1179-1201, October.
    3. Yiwei Chen & Ming Hu, 2020. "Pricing and Matching with Forward-Looking Buyers and Sellers," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 717-734, July.
    4. Chai, Xudong & Liu, Liwei & Chang, Baoxian & Jiang, Tao & Wang, Zhen, 2019. "On a batch matching system with impatient servers and boundedly rational customers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 308-328.
    5. Chai, Xudong & Jiang, Tao & Chang, Baoxian & Liu, Liwei, 2021. "On a multiple priorities matching system with heterogeneous delay sensitive individuals," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. Ying Shi & Zhaotong Lian, 2016. "Equilibrium Strategies and Optimal Control for a Double-Ended Queue," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-18, June.
    7. Gideon Weiss, 2020. "Directed FCFS infinite bipartite matching," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 387-418, December.
    8. Xin Liu, 2019. "Diffusion approximations for double-ended queues with reneging in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 49-87, February.
    9. Yang, Qiaoli & Qiao, Zheng & Yang, Bo & Shi, Zhongke, 2021. "Modeling and uncovering the passenger–taxi dynamic queues at taxi station with multiple boarding points using a Markovian environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    10. Yang, Qiaoli & Yang, Bo & Qiao, Zheng & Tang, Min-an & Gao, Fengyang, 2021. "Impact of possible random factors on queue behaviors of passengers and taxis at taxi stand of transport hubs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).

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