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Queueing Analysis of a Jockeying Model

Author

Listed:
  • Yiqiang Zhao

    (University of Winnipeg, Winnipeg, Manitoba, Canada)

  • Winfried K. Grassmann

    (University of Saskatchewan, Saskatoon, Saskatchewan, Canada)

Abstract

In this paper, we solve a type of shortest queue problem, which is related to multibeam satellite systems. We assume that the packet interarrival times are independently distributed according to an arbitrary distribution function, that the service times are Markovian with possibly different service rates, that each server has its own buffer for packet waiting, and that jockeying among buffers is permitted. Packets always join the shortest buffer(s). Jockeying takes place as soon as the difference between the longest and shortest buffers exceeds a preset number (not necessarily 1). In this case, the last packet in a longest buffer jockeys instantaneously to the shortest buffer(s). We prove that the equilibrium distribution of packets in the system is modified vector geometric. Expressions of main performance measures, including the average number of packets in the system, the average packet waiting time in the system, and the average number of jockeying, are given. Based on these solutions, numerical results are computed. By comparing the results for jockeying and nonjockeying models, we show that a significant improvement of the system performance is achieved for the jockeying model.

Suggested Citation

  • Yiqiang Zhao & Winfried K. Grassmann, 1995. "Queueing Analysis of a Jockeying Model," Operations Research, INFORMS, vol. 43(3), pages 520-529, June.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:3:p:520-529
    DOI: 10.1287/opre.43.3.520
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    Cited by:

    1. Sergei A. Dudin & Olga S. Dudina & Olga I. Kostyukova, 2023. "Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    2. Qi‐Ming He & Jingui Xie & Xiaobo Zhao, 2012. "Priority queue with customer upgrades," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 362-375, August.
    3. P. Patrick Wang, 2000. "Workload distribution of discrete‐time parallel queues with two servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(5), pages 440-454, August.
    4. 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.
    5. 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.

    More about this item

    Keywords

    queues; multichannel; jockeying;
    All these keywords.

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