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Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues

Author

Listed:
  • Donald A. Dawson

    (School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada)

  • Jiashan Tang

    (School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada2College of Science, Nanjing University of Posts, and Telecommunications, Nanjing, Jiangsu 210023, P. R. China)

  • Yiqiang Q. Zhao

    (School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada)

Abstract

Consider a queueing network with a large number N nodes, in which each queue has a dedicated input stream, and, in addition, there is an extra input stream, balancing the network load by directing its arrivals to the shortest queue(s). A mean field interaction model is set up to study the performance of this network in terms of limiting results. One of our results shows that the stationary behavior of any of the queues is approximated by that of the M/M/1 queue with a modified arrival rate when the queue length is around zero.

Suggested Citation

  • Donald A. Dawson & Jiashan Tang & Yiqiang Q. Zhao, 2019. "Performance Analysis of Joining the Shortest Queue Model Among a Large Number of Queues," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-23, August.
    • Handle: RePEc:wsi:apjorx:v:36:y:2019:i:04:n:s0217595919500192
    DOI: 10.1142/S0217595919500192
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    References listed on IDEAS

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    1. Johri, Pravin K., 1989. "Optimality of the shortest line discipline with state-dependent service rates," European Journal of Operational Research, Elsevier, vol. 41(2), pages 157-161, July.
    2. Yang Zhang & Edwin K. P. Chong & Jan Hannig & Donald Estep, 2013. "Continuum Modeling and Control of Large Nonuniform Wireless Networks via Nonlinear Partial Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-16, April.
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