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

Donald A. Dawson (), Jiashan Tang and Yiqiang Q. Zhao ()
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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

Asia-Pacific Journal of Operational Research (APJOR), 2019, vol. 36, issue 04, 1-23

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.

Keywords: Join the shortest queue; performance analysis; M/M/1 queue; birth-and-death process; mean-field; nonlinear master equation; law of large numbers (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0217595919500192

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