Title: The M/M/1 queue with single working vacation and set-up times

Authors: Xiuli Xu, Zhongjun Zhang, Naishuo Tian

Addresses: College of Science, Yanshan University, Qinhuangdao, Hebei, 066004, China. ' College of Science, Yanshan University, Qinhuangdao, Hebei, 066004, China. ' College of Science, Yanshan University, Qinhuangdao, Hebei, 066004, China

Abstract: Using quasi birth and death process and matrix-geometric solution method, an M/M/1 queue with single working vacation and set-up times is discussed in this paper. The distributions for the stationary queue length and waiting time of a customer in the system are derived. Furthermore, stochastic decomposition structures of stationary indices are obtained, and the distributions of the additional queue length and additional delay are gained. Finally, several special cases and numerical examples demonstrate the results.

Keywords: single working vacations; set-up times; quasi birth and death; QBD process; matrix-geometric solution; stochastic decomposition; M/M/1 queues; queuing; stationery indices; stationary queue length; waiting times.

DOI: 10.1504/IJOR.2009.026941

International Journal of Operational Research, 2009 Vol.6 No.3, pp.420 - 434

Published online: 09 Jul 2009 *

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