Analysis of Queueing Systems with Synchronous Single Vacation for Some Servers

Authors:
Zhe G. Zhang;Naishuo Tian
Affiliations:
Department of Decision Sciences, College of Business and Economics, Western Washington University, Bellingham, WA 98225-9077, USA george.zhang@wwu.edu;Department of Mathematics, Yanshan University, Qinhuangdao, 066004, China
Venue:
Queueing Systems: Theory and Applications
Year:
2003

Citing 5
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Abstract

We study a multi-server M/M/c type queue with a single vacation policy for some idle servers. In this queueing system, if at a service completion instant, any d (d ⩽c) servers become idle, these d servers will take one and only one vacation together. During the vacation of d servers, the other c−d servers do not take vacation even if they are idle. Using a quasi-birth-and-death process and the matrix analytic method, we obtain the stationary distribution of the system. Conditional stochastic decomposition properties have been established for the waiting time and the queue length given that all servers are busy.