Discrete-time GeoX/G/1 queue with unreliable server and multiple adaptive delayed vacations

Authors:
Yinghui Tang;Xi Yun;Shujuan Huang
Affiliations:
School of Mathematics & Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China;School of Applied Mathematics, University of Electronic Science & Technology of China, Chengdu, Sichuan 610054, China;School of Applied Mathematics, University of Electronic Science & Technology of China, Chengdu, Sichuan 610054, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

In this paper we consider a discrete-time Geo^X/G/1 queue with unreliable server and multiple adaptive delayed vacations policy in which the vacation time, service time, repair time and the delayed time all follow arbitrary discrete distribution. By using a concise decomposition method, the transient and steady-state distributions of the queue length are studied, and the stochastic decomposition property of steady-state queue length has been proved. Several common vacation policies are special cases of the vacation policy presented in this study. The relationship between the generating functions of steady-state queue length at departure epoch and arbitrary epoch is obtained. Finally, we give some numerical examples to illustrate the effect of the parameters on several performance characteristics.