Discrete-time GI/Geo/1 queue with multiple working vacations

Authors:
Ji-Hong Li;Nai-Shuo Tian;Wen-Yuan Liu
Affiliations:
College of Economics and Management, YanShan University, Qinhuangdao, People's Republic of China 066004;College of Science, YanShan University, Qinhuangdao, People's Republic of China 066004;College of Economics and Management, YanShan University, Qinhuangdao, People's Republic of China 066004
Venue:
Queueing Systems: Theory and Applications
Year:
2007

Citing 11
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Abstract

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.