On stochastic decomposition in the GI/M/1 queue with single exponential vacation

Authors:
Kyung C. Chae;Sang Min Lee;Ho Woo Lee
Affiliations:
Department of Industrial Engineering, KAIST, Daejeon 305-701, South Korea;Department of Industrial Engineering, KAIST, Daejeon 305-701, South Korea;Department of Systems Management Engineering, Sungkyunkwan University, Suwon 440-746, South Korea
Venue:
Operations Research Letters
Year:
2006

Citing 6
Cited 1

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The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation

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Abstract

We consider a GI/M/1 queueing system in which the server takes exactly one exponential vacation each time the system empties. We derive the PGF of the stationary queue length and the LST of the stationary FIFO sojourn time. We show that both the queue length and the sojourn time can be stochastically decomposed into meaningful quantities.