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Sojourn time analysis of a queueing system with two‐phase service and server vacations

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  • Tsuyoshi Katayama
  • Kaori Kobayashi

Abstract

We consider a two‐phase service queueing system with batch Poisson arrivals and server vacations denoted by MX/G1‐G2/1. The first phase service is an exhaustive or a gated bulk service, and the second phase is given individually to the members of a batch. By a reduction to an MX/G/1 vacation system and applying the level‐crossing method to a workload process with two types of vacations, we obtain the Laplace–Stieltjes transform of the sojourn time distribution in the MX/G1‐G2/1 with single or multiple vacations. The decomposition expression is derived for the Laplace–Stieltjes transform of the sojourn time distribution, and the first two moments of the sojourn time are provided. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007

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  • Tsuyoshi Katayama & Kaori Kobayashi, 2007. "Sojourn time analysis of a queueing system with two‐phase service and server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 59-65, February.
    • Handle: RePEc:wly:navres:v:54:y:2007:i:1:p:59-65
    DOI: 10.1002/nav.20183
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    References listed on IDEAS

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    1. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
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