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

Tsuyoshi Katayama and Kaori Kobayashi

Naval Research Logistics (NRL), 2007, vol. 54, issue 1, 59-65

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

Date: 2007
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