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Stochastic decomposition in discrete-time queues with generalized vacations and applications
October  2012, 8(4): 939-968. doi: 10.3934/jimo.2012.8.939

## M/M/c multiple synchronous vacation model with gated discipline

 1 Department of Telecommunications, Budapest University of Technology and Economics, Budapest 2 Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501

Received  September 2011 Revised  July 2012 Published  September 2012

In this paper we present the analysis of an M/M/c multiple synchronous vacation model. In contrast to the previous works on synchronous vacation model we consider the model with gated service discipline and with independent and identically distributed vacation periods. The analysis of this model requires different methodology compared to those ones used for synchronous vacation model so far. We provide the probability-generating function and the mean of the stationary number of customers at an arbitrary epoch as well as the Laplace-Stieljes transform and the mean of the stationary waiting time. The stationary distribution of the number of busy servers and the stability of the system are also considered. In the final part of the paper numerical examples illustrate the computational procedure.
This vacation queue is suitable to model a single operator controlled system consisting of more machines. Hence the provided analysis can be applied to study and optimize such systems.
Citation: Zsolt Saffer, Wuyi Yue. M/M/c multiple synchronous vacation model with gated discipline. Journal of Industrial & Management Optimization, 2012, 8 (4) : 939-968. doi: 10.3934/jimo.2012.8.939
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