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1Dr. Indra Rani is a Professor and Chairperson of the Department of Statistics & O.R., Kurukshetra University, Kurukshetra. Her research interests are Application of Stochastic Process in Operations Research. She has published various research papers at international and national journals. She can be reached at radha_indra@rediff.com
2Ms. Ruchi is currently a research scholar in the Department of Statistics & O.R., Kurukshetra University, Kurukshetra. Her research interest is Working Vacation Queueing Systems. She can be reached at rup_ruchi@yahoo.co.in
This paper analyses the transient behaviour of a first-come, first-served, two-dimensional state, non-Markovian queueing system with multiple working vacations such that the server works with different service rate rather than completely stop service during a vacation period. This queue approximates a multi-queue system in which each queue operates either at a fast service rate or a nominal service rate, and the fast service mode cyclically moves from queue to queue with an exhaustive schedule. For such a queue, we provide a recursive method, using the supplementary variable technique as the remaining service time during busy period, to obtain the Laplace transform of the probabilities of exact number of arrivals and departures by a given time t, number of units arrived by time t and number of units departed by time t. It is assumed that the service time during working vacation period and working vacation times are both exponentially distributed. The emphasis in this paper is theoretical, but numerical assessment of operational consequences is also given and presented graphically for exponential service time during the busy period. Finally, some particular cases are derived.
Non-Markovian queueing model; Multiple working vacations; Two-dimensional state queueing model; Laplace transform; Supplementary variable technique
JEL Classification: C44
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