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Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service

Indra, Ruchi Published in

International Journal of Applied Information Systems
Year of Publication 2012
© 2010 by IJAIS Journal
Info Co-published with IJCA
Authors Indra, Ruchi
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  1. Indra and Ruchi. Article: Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service. International Journal of Applied Information Systems 1(8):36-44, April 2012. BibTeX

    	author = "Indra and Ruchi",
    	title = "Article: Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service",
    	journal = "International Journal of Applied Information Systems",
    	year = 2012,
    	volume = 1,
    	number = 8,
    	pages = "36-44",
    	month = "April",
    	note = "Published by Foundation of Computer Science, New York, USA"


This paper studies the two-dimensional state M/G/1 queue with multiple working vacations in which the server works with different service rate rather than completely terminating the service during a working vacation period, also the server is following non-exhaustive service policy i. e. the server may go on vacation even if there are some customers present in the system. We assume that the server begins the working vacation when the system is empty. The service time during busy period is having general distribution whereas the service time during working vacation period, working vacation time and vacation time of the server are assumed to be exponentially distributed. Explicit probabilities of exact number of arrivals & departures by a given time are obtained. Number of units arrive by time t, number of units depart by time t, waiting time distribution, cumulative distribution for sojourn time, server's utilization time are also presented numerically and graphically both. Some particular cases are derived there from.


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Two-dimensional State Model, Multiple Working Vacation, Non-exhaustive Service, Laplace Transform, Supplementary Variable Technique