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

by Indra, Ruchi
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International Journal of Applied Information Systems
Foundation of Computer Science (FCS), NY, USA
Volume 1 - Number 8
Year of Publication: 2012
Authors: Indra, Ruchi
10.5120/ijais12-450212

Indra, Ruchi . Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service. International Journal of Applied Information Systems. 1, 8 ( April 2012), 36-44. DOI=10.5120/ijais12-450212

@article{ 10.5120/ijais12-450212,
author = { Indra, Ruchi },
title = { Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service },
journal = { International Journal of Applied Information Systems },
issue_date = { April 2012 },
volume = { 1 },
number = { 8 },
month = { April },
year = { 2012 },
issn = { 2249-0868 },
pages = { 36-44 },
numpages = {9},
url = { https://www.ijais.org/archives/volume1/number8/119-0212/ },
doi = { 10.5120/ijais12-450212 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2023-07-05T10:41:55.296477+05:30
%A Indra
%A Ruchi
%T Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service
%J International Journal of Applied Information Systems
%@ 2249-0868
%V 1
%N 8
%P 36-44
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

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.

References
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Index Terms

Computer Science
Information Sciences

Keywords

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

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