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Transient Analysis of Markovian Queueing Model with Bernoulli Schedule and Multiple Working Vacations

by Indra, Renu
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 20 - Number 5
Year of Publication: 2011
Authors: Indra, Renu
10.5120/2426-3257

Indra, Renu . Transient Analysis of Markovian Queueing Model with Bernoulli Schedule and Multiple Working Vacations. International Journal of Computer Applications. 20, 5 ( April 2011), 43-48. DOI=10.5120/2426-3257

@article{ 10.5120/2426-3257,
author = { Indra, Renu },
title = { Transient Analysis of Markovian Queueing Model with Bernoulli Schedule and Multiple Working Vacations },
journal = { International Journal of Computer Applications },
issue_date = { April 2011 },
volume = { 20 },
number = { 5 },
month = { April },
year = { 2011 },
issn = { 0975-8887 },
pages = { 43-48 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume20/number5/2426-3257/ },
doi = { 10.5120/2426-3257 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:07:20.106685+05:30
%A Indra
%A Renu
%T Transient Analysis of Markovian Queueing Model with Bernoulli Schedule and Multiple Working Vacations
%J International Journal of Computer Applications
%@ 0975-8887
%V 20
%N 5
%P 43-48
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Present study obtains the time dependent probabilities of exactly i arrivals and j departures by time t for M/M/1 queueing model with Bernoulli schedule and Multiple working vacation. When a customer has just been served and other customers are present, the server accepts a customer with fix probability p or commences a working vacation of random duration with probability (1- p). Whenever no customers are present, after a service completion or a vacation completion, the server always takes a vacation. And the server is allowed to work at a lower rate during the vacation period. And it is shown that the transient state probabilities can be easily computed with recurrence relations. Also, some important performance measures of this model are evaluated numerically and represented graphically.

References
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Index Terms

Computer Science
Information Sciences

Keywords

Two-dimensional state model Bernoulli schedule Multiple working vacation Laplace transform

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