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Time Dependent Solution of M^[X]/G/1 Queuing Model with Bernoulli Vacation and Balking

by G. Ayyappan, S. Shyamala
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 61 - Number 21
Year of Publication: 2013
Authors: G. Ayyappan, S. Shyamala
10.5120/10204-4992

G. Ayyappan, S. Shyamala . Time Dependent Solution of M^[X]/G/1 Queuing Model with Bernoulli Vacation and Balking. International Journal of Computer Applications. 61, 21 ( January 2013), 20-24. DOI=10.5120/10204-4992

@article{ 10.5120/10204-4992,
author = { G. Ayyappan, S. Shyamala },
title = { Time Dependent Solution of M^[X]/G/1 Queuing Model with Bernoulli Vacation and Balking },
journal = { International Journal of Computer Applications },
issue_date = { January 2013 },
volume = { 61 },
number = { 21 },
month = { January },
year = { 2013 },
issn = { 0975-8887 },
pages = { 20-24 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume61/number21/10204-4992/ },
doi = { 10.5120/10204-4992 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:10:13.128168+05:30
%A G. Ayyappan
%A S. Shyamala
%T Time Dependent Solution of M^[X]/G/1 Queuing Model with Bernoulli Vacation and Balking
%J International Journal of Computer Applications
%@ 0975-8887
%V 61
%N 21
%P 20-24
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we consider a queueing model, wherein the customers are arriving as batches following compound Poisson process. With one of the customer behavior, Balking such that the batch upon arrival may refuses to enter in to the system due to some reasons. Also after completing a service the server may opt for a vacation with probability p, or remain stay back in the system to serve the next customer if any, with probability 1-p. In this model, the customer behavior balking is considered in both the busy time and server vacation time of the system. For this mode. We obtain the time dependent solution and the corresponding steady state solutions. Also, we derive the performance measures, the mean queue size and the average waiting time explicitly.

References
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Index Terms

Computer Science
Information Sciences

Keywords

Batch Arrival Single server Balking Bernoulli vacation Transient state solution Steady state Analysis

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