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Published in:

Volume 7 Issue 9
September-2020
eISSN: 2349-5162

Unique Identifier

JETIR2009170

Page Number

1250-1257

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Title

A Batch Arrival Queue with an Additional Multiphase Service Channel, Setup and Unreliable Server

ISSN

2349-5162

Cite This Article

"A Batch Arrival Queue with an Additional Multiphase Service Channel, Setup and Unreliable Server", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.7, Issue 9, page no.1250-1257, September-2020, Available :http://www.jetir.org/papers/JETIR2009170.pdf

Abstract

In this paper, we deal with a single non reliable server Mx/G/1 queue with multiphase service and setup. The customers arrive in batches according to a Poisson process. Two types of services are provided to the customers, the first “essential” service and second multiphase “optional” service. After the completion of the essential service, the customer either leaves the system with probability (1-r1) or join the first optional service with probability r1; again after completing the first phase optional service, either he leaves or joins second phase of optional service with probability r2 and similarly in continuation at the end of (k-1)th phase optional service, he may opt kth phase of optional service with probability rk or may leave the system with probability (1-rk). Both essential and optional services are provided by same single server. While the server is working, he is subject to breakdown according to Poisson process. When the server breaks down, he requires repair at repair facility where a repairman renders repair of failed server according to general distribution. By introducing supplementary variable technique and generating function method, some queueing and reliability characteristics of the system are derived. We facilitate numerical results to illustrate the effect of different parameters on several performance indices.

Key Words

Batch arrivals, Unreliable server, Setup time, Multiphase optional service, Supplementary variable, Generating function, Queue size, Reliability.

Cite This Article

"A Batch Arrival Queue with an Additional Multiphase Service Channel, Setup and Unreliable Server", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.7, Issue 9, page no. pp1250-1257, September-2020, Available at : http://www.jetir.org/papers/JETIR2009170.pdf

Publication Details

Published Paper ID: JETIR2009170
Registration ID: 300954
Published In: Volume 7 | Issue 9 | Year September-2020
DOI (Digital Object Identifier):
Page No: 1250-1257
ISSN Number: 2349-5162

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Cite This Article

"A Batch Arrival Queue with an Additional Multiphase Service Channel, Setup and Unreliable Server", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.7, Issue 9, page no. pp1250-1257, September-2020, Available at : http://www.jetir.org/papers/JETIR2009170.pdf




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