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313822

On A Single Server Queue with Two-Stage Heterogeneous Service and Binomial Schedule Server Vacations

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Last updated: 28 Dec 2024

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Abstract

We analyze a single server queue with Poisson arrivals, two stages of heterogeneous service with different general (arbitrary) service time distributions and binomial schedule server vacations with exponential mean vacation time. After first stage service, the server must provide the second stage service. However, after second stage service, he may take a vacation or may decide to stay in the system. For convenience, we designate this model as M/G1,G2,/M/1 queue. We obtain steady state probability generating functions of queue length for various states of the server. Some particular cases of interest such as M/G1,G2,/M/1, M/M1,M1,/M/1, M/E1/M/1, M/Ek/1 and M/G/1 have been discussed and some known results have been derived.  

DOI

10.21608/esju.2000.313822

Keywords

Poisson arrivals, two-stage heterogeneous service, Steady state, Probability generating function, binomial schedule sever vacations

Volume

44

Article Issue

1

Related Issue

43031

Issue Date

2000-06-01

Publish Date

2000-06-01

Page Start

39

Page End

55

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_313822.html

Detail API

https://esju.journals.ekb.eg/service?article_code=313822

Order

4

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

On A Single Server Queue with Two-Stage Heterogeneous Service and Binomial Schedule Server Vacations

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Article

Created At

28 Dec 2024