A Queueing Model with Server Breakdowns, Repairs, Vacations, and Backup Server

Document Type

Article

Publication Date

2020

Publication Title

Operations Research Perspectives

Abstract

Queueing models wherein having a backup server during the absences (caused by vacations and breakdowns) of the main server have found many applications in practice. Such services offered by a backup server can be viewed as the (main) server working during a vacation or during a breakdown period. A backup server offering services can be thought of as the main server working (at a reduced rate) on vacations/repairs. Using Neuts’ versatile point process for the arrivals and modeling the service times with phase type distributions, we propose a model that generalizes some of the previously published ones on working-vacation-breakdown-repair queues. We carry out the steady-state analysis and report interesting illustrative numerical examples. We also prove decomposition results for the rate matrix and the mean number in the system under some special cases.

Volume

7

First Page

1

Last Page

13

DOI

10.1016/j.orp.2019.100131

ISSN

ESSN: 2214-7160

Rights

© 2019 The Authors. Published by Elsevier Ltd

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