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A queueing model with server breakdowns, repairs, vacations, and backup server

Srinivas R. Chakravarthy, Shruti, and Rakhee Kulshrestha

Operations Research Perspectives, 2020, vol. 7, issue C

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.

Keywords: Markovian arrival process; Working vacation; Server breakdown and repairs; Phase type distribution; Matrix analytical method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.orp.2019.100131

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