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Title: | A queueing model with server breakdowns, repairs, vacations, and backup server |
Authors: | Kulshrestha, Rakhee |
Keywords: | Mathematics Markovian arrival process Working vacation Server breakdown and repairs Phase type distribution Matrix analytical method |
Issue Date: | 2020 |
Publisher: | Elsevier |
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. |
URI: | https://www.sciencedirect.com/science/article/pii/S2214716019302076 http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/11180 |
Appears in Collections: | Department of Mathematics |
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