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dc.contributor.advisor | Korzeniowski, Andrzej | |
dc.creator | Patterson, Joshua Kent | |
dc.date.accessioned | 2019-05-28T21:58:50Z | |
dc.date.available | 2019-05-28T21:58:50Z | |
dc.date.created | 2019-05 | |
dc.date.issued | 2019-05-08 | |
dc.date.submitted | May 2019 | |
dc.identifier.uri | http://hdl.handle.net/10106/28134 | |
dc.description.abstract | We define the new term ’unreliable service’ where the service itself is unreliable (i.e. may fail). We discuss how this differs from the current literature, and give examples showing just how common this phenomena is in many real-world scenarios. We first consider the classic M/M/1 queue with unreliable service and find some striking similarities with the well studied M/M/1 derivation. Next, we consider the M/M/1 queue with unreliable service and a working vacation. In each of these cases, surprising explicit results are found including positive recurrence conditions, the stationary queue length distribution, and a decomposition of both the queue length and waiting time. We also purpose a number of ideas for future research based on this newly defined phenomenon. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.subject | M/M/1 | |
dc.subject | Unreliable service | |
dc.subject | Queue theory | |
dc.subject | Vacation | |
dc.subject | Working vacation | |
dc.subject | Stochastic processes | |
dc.title | Modeling an M/M/1 Queue with unreliable service and a working vacation | |
dc.type | Thesis | |
dc.degree.department | Mathematics | |
dc.degree.name | Doctor of Philosophy in Mathematics | |
dc.date.updated | 2019-05-28T22:01:00Z | |
thesis.degree.department | Mathematics | |
thesis.degree.grantor | The University of Texas at Arlington | |
thesis.degree.level | Doctoral | |
thesis.degree.name | Doctor of Philosophy in Mathematics | |
dc.type.material | text | |
dc.creator.orcid | 0000-0002-7087-1018 | |
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