ORCID Identifier(s)

0000-0002-7087-1018

Graduation Semester and Year

2019

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Andrzej Korzeniowski

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.

Keywords

M/M/1, Unreliable service, Queue theory, Vacation, Working vacation, Stochastic processes

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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