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
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Patterson, Joshua Kent, "Modeling an M/M/1 Queue with unreliable service and a working vacation" (2019). Mathematics Dissertations. 168.
https://mavmatrix.uta.edu/math_dissertations/168
Comments
Degree granted by The University of Texas at Arlington