Graduation Semester and Year
2016
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Andrzej Korzeniowski
Abstract
There are many types of systems which can be dubbed servers, i.e. a retail checkout counter, a shipping company, a web server, or a customer service hotline. All of these systems have common general behavior: requests or customers arrive via a stochastic process, the service times vary randomly, and each request increases the stress on the server for some interval of time. A general stochastic model that describes the reliability of a server can provide the necessary informationfor optimal resource allocation and efficient task scheduling, leading to significant cost savings and improved performance metrics. In this work, we consider several generalizations of existing stochastic reliability models that incorporate random workloads, load-balancing allocation, and clustered tasks. The efficiency of the described servers is studied extensively in order to facilitate the design and implementation of control policies for fast-paced environments such as IT applications. Finally, a method to determine the reliability of any network of general servers, both correlated and uncorrelated, is presented.
Keywords
Reliability theory, Stochastic processes, Networks, Non homogenous Poisson process, Servers, Queuing theory
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
Traylor, Rachel, "Stochastic Reliability Models for a General Server and Related Networks" (2016). Mathematics Dissertations. 223.
https://mavmatrix.uta.edu/math_dissertations/223
Comments
Degree granted by The University of Texas at Arlington