ORCID Identifier(s)

0000-0002-0997-5766

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

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

Share

COinS