Date of Award

Fall 2017

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics and Statistics

First Advisor

Myron Hlynka

Second Advisor

Percy Brill

Keywords

Fluid queues, level crossing, queues, sample path

Rights

CC BY-NC-ND 4.0

Abstract

This dissertation is concerned with the application of the level crossing method on fluid queues driven by a background process. The basic assumption of the fluid queue in this thesis is that during the busy period of the driving process, the fluid content fills at net rate r_1, and during the idle period of the driving process, the fluid content, if positive-valued, empties at a rate r_2. Moreover, nonempty fluid content, leaks continuously at a rate r_2. The fluid models considered are: the fluid queue driven by an M/G/1 queue in Chapter 2, the fluid queue driven by an M/G/1 queue with net input and leaking rate depending on fluid level, and type of arrivals in the driving M/G/1 queue, in chapter 3, and the fluid queue driven by an M/G/1 queue with upward fluid jumps in Chapter 4. In addition, a triangle diagram has been introduced in this thesis as a technique to visualize the proportion of time that the content of the fluid queue is increasing or decreasing during nonempty cycles. Finally, we provide several examples on how the probability density function of the fluid level is related to the probability density function of the waiting time of M/G/1 queues with different disciplines.

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