Date of Award

2019

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Dr. Alfred Akinsete, Committee Chairperson

Second Advisor

Dr. Anna Mummert, Co-Chairperson

Third Advisor

Dr. Avishek Mallick, Committee Member

Abstract

Queuing theory is the mathematical study of queues or waiting lines. A queue is formed whenever the demand for service exceeds the capacity to provide service at that point in time. In this thesis, the birth-and-death process is used to model the movement of customers or units into and out of a network of queues in tandem. We start with the theoretical analysis of M/M/1 queues with Poisson arrival and exponential service time with first-come first-served (FCFS) discipline and one service station. We derive the global balance equation for each network. Using both the iterative and the probability generating function, we obtain the probabilities of the state for each service point in the network at equilibrium, and also discuss the statistical properties of the migration of customers from one service point to another. We generalize the probability generating function for the system with n states, and also the marginal for each of the queues in tandem. Specifically, two networks are considered, namely, one that allows customers into the system from the leading queue, and another with porous medium, which allows customers into the system of queues through any service stations. Finally, we simulate a queue network of 10,000 customers and generalize the traffic intensity, the proportion of customers moving from one station to another.

Subject(s)

Queuing theory.

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