Date of Award
College of Science
Type of Degree
Dr. Alfred Akinsete, Committee Chairperson
Dr. Anna Mummert, Co-Chairperson
Dr. Avishek Mallick, Committee Member
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.
Adepoju, Gboyega David, "Statistical Analysis of Tandem Queues With Markovian Passages in Porous Mediums" (2019). Theses, Dissertations and Capstones. 1257.