Steven Lacek

Date of Award

2008

Degree Name

Mathematics

College

College of Science

Type of Degree

M.A.

Document Type

Thesis

First Advisor

Alfred Akinsete

Second Advisor

Yulia Dementieva

Third Advisor

Ariyadasa Aluthge

Abstract

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in which a server with infinite capacity moves among indexed linear service nodes, receives customers at various nodes, and transports the customers to other indexed nodes in the hierarchy. We determine the expected waiting times at the nodes, expected service times, expected number of customers at a given node, expected number in the system, and expected number in service. The probabilities that an arrival finds n customers at a particular node, and in the entire system are obtained.

Subject(s)

Queuing theory.

Customer services - Mathematical models.

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