Title

Non-existence of product-form solutions for some closed discrete-time queueing networks

Date of Award

2006

Availability

Article

Degree Name

Doctor of Philosophy (Ph.D.)

Department

Mathematics

First Committee Member

Victor C. Pestien, Committee Chair

Abstract

This paper illustrates that for some closed discrete-time queueing networks, product-form solutions do not exist. We begin by formulating a precise definition of "product-form family of equilibrium vectors". We then proceed by considering those networks where customers after being served at any given node can either stay put or move to one of the two adjacent nodes. Afterwards we present a similar result for a more general First-Come-First-Served protocol where customers can either move to any other node in the system or stay put. In some cases, explicit solutions for the equilibrium vectors will be displayed and utilized within the proofs, and in other cases all the work will be done without the aid of explicit solutions.

Keywords

Mathematics

Link to Full Text

http://access.library.miami.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3243118