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Product-Form Solution in PEPA via the Reversed Process

Peter G. Harrison, Nigel Thomas

Book Chapter
Network Performance Engineering: A Handbook on Convergent Multi-Service Networks and Next Generation Internet
Lecture Notes in Computer Science
Volume 5233
pp.343–356
May, 2011
Springer
ISBN 3642027415
DOI 10.1007/978-3-642-02742-0_16
Abstract

In this paper we use the reversed process to derive expressions for the steady state probability distribution of a class of product-form PEPA models. In doing so we exploit the Reversed Compound Agent Theorem (RCAT) to compute the rates within reversed components of a model. The class of model is, in essence, a generalised, closed, queueing network that might also be solved by mean value analysis, if full distributions are not needed, or approximated using a fluid flow approximation. A general formulation of RCAT is given and the process is illustrated with a running example, including several new variations that consider effects such as multiple servers, competing services and functional rates within actions.

Information from pubs.doc.ic.ac.uk/reversed-process-product-form.