Computing Publications

Publications Home » Reversed processes, product forms...

Reversed processes, product forms and a non-product form

Peter G. Harrison

Journal Article
Linear Algebra and Its Applications
Volume 386
pp.359–381
July, 2004
Elsevier
DOI 10.1016/j.laa.2004.02.020
Abstract

The equilibrium joint state probabilities of interacting Markov processes are obtained in a hierarchical way, by finding the reversed process of the interaction in terms of the reversed processes of its components. From a reversed process, a product-form solution for the joint state probabilities follows directly. The method uses a Markovian process algebra formalism and generalizes the recent Reversed Compound Agent Theorem (RCAT) to solve a diverse class of concurrent systems. This class includes processes with shared, exclusive resources, a customer-oriented specification of a last-come-first-served (LCFS) queue with Coxian service times and an extended PS queue with a non-product form solution. From these results, a new, very short proof of the BCMP theorem ensues. The principal advantage of the methodology is its potential for mechanisation and symbolic implementation. Indeed, many non-standard product-forms have emerged directly from the compositional approach.

Keywords
AESOP
PDF of full publication (307 kilobytes)
(need help viewing PDF files?)
GZipped Postscript of full publication (208 kilobytes)
(need help viewing GZipped Postscript files?)
BibTEX file for the publication
N.B.
Conditions for downloading publications from this site.
 

pubs.doc.ic.ac.uk: built & maintained by Ashok Argent-Katwala.