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Distributed Computation of Transient State Distributions and Passage Time Quantiles in Large Semi-Markov Models

Jeremy T. Bradley, Nicholas J. Dingle, Peter G. Harrison, William J. Knottenbelt

Journal Article
Future Generation Computer Systems
Volume 22
Issue 7
pp.828–837
August, 2006
Elsevier
DOI 10.1016/j.future.2006.02.011
Abstract

Semi-Markov processes (SMPs) are expressive tools for modelling parallel and distributed systems; they are a generalisation of Markov processes that allow for arbitrarily distributed sojourn times. This paper presents an iterative technique for transient and passage time analysis of large structurally unrestricted semi-Markov processes. Our method is based on the calculation and subsequent numerical inversion of Laplace transforms and is amenable to a highly scalable distributed implementation. Results for a distributed voting system model with up to 1.1 million states arepresented and validated against simulation.

Keywords
AESOP
Stochastic Modelling
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