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

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

Conference or Workshop Paper
PMEO-PDS 2003, International Workshop on Performance Modelling, Evaluation, and Optimization of Parallel and Distributed Systems
April, 2003
IEEE Computer Society Press
ISBN 0-7695-1926-1
DOI 10.1109/IPDPS.2003.1213505

Semi-Markov processes (SMPs) are expressive tools for modelling concurrent systems; they are a generalisation of Markov processes that allow for arbitrarily distributed sojourn times. This paper presents an iterative technique for passage time and transient 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 are presented and compared against simulation.

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