Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Authors:
Jeremy T. Bradley;Nicholas J. Dingle;Peter G. Harrison;William J. Knottenbelt
Affiliations:
Department of Computing, Imperial College London, London, United Kingdom;Department of Computing, Imperial College London, London, United Kingdom;Department of Computing, Imperial College London, London, United Kingdom;Department of Computing, Imperial College London, London, United Kingdom
Venue:
Future Generation Computer Systems - Systems performance analysis and evaluation
Year:
2006

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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 are presented and validated against simulation.