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

Author

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

Author_Institution

Dept. of Comput., Imperial Coll. of Sci., Technol. & Med., London, UK

fYear

2003

Abstract

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. The 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.

Keywords

Laplace transforms; Markov processes; iterative methods; parallel processing; Laplace transforms; Markov processes; arbitrarily distributed sojourn times; concurrent systems modelling; distributed computation; distributed voting system model; highly scalable distributed implementation; iterative technique; large semi-Markov models; large structurally unrestricted semi-Markov processes; numerical inversion; passage time; passage time quantiles; transient analysis; transient state distributions; Concurrent computing; Distributed computing; Educational institutions; Iterative algorithms; Kernel; Markov processes; Performance analysis; Stochastic processes; Transient analysis; Voting;

fLanguage

English

Publisher

ieee

Conference_Titel

Parallel and Distributed Processing Symposium, 2003. Proceedings. International

ISSN

1530-2075

Print_ISBN

0-7695-1926-1

Type

conf

DOI

10.1109/IPDPS.2003.1213505

Filename

1213505