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Passage-time Computation and Aggregation Strategies for Large Semi-Markov Processes

Marcel C. Guenther, Nicholas J. Dingle, Jeremy T. Bradley, William J. Knottenbelt

Journal Article
Performance Evaluation
Volume 68
Issue 3
March, 2011
DOI 10.1016/j.peva.2010.10.003

High-level semi-Markov modelling paradigms such as semi-Markov stochastic Petri nets and process algebras are used to capture realistic performance models of computer and communication systems but often have the drawback of generating huge underlying semi-Markov processes. Extraction of performance measures such as steady-state probabilities and passage-time distributions therefore relies on sparse matrix-vector operations involving very large transition matrices. Previous studies have shown that exact state-by-state aggregation of semi-Markov processes can be applied to reduce the number of states. This can, however, lead to a dramatic increase in matrix density caused by the creation of additional transitions between remaining states. Our paper addresses this issue by presenting the concept of state space partitioning for aggregation.

We present a new deterministic partitioning method which we term barrier partitioning. We show that barrier partitioning is capable of splitting very large semi-Markov models into a number of partitions such that first passage-time analysis can be performed more quickly and using up to 99% less memory than existing algorithms.

Performance Modelling and Analysis
Stochastic Modelling

Submitted September 2009. Accepted 25 October 2010.

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