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Uniformization and Hypergraph Partitioning for the Distributed Computation of Response Time Densities in Very Large Markov Models

Nicholas J. Dingle, Peter G. Harrison, William J. Knottenbelt

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Journal Article
Journal of Parallel and Distributed Computing
Volume 64
Issue 8
July, 2004
DOI 10.1016/j.jpdc.2004.03.017

Fast response times and the satisfaction of response time quantile targets are important performance criteria for almost all transaction processing and computer-communication systems. We present a distributed uniformization-based technique for obtaining response time densities from very large unstructured Markov models. Our method utilizes hypergraph partitioning to minimize inter-processor communication while maintaining a good load balance. The resulting algorithm scales well on a distributed-memory parallel computer and, unusually for a problem of this nature, also produces near-linear speed-ups on a network of commodity PCs linked by 100 Mbps ethernet. We demonstrate our approach by calculating passage time densities in a 1.6 million state Markov chain derived from a Generalized Stochastic Petri net model and a 10.8 million state Markov chain derived from a closed tree-like queueing network. We compare the accuracy of our results with simulation and known analytical solutions and contrast the run-time performance of our technique with an approach based on numerical Laplace transform inversion.

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