Uniformization and hypergraph partitioning for the distributed computation of response time densities in very large Markov models

  • Authors:

  • Nicholas J. Dingle;Peter G. Harrison;William J. Knottenbelt

  • Affiliations:

  • Department of Computing, Imperial College London, 180 Queens Gate, London SW7 2AZ, UK;Department of Computing, Imperial College London, 180 Queens Gate, London SW7 2AZ, UK;Department of Computing, Imperial College London, 180 Queens Gate, London SW7 2AZ, UK

  • Venue:
  • Journal of Parallel and Distributed Computing
  • Year:
  • 2004

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Abstract

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.