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An efficient disk-based tool for solving very large Markov models

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Computer Performance Evaluation Modelling Techniques and Tools (TOOLS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1245))

Abstract

Very large Markov models often result when modeling realistic computer systems and networks. We describe a new tool for solving large Markov models on a typical engineering workstation. This tool does not require any special properties or a particular structure in the model, and it requires only slightly more memory than what is necessary to hold the solution vector itself. It uses a disk to hold the state-transition-rate matrix, a variant of block Gauss-Seidel as the iterative solution method, and an innovative implementation that involves two parallel processes: the first process retrieves portions of the iteration matrix from disk, and the second process does repeated computation on small portions of the matrix. We demonstrate its use on two realistic models: a Kanban manufacturing system and the Courier protocol stack, which have up to 10 million states and about 100 million nonzero entries. The tool can solve the models efficiently on a workstation with 128 Mbytes of memory and 4 Gbytes of disk.

This work was supported, in part, by NASA Grant NAG 1-1782.

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Authors and Affiliations

  1. Center for Reliable and High-Performance Computing Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, USA

    Daniel D. Deavours & William H. Sanders

Authors
  1. Daniel D. Deavours
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  2. William H. Sanders
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Editor information

Raymond Marie Brigitte Plateau Maria Calzarossa Gerardo Rubino

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© 1997 Springer-Verlag Berlin Heidelberg

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Deavours, D.D., Sanders, W.H. (1997). An efficient disk-based tool for solving very large Markov models. In: Marie, R., Plateau, B., Calzarossa, M., Rubino, G. (eds) Computer Performance Evaluation Modelling Techniques and Tools. TOOLS 1997. Lecture Notes in Computer Science, vol 1245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022197

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  • DOI: https://doi.org/10.1007/BFb0022197

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63101-9

  • Online ISBN: 978-3-540-69131-0

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