Passage-time computation and aggregation strategies for large semi-Markov processes

Department of Computing, Imperial College London, 180 Queen’s Gate, London SW7 2BZ, United Kingdom
Performance Evaluation (Impact Factor: 1.25). 03/2011; 68(3):221-236. DOI: 10.1016/j.peva.2010.10.003
Source: DBLP


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.

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    • "The biggest drawback is the limitation this imposes of having to hold the entire state-space of the model in the memory of one machine, whereas with HYDRA it is distributed across multiple machines. Our recent work on aggregation suggests ways in which the state-spaces of models could be reduced in size, however [25]. We will also investigate the benefits of exploiting Amazon's dedicated Elastic Block Store (EBS) to produce a diskbased tool [26], [27], [28]. "
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