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      Lumpable continuous-time stochastic automata networks

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      Author
      Gusak, O.
      Dayar, T.
      Fourneau, J. M.
      Date
      2003-07-16
      Source Title
      European Journal of Operational Research
      Print ISSN
      0377-2217
       
      1872-6860
       
      Publisher
      Elsevier
      Volume
      148
      Issue
      2
      Pages
      436 - 451
      Language
      English
      Type
      Article
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      Abstract
      The generator matrix of a continuous-time stochastic automata network (SAN) is a sum of tensor products of smaller matrices, which may have entries that are functions of the global state space. This paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous-time SAN in which aggregation is performed automaton by automaton. When there exists a lumpable partitioning induced by the tensor representation of the generator, it is shown that an efficient aggregation-iterative disaggregation algorithm may be employed to compute the steady-state distribution. The results of experiments with two SAN models show that the proposed algorithm performs better than the highly competitive block Gauss-Seidel in terms of both the number of iterations and the time to converge to the solution. © 2002 Elsevier Science B.V. All rights reserved.
      Keywords
      Markov Processes
      Stochastic Automata Networks
      Ordinary Lumpability
      Aggregation With Iterative Disaggregation
      Permalink
      http://hdl.handle.net/11693/11258
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/S0377-2217(02)00431-9
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      • Department of Computer Engineering 1370
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