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Issue No.09 - September (1996 vol.22)
pp: 615-628
ABSTRACT
<p><b>Abstract</b>—The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix <it>Q</it> of the underlying continuous time Markov chain, where <it>Q</it> is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper we describe such a representation for the class of superposed generalized stochastic Petri nets (SGSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory efficient representation of iteration vectors as well as to a memory efficient structured representation of <it>Q</it>. In consequence the new algorithm is able to solve models which have state spaces with several millions of states, where other exact numerical methods become impracticable on a common workstation.</p>
INDEX TERMS
Stochastic Petri net, superposed GSPN, Markov process, numerical solution algorithm for steady-state analysis tensor/Kronecker algebra, decomposition, reachability analysis, structured representation.
CITATION
Peter Kemper, "Numerical Analysis of Superposed GSPNs", IEEE Transactions on Software Engineering, vol.22, no. 9, pp. 615-628, September 1996, doi:10.1109/32.541433