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Numerical analysis of superposed GSPNs

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1 Author(s)
P. Kemper ; Fachbereich Inf., Dortmund Univ., Germany

The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous-time Markov chain, where Q 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 (GSPNs), 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 Q in consequence the new algorithm is able to solve models which have state spaces with several million states, where other exact numerical methods become impracticable on a common workstation

Published in:

IEEE Transactions on Software Engineering  (Volume:22 ,  Issue: 9 )