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Transient Analysis of Superposed GSPNs
March/April 1999 (vol. 25 no. 2)
pp. 182-193

Abstract—The paper considers transient analysis using randomization for superposed generalized stochastic Petri nets (GSPNs). Since state space explosion implies that space is the bottleneck for numerical analysis, superposed GSPNs profit from the structured representation known for its associated Markov chain. This moves the bottleneck for analysis from space for generator matrices to space for iteration vectors. Hence a variation of randomization is presented which allows to reduce space requirements for iteration vectors. An additional and welcome side effect is that during an initial phase, this algorithm avoids useless multiplications involving states with zero probability. Furthermore, it accommodates to adaptive randomization in a natural way. Although the algorithm has been developed for superposed GSPNs, it applies to continuous time Markov chains in a more general setting.

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Index Terms:
Stochastic Petri net, Markov chain analysis, standard and adaptive randomization, Kronecker algebra.
Peter Kemper, "Transient Analysis of Superposed GSPNs," IEEE Transactions on Software Engineering, vol. 25, no. 2, pp. 182-193, March-April 1999, doi:10.1109/32.761444
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