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Computing Bounds for the Performance Indices of Quasi-Lumpable Stochastic Well-Formed Nets
July 1994 (vol. 20 no. 7)
pp. 516-525

Structural symmetries in stochastic well-formed colored Petri nets (SWN's) lead to behavioral symmetries that can be exploited by using the symbolic reachability graph (SRG) construction algorithm. The SRC allows one to compute an aggregated reachability graph (RG) and a "lumped" continuous time Markov chain (CTMC) that contain all the information needed to study the qualitative properties and the performance of the modeled system, respectively. Some models exhibit qualitative behavioral symmetries that are not completely reflected at the CTMC level. We call them quasi-lumpable SWN models. In these cases, exact performance indices can be obtained by avoiding the aggregation of those markings that are qualitatively, but not quantitatively, equivalent. An alternative approach consists of aggregating all the qualitatively equivalent states and computing approximated performance indices. In this paper, a technique is proposed to compute bounds on the performance of SWN models of this kind, using the results we have presented elsewhere. The technique is based on the Courtois and Semal bounded aggregation method.

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Index Terms:
Petri nets; stochastic processes; Markov processes; performance evaluation; performance indices; quasilumpable stochastic well-formed Nets; stochastic well-formed colored Petri nets; symbolic reachability graph; aggregated reachability graph; continuous time Markov chain; qualitative properties; quasilumpable SWN models; approximated performance indices; SWN models; bounded aggregation method
G. Franceschinis, R.R. Muntz, "Computing Bounds for the Performance Indices of Quasi-Lumpable Stochastic Well-Formed Nets," IEEE Transactions on Software Engineering, vol. 20, no. 7, pp. 516-525, July 1994, doi:10.1109/32.297940
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