Hierarchical Evaluation of Generalized Stochastic Petri Nets based on Subnetwork Time Distribution
In this paper a hierarchical evaluation procedure for Generalized Stochastic Petri Nets (GSPN) is presented which is based on aggregation algorithms that are extensions of Flow Equivalent Aggregation (FEA) and that use transient analysis of Markov Chains. In order to aggregate a subnetwork to a substitute network we consider, as criterion for the similarity of the networks, the Subnetwork Time Distribution (STD) defined as the distribution of the time a token X needs to proceed through a subnetwork conditioned on the token distribution at the epoch of arrival of X and the context into which the net is embedded just for the experiment of determining a characteristic sojourn time distribution for token X in the subnetwork. The consideration of the second condition may be regarded as the major extension to previous work. The substitute network with the least discrepancy in Subnetwork Time Distribution to the original subnetwork is chosen as the aggregate. Several variants of the aggregation algorithm called FEAD (FEA based on Subnetwork Time Distribution) have been implemented and tested. Their performance is discussed by means of an example and they are shown to outperform Flow Equivalent Aggregation when applied to GSPN.
KeywordsGeneralized Stochastic Petri Nets Hierarchical Evaluation Aggregation Subnetwork Time Distribution.
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