On bounds for token probabilities in a class of generalized stochastic Petri nets

Methods to compute tight bounds for steady-state token probabilities of a class of generalized stochastic Petri net (GSPN) models are presented. Such bounds also give a better estimate of the error produced when decompositions and aggregations are used to compute the various performance measures. A method to compute the best lower and upper bounds for conditional token probability of a class of GSPN subnets when only the subnet is considered is described. Such bounds can be improved when additional information about other subnets can be used. This technique is extended, and an algorithm to compute the bounds for error due to aggregation and decomposition at the GSPN level is outlined. An example is presented to illustrate the technique and algorithm