Petri nets are a popular system modeling methodology, although the typical state-space explosion is problematic. An estimate of the state-space size has many uses: determining the appropriateness of a particular analysis technique; evaluating the trade-off between model detail and solution complexity; and providing data for state-space size reduction algorithms. This paper presents an estimation algorithm based on subnets and interconnections (i.e., a bottom-up approach). The algorithm allows relatively arbitrary subnets and is extendable via development of additional interconnections. Several subnets and interconnections are developed, and a multiworkcell manufacturing example is presented.>

The authors present the results of an investigation of the relationships between a Petri net (PN) and the size of its associated state-space. Four estimators are developed for estimating the number of states in a PN and understanding the sensitivity of this number to increases in tokens, places, and transitions. An estimator for conservative PNs demonstrated excellent accuracy. Estimators based on place boundedness and net boundedness had poor performance, but were amenable to analytical sensitivity analysis.>

An investigation into the relationships between Petri net (PN) models and their associated state-space is discussed. An algorithm to estimate an upper bound on the number of states in a PN is presented. This algorithm is based on the weight vector associated with conservative PNs. PN constructs that hinder the algorithm's accuracy are discussed. Additionally, the structural and behavioral nature of PN weighted conservatism is developed, and a clarification of a test of weighted conservativeness is presented.>

Although generalized stochastic Petri nets (GSPNs) are restricted to only immediate and exponential transitions, they are used for performance analysis of a variety of systems. Flexible manufacturing systems (FMSs) typically contain nonexponential state transitions. GSPN models developed for FMSs present a concern that the above restriction limits the accuracy of performance results. Throughput subnets and s-transitions are introduced. These GSPN constructs allow nonexponential state transitions in a system to be accurately modeled within a GSPN. A GSPN performance model for an FMS example is developed using s-transitions. This system had been previously analyzed using probability theory. Performance analysis results are compared.>

Generalized stochastic Petri nets (GSPNs) are applied to flexible manufacturing systems (FMSs). Throughput subnets and s-transitions are presented. Two FMS examples containing nonexponential distributions, which were analyzed in previous papers by queuing theory and probability theory respectively, are treated using GSPNs developed using throughput subnets and s-transitions. The GSPN results agree with the previous results, and developing and analyzing the GSPN models are straightforward and relatively easy compared to other methodologies.>