In: Rozenberg, G.: Lecture Notes in Computer Science, Vol. 609; Advances in Petri Nets 1992, pages 352-391. Springer-Verlag, 1992.
Abstract: In this paper we overview some recent results obtained by the authors and collaborators on the performance bounds analysis of some stochastic Petri net systems. The mathematical model can be seen either as a result of the addition of a particular random timing interpretation to an `autonomous' Petri net or as a generalization of classical queueing networks with the addendum of a general synchronization primitive. It constitutes an adequate tool for both the validation of logical properties and the evaluation of performance measures of concurrent and distributed systems. Qualitative and quantitative understands of Petri net models are stressed here making special emphasis on structural techniques for the analysis of logical and performance properties. Important aspects from the performance point of view such as relative throughput of stations (transitions), and number of servers present at them, are related to Petri net concepts like P- or T-semiflows or liveness bounds of transitions. For the particularly interesting case of Markovian Petri net systems, some improvements of the bounds can be achieved. Marked graphs and free choice are net subclasses for which the obtained results have special quality, therefore an additional attention is focussed on them.
Keywords: graph theory; linear algebra and linear programming techniques; Markovian systems; performance evaluation; P- and T-semiflows; qualitative and quantitative analysis; stochastic Petri net systems; structural techniques; synchronized queueing networks; throughput bounds; transformation/reduction techniques.