Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets

Analysis of stochastic Petri nets with signals

“…In the paper we show how this follows from RCAT's rate equations. Rate dependent product-form conditions are very important in stochastic Petri nets, as initially shown in [8] and, more recently, in [26,35,3]. We add to this topic by giving a compositional interpretation of such conditions in terms of our building block basic structures.…”

“…In relation to other product-form models, we can say first that SPNs with signals generalise G-networks with negative customers, triggers and catastrophes [14,16,15,10]. Moreover, they subsume the product-form SPN of [8], without batch token movements. It is worthwhile noting that, differently from [31,8], we deal mainly with open models, since triggers may cause token destructions, leading to an empty network in the long-term.…”

“…[31,8,35,3]. One of the interesting aspects of the models studied in these papers is that synchronised token arrivals and departures may lead to rate-dependent product-form conditions.…”

“…Moreover, they subsume the product-form SPN of [8], without batch token movements. It is worthwhile noting that, differently from [31,8], we deal mainly with open models, since triggers may cause token destructions, leading to an empty network in the long-term.…”

“…One of the interesting aspects of the models studied in these papers is that synchronised token arrivals and departures may lead to rate-dependent product-form conditions. In [31,8] the rate conditions arise from the application of a so-called "rank theorem", in which the rank of a matrix of rates must be checked, whereas in [3], these conditions can be checked in a modular way as a consequence of a structural decomposition of the model. This helps in giving a physical interpretation to conditions that would otherwise be purely algebraic.…”