Analysis of stochastic Petri nets with signals

Product-form models facilitate the efficient analysis of large stochastic models and have been sought after for some three decades. Apart from the dominating work on queueing networks, some product-forms were found for stochastic Petri nets (SPNs) that allow fork-join constructs and for queueing networks extended to include special customers called signals, viz. G-networks. We appeal to the Reversed Compound Agent Theorem (RCAT) to prove new product-form solutions for SPNs in which there are special transitions, the firings of which act in a similar way to signals in G-networks, but which may be generated by synchronised firings (or service completions) and may affect several places simultaneously. We show that SPNs with signals are strict generalisations of G-networks with negative customers, triggers and catastrophes, and illustrate with copious examples.