(Stochastic) Petri Nets

Petri nets, introduced by Carl Adam Petri more than fifty years ago, is a graphical mathematical modeling framework that comes in many flavors. Despite considerable efforts for standardization of Petri nets, there is still an often confusing abundance of different versions. To this end, an Italian proverb Ogni sacarrafone è bello a mamma sua ("Every cockroach is beautiful to his mother") ¹ is quite apt indeed.

Original Petri nets were "timeless" i.e., without a concept of time. A Petri net describes the possible states of the system and paths for changes of those states. Critically, the perspective is "local": instead of describing the system in its entirety, description of components that comprise the system is provided, and the state of the entire system is inferred. The situation is not unlike using digits (glyphs) in the Hindu-Arabic numeralal system. If we want to describe all numbers from 0 to 999, we need only three "components" (digits), each being in one of the possible 10 states (0 to 9). This is effectively the Petri Net approach. In contrast the Markov approach would be to assign a distinct state (symbol) to every number between 0 and 999.

My version of a Petri Net cockroach is Abridged Petri Nets (APN).