Synthesis and Analysis of Product-form Petri Nets

TL;DR

This paper advances the understanding of product-form Petri nets by providing synthesis rules, analyzing problem complexity, and identifying a subclass with efficient normalizing constant computation.

Contribution

It offers a complete synthesis framework, characterizes problem complexity, and introduces a subclass enabling efficient calculations for product-form Petri nets.

Findings

Complete synthesis rules for product-form Petri nets

Complexity characterization of classical problems

Identification of a subclass with efficient normalizing constant computation

Abstract

For a large Markovian model, a "product form" is an explicit description of the steady-state behaviour which is otherwise generally untractable. Being first introduced in queueing networks, it has been adapted to Markovian Petri nets. Here we address three relevant issues for product-form Petri nets which were left fully or partially open: (1) we provide a sound and complete set of rules for the synthesis; (2) we characterise the exact complexity of classical problems like reachability; (3) we introduce a new subclass for which the normalising constant (a crucial value for product-form expression) can be efficiently computed.