Algebraic Approach to Timed Petri Nets

Abstract

One aspect often needed when modelling systems of any kind is time-based analysis, especially for real-time or in general time-critical systems. Algebraic place/transition (P/T) nets do not inherently provide a way to model the passing of time or to restrict the firing behaviour with regards to passing time. In this paper, we present an extension of algebraic P/T nets by adding time durations to transitions and timestamps to tokens. We define categories for different timed net classes and functorial relations between them. Our first result is the definition of morphisms preserving firing behaviour for all timed net classes. As second result, we define structuring techniques for timed P/T nets in a way that our category fulfills the properties of M-adhesive systems, a general categorical framework for structuring and transforming high-level algebraic structures. We demonstrate our approach by applying it to model a real-time communication network.