Faster Simulation of (Coloured) Petri Nets Using Parallel Computing

Abstract

Fast simulation, i.e., automatic computation of sequential runs, is widely used to analyse Petri nets. In particular, it enables for quantitative statistical analysis by observing large sets of runs. Moreover, fast simulation may be used to actually run a Petri net model as a (prototype) implementation of a system, in which case such a net would embed fragments of the code of the system. In both these contexts, being able to perform faster simulation is highly desirable. In this paper, we propose a way to accelerate fast simulation by exploiting parallel computing, targeting both the multi-core cpus available nowadays in every laptop or workstation, and larger parallel computers including those with distributed memory (clusters). We design an algorithm to do so and assess in particular its correctness and completeness through its formal modelling as a Petri net whose state space is analysed. We also present a benchmark of a prototype implementation that clearly shows how our algorithm effectively accelerates fast simulation, in particular in the case of large concurrent coloured Petri nets, which is precisely the kind of nets that are usually slow to simulate.

A single changing hypernetwork to represent (social-)ecological dynamics

“…3b). Petri nets were developed in the 1930s for modeling chemical reactions requiring precisely such connections and have since been used in many other fields (Pommereau, 2010;Reisig, 2013;Pommereau et al, 2022b). In such a representation, variables are known as places (round-shaped nodes) and interact through processes called transitions (square-shaped nodes), shown as arcs.…”

Discrete-event models for conservation assessment of integrated ecosystems

“…2). Additional details on the principle and uses of Petri nets can be found in literature (Gaucherel and Pommereau 2019;Pommereau 2010;Reisig 2013) and in Appendix D. The ecosystem Petri net itself is developed in three successive steps: a) an intuitive graph (i.e. a set of components and their related processes called the ecosystem graph) is built to represent the studied ecosystem based on the leading question; b) we then transformed this ecosystem graph into a formal model based on Boolean components and changing rules.…”

“…Tools to handle the ecosystem integration with a rigorous (formalized) framework are still lacking. In this paper, we developed a discrete-event, qualitative and non-stochastic model, based on Petri nets (Pommereau 2010;Reisig 2013), to analyse system properties and long term changes of any ecosystem. These kinds of models can potentially be extended into quantitative, spatially explicit and multi-temporal schemes to allow more realistic and applied analyses.…”

“…To develop an integrated model of such marshes, we borrowed the formalism (mathematical framework) from theoretical computer science precisely built to handle structural network changes: a qualitative Petri net. Petri nets belong to the wide category of discrete-event models (Giavitto and Michel 2003;Pommereau 2010). Such models have proven powerful when applied to biological networks but, to our knowledge, are almost absent in ecology (but see Baldan et al 2015;Gaucherel and Pommereau 2019;Gaucherel et al 2017).…”

Diagnosis of planktonic trophic network dynamics with sharp qualitative changes

“…As a second subquestion, we assessed whether a detailed model could exhibit new or counter-intuitive TN trajectories. We assumed that the system may be qualified and thus exhibit a finite number of states, computed and gathered into a Petri net state space (Pommereau 2010, Reisig 2013. A detailed and automatic analysis of this state space then exhaustively provides the possible fates (e.g., stabilities, collapses, if any) of the studied system.…”