Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks

TL;DR

This paper introduces a method combining Bayesian networks with probabilistic Petri nets to perform uncertainty reasoning, enabling more effective modeling and analysis of complex stochastic systems.

Contribution

It extends Bayesian networks to handle Petri nets with probabilistic transitions, providing a modular approach for uncertainty reasoning and efficient marginal probability computation.

Findings

Successfully modeled disease spread and social network diffusion.

Implemented the approach with promising runtime performance.

Generalized variable elimination for modular Bayesian nets.

Abstract

This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions, modelling the observer's knowledge about the tokens in the net. The observer can study the net by monitoring successful and failed steps. An update mechanism for Bayesian nets is enabled by relaxing some of their restrictions, leading to modular Bayesian nets that can conveniently be represented and modified. As for every symbolic representation, the question is how to derive information - in this case marginal probability distributions - from a modular Bayesian net. We show how to do this by generalizing the known method of variable elimination. The approach is illustrated by examples about the spreading of diseases (SIR model) and information diffusion in social networks. We have implemented our approach and provide runtime results.