Multidimensional Stochastic Petri Nets: A Novel Approach to Modeling and Simulation of Stochastic Discrete-Event Systems

Process Mining (PM) has been proven valuable for extracting process flows from data, also in the form of stochastic Petri net (SPN) models of systems. SPNs are widely recognized for their ability to model complex, stochastic systems and are extensively used in combination with PM. While SPNs provide an intuitive and straightforward way to model complex systems, representing changes across multiple dimensions, such as energy and waste, remains challenging in their standard frameworks. In this paper, we introduce an extension of stochastic Petri nets, termed Multidimensional SPNs (MDSPNs), by extending the SPN framework to capture dynamics along different dimensions. MDSPNs facilitate a comprehensive modeling of systems’ behaviors from multiple perspectives, which can correspond to the diverse objectives of systems. To facilitate design and simulation of MDSPNs, we designed and developed MDPySPN, a Python library, which we also introduce in this paper. MDPySPN enables the simulation of MDSPNs by supporting alterations of multiple values at system events. With MDPySPN, we aim to provide researchers, engineers, and simulation professionals with a practical and extensible toolkit to model, simulate, and analyze MDSPNs, thereby supporting multi-objective optimization of stochastic processes in systems. Through a case study, we demonstrate the capabilities of modeling and simulation of MDSPNs using MDPySPN.