From Symmetric Nets to Differential Equations exploiting Model Symmetries

Stochastic Symmetric Nets (SSNs) are a High-Level Stochastic Petri Net formalism which provides a parametric system description and an efficient analysis technique that exploit system symmetries to automatically aggregate its states. Even if significant reductions can be achieved in highly symmetric models, the reduced state space can still be too large to derive and/or solve the underlying stochastic process, so that Monte Carlo simulation and fluid approximation remain the only viable ways that need to be explored. In this paper, we contribute to this line of research by proposing a new approach based on fluid approximation to automatically derive from an SSN model a set of ordinary differential equations (ODEs) which mimic the system behavior, and by showing how the SSN formalism allows us to define an efficient translation method which reduces the size of the corresponding ODE system with an automatic exploitation of system symmetries. Additionally, some case studies are presented to show the effectiveness of the method and the relevance of its application in practical cases.