Distributed Simulation of Bio-interpreted (Coloured) Stochastic Petri Nets

Abstract

To increase our understanding of the interactions between the different cellular and intercellular processes, it is imperative to construct accurate biological models. An important class of these models are usually used to predict the time evolution of the corresponding chemical species over a specified period of time. Stochastic and coloured stochastic Petri nets can be adopted to construct graphical models that can be executed to simulate the firing of a set of reactions in a well-mixed chemical system. For the purpose of this specific application, (coloured) stochastic Petri nets employ internally the stochastic simulation algorithm (SSA) to perform the simulation. Although the result of the SSA is accurate in comparison with similar numerical simulation approaches (e.g., the systems of ordinary differential equations), it is empirically considered as a computationally expensive algorithm. In this paper, we propose an efficient parallel simulation algorithm for SSA to improve the execution of (coloured) stochastic Petri nets. We illustrate our proposal by applying it to a well-known model in the biological context: reaction diffusion. Furthermore, we evaluate the performance of the parallel algorithm and compare its runtime behaviour with the sequential one.