Matrix Approach to Solving Reachability Problems in Stochastic Petri Nets

Abstract

The purpose of the research was to develop the theory of stochastic Petri nets and consider its practical application when studying discrete systems. The paper considers the possibility of solving the reachability problem in stochastic Petri nets by means of matrix equations widely used in Petri nets; describes the stages and features of generating matrix equations for stochastic networks; formulates the rules for introducing virtual elements, i.e., positions and transitions, into the stochastic Petri net to generate and solve matrix equations. Stochastic Petri nets different in structure and composition were used to explore the possibility of applying matrix equations. Findings of the research show that the reachability of the required states of the networks is determined through the firing of transitions, which are the solution of the matrix equation. Within the study, we interpreted the obtained results and developed an algorithm that allowed us to validate the assumption made and visually determine the restrictions on the use of matrix equations for various initial states of the simulated system. The results of the proposed algorithm are presented in graphical form on the examples of stochastic Petri nets that model the process of forensic handwriting analysis. The conclusion is made about the applicability of matrix equations in stochastic Petri nets and the need for further research in this area