A stochastic Petri net synthesis method with known lower bound of the second dominant eigenvalue

Abstract

Stochastic Petri nets are widely used to get the steady state performance of a discrete event dynamic system. This is usually done with little concern about how fast the system reaches its steady state. The length of the transient state is known as the rise time in control theory or, the relaxation time in a Markov process. These are governed by the eigenvalue called the second dominant eigenvalues. Also, the separation of the most dominant and second dominant eigenvalue plays a role in the convergence of the numerical solution of the Markov process. A stochastic Petri net synthesis method which preserves the ergodicity and the irreducibility of the underlying Markov process, and gives the lower bound of the second dominant eigenvalue and the number of states is proposed.