Eigenvalue bounds of a stochastic Petri net

Stochastic Petri nets are strong tools to model discrete event dynamic systems. To describe the transient properties of the system, it is necessary to find the eigenvalues of the underlying Markov process. However, the state explosion problem, the stiffness problem appearing in many applications, and the intrinsic numerical instability hinder us from getting the complete eigenvalue set. In this paper, the location of the eigenvalues are obtained without generating the reachability set of the stochastic Petri net.