Numerical analysis of superposed GSPNs

The numerical analysis of various modeling formalisms profits from a structured representation for the generator matrix Q of the underlying continuous time Markov chain, where Q is described by a sum of tensor (Kronecker) products of much smaller matrices. In this paper we describe such a representation for the class of superposed generalized stochastic Petri nets (SGSPNs), which is less restrictive than in previous work. Furthermore a new iterative analysis algorithm is proposed. It pays special attention to a memory efficient representation of iteration vectors as well as to a memory efficient structured representation of Q. In consequence the new algorithm is able to solve models which have state spaces with several millions of states, where other exact numerical methods become impracticable on a common workstation.