Superposed generalized stochastic petri nets: Definition and efficient solution

Abstract

In a previous paper we have defined Superposecl Stochastic Automata (SSA) [13], a class of Stochastic Petri Nets (SPN) whose solution can be efficiently computed since it never requires the construction of the complete Markov chain of the underlying Markovian process. The efficient solution of SSA is based on a method proposed by Plateau in [23] for the analysis of stochastic processes generated by the composition of stochastic automata. Efllcicnt analysis is there achieved (both in terms of space and time) with a technique based on Kronecker (tensor) algebra for matrices. A SSA is basicMly a set of Stochastic State machines that interact through transition superposltion: their application to real models is therefore limited. The technique defined for SSA is here extended to Superposed Generalized Stochastic Petri Nets (SGSPN), a set of GSPN nets that interact through transition supcrposition. In this paper we define SGSPN, explain how the solution method proposed by Plateau in [23] and already used for SSA can be adapted to work for this largcr class of SPN, and discuss the possibility of using SGSPN for the performance evaluation of concurrent processes. The solution is implemented by a set of programs that interact with the GrcatSPN [8] package: a SGSPN net is specified through the GreatSPN graphical interface, so that also all classical analysis methods already avaJJable for GSPN in the package can still bc applied.