Structured Solution of Asynchronously Communicating Stochastic Modules

• Authors: Javier Campos;Susanna Donatelli;Manuel Silva
• Venue: IEEE Transactions on Software Engineering
• Year: 1999

Asynchronously Communicating Stochastic Modules (SAM) are Petri nets that can be seen as a set of modules that communicate through buffers, so they are not (yet another) Petri net subclass, but they complement a net with a structured view. This paper considers the problem of exploiting the compositionality of the view to generate the state space and to find the steady-state probabilities of a stochastic extension of SAM in a net-driven, efficient way. Essentially, we give an expression of an auxiliary matrix, ${\schmi{\bf G}}$, which is a supermatrix of the infinitesimal generator of a SAM. ${\schmi{\bf G}}$ is a tensor algebra expression of matrices of the size of the components for which it is possible to numerically solve the characteristic steady-state solution equation ${\schmi {\bf \pi}} \; \cdot \; {\schmi{\bf G}}={\schmi{\bf 0}},$ without the need to explicitly compute ${\schmi{\bf G}}$. Therefore, we obtain a method that computes the steady-state solution of a SAM without ever explicitly computing and storing its infinitesimal generator, and therefore without computing and storing the reachability graph of the system. Some examples of application of the technique are presented and compared to previous approaches