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## Structured Solution of Asynchronously Communicating Stochastic Modules.

Campos, J.;
Donatelli, S.;
Silva, M.
In:
*IEEE Transactions on Software Engineering, vol.25, no.2*, pages 147-165.
March 1999.

Abstract:
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, G, which is a
supermatrix of the infinitesimal generator of a SAM. G is a tensor algebra
[Davio 1981] expression of matrices of the size of the components for
which it is possible to numerically solve the characteristic steady-state
solution equation pi.G = 0, without the need to explicitly compute 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.

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