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## Structured Solution of Stochastic DSSP Systems.

Campos, J.;
Silva, M.;
Donatelli, S.
In:
*Proceedings of the Seventh International Workshop on Petri Nets and Performance Models, June 3-6, 1997, Saint Malo, France*, pages 91-100.
Los Alamitos, California: IEEE Computer Society,
June 1997.

Abstract:
Deterministically Synchronized Sequential Processes (DSSP) are essentially
states machines that communicate, may be in complex forms but under some
restricted patterns, through buffer places; their definition is
compositional by nature. This paper considers the problem of exploiting
this compositionality to generate the state space and to find the steady
state probabilities of a stochastic extension of DSSP in a net-driven,
efficient way. Essentially, we give an expresion of an auxiliary matrix,
G, which is a supermatrix of the infinitesimal generator of a DSSP. G is a
tensor algebra expression of matrices of the size of the components for
which it is possible to numerically solve the characteristic equation pi.G
= 0, without the need to explicitly compute G. Therefore, we obtain a
method that computes the steady state solution of a DSSP without ever
explicitly computing and storing its infinitesimal generator, and
therefore without computing and storing the reachability graph of the
system.

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