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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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