Structured solution of stochastic DSSP systems

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 expression 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 π·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