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Superposed stochastic automata: A class of stochastic Petri nets with parallel solution and distributed state space. (English) Zbl 0795.68141
The solution of stochastic Petri nets (SPN) requires the construction of the associated continuous time Markov chain and so its infinitesimal generator and the solution of a number of linear solutions are equal to the number of states of SPN. In the usual approaches one tries to investigate the stochastic process associated with SPN without generating and complete Markov chain, but the applicability of these results to real problems is rather limited.
The paper presents a subclass of SPN called superposed stochastic automata (SSA) from which one can derive automatically a Kronecker expression for the infinitesimal generator coming in such way to a framework with well developed tools. This gives the possibility of automatic definition of performance indices, steady-state, transient and approximate solutions. The complexities and major steps of sequential and parallel implementations and their comparison are also discussed.

68Q45 Formal languages and automata
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68M10 Network design and communication in computer systems
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