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## Regular Stochastic Petri Nets.

Dutheillet, C.;
Haddad, S.
In:
*Proceedings of the 10th International Conference on Application and Theory of Petri Nets, 1989, Bonn, Germany; Supplement*, pages 43-62.
1989.

Also in:
Rozenberg, G.: *Lecture Notes in Computer Science, Vol. 483; Advances in Petri Nets 1990*, pages 186-209.
Berlin, Germany: Springer-Verlag,
1991.

Abstract:
An extension of regular nets, a class of colored nets, to a stochastic
model is proposed. The authors show that the symmetries in this class of
nets make it possible to develop a performance evaluation by constructing
only a graph of symbolic markings, which vertices are classes of states,
instead of the whole reachability graph. Using algebraic techniques, the
authors prove that all the states in a class have the same probability,
and that the coefficients of the linear system describing the lumped
Markov process can be calculated directly from the graph of symbolic
markings.

Keywords:
extended regular stochastic net; coloured net; performance evaluation;
symbolic marking; reachability graph; lumped Markov process.

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