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## Superposed Generalized Stochastic Petri nets: definition and efficient solution.

Donatelli, Susanne
In:
Valette, R.: *Lecture Notes in Computer Science, Vol. 815; Application and Theory of Petri Nets 1994, Proceedings 15th International Conference, Zaragoza, Spain*, pages 258-277.
Springer-Verlag,
1994.

Abstract:
In a previous paper we have defined Superposed Stochastic Automata (SSA),
a class of Stochastic Petri Nets (SPN) whose solution can be efficiently
computed since it never requires the construction of the complete Markov
chain of the underlying Markovian process. The efficient solution of SSA
is based on a method proposed by Plateau for the analysis of stochastic
processes generated by the composition of stochastic automata. Efficient
analysis is there achieved (both in terms of space and time) with a
technique b ased on Kronecker (tensor) algebra for matrices. A SSA is
basically a set of Stochastic State machines that interact through
transition superposition: their application to real models is therefore
limited. The technique defined for SSA is here extended to Superposed
Generalized Stochastic Petri Nets (SGSPN), a set of GSPN nets that
interact through transition superposition. In this paper we define SGSPN,
explain how the solution method proposed by Plateau and already used for
SSA can be adapted to work for this larger class of SPN, and discuss the
possibility of using SGSPN for the performance evaluation of concurrent
processes. The solution is implemented by a set of programs that interact
with the GreatSPN package: a SGSPN net is specified through the GreatSPN
graphical interface, so that also all classical analysis methods already
available for GSPN in the package can still be applied

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