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## Hierarchical Structuring of Superposed GSPNs.

Buchholz, Peter
In:
*Proceedings of the Seventh International Workshop on Petri Nets and Performance Models, June 3-6, 1997, Saint Malo, France*, pages 81-90.
Los Alamitos, California: IEEE Computer Society,
June 1997.

Abstract:
Superposed Generalized Stochastic Petri Nets (SGSPNs) and Stochastsic
Automata Networks (SANs) are formalisms to describe Markovian models as a
collection of synchronously communicating components. Both formalisms
allow a compact representation of the generator matrix of the Markov
techniques. The main drawback of the approaches is that for many models
the compositional description introduces a large number of unreachable
states, such that the gain is completely lost. This paper proposes a new
approach to represent the generator matrix in a compact form. The central
idea is to introduce a pre-processing step to generate a hierarchical
structure which defines a block structure of the generator matrix, where
every block can be represented in a compact form similar to the
representation of generator matrices originally proposed for SGSPNs or
SANs. The resulting structure includes no unreachable states, needs only
slightly more space than the compact representation developed for SANs and
can still be exploited in efficient numerical solution techniques.

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