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## Numerical Analysis of Stochastic Marked Graph Nets.

Buchholz, Peter;
Kemper, Peter
In:
*IEEE Computer Soc. Press, Proc. of 6th International Workshop on Petri Nets and Performance Models - PNPM'95, Durham, N. Carolina, USA*, pages 32-41.
1995.

Abstract:
The analysis of stochastic marked graphs is considered. The underlying
idea is to decompose the marked graph into subnets, to generate state
spaces and transition matrices for these isolated parts and then to
represent the generator matrix underlying the complete net by means of
much smaller subnet matrices combined via tensor operations. Based on this
matrix representation efficient numerical analysis techniques can be used
to compute the stationary solution. Furthermore we propose an
approximation technique which is similar to known approximate solution
techniques for this kind of nets, but our approach is completely
integrated in the structured description of the generator matrix. This
allows an estimation of the approximation error and the usage of the
approximate results as an initial guess for a subsequent iterative
analysis, such that the number of required iterations is often
significantly reduced.

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