Numerical analysis of stochastic marked graph nets

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 on 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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