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"On-the-Fly" Solution Techniques for Stochastic Petri Nets and Extensions
October 1998 (vol. 24 no. 10)
pp. 889-902

Abstract—High-level modeling representations, such as stochastic Petri nets, frequently generate very large state spaces and corresponding state-transition-rate matrices. In this paper, we propose a new steady-state solution approach that avoids explicit storing of the matrix in memory. This method does not impose any structural restrictions on the model, uses Gauss-Seidel and variants as the numerical solver, and uses less memory than current state-of-the-art solvers. An implementation of these ideas shows that one can realistically solve very large, general models in relatively little memory.

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Index Terms:
Markov models, stochastic Petri nets, matrix-free methods.
Daniel D. Deavours, William H. Sanders, ""On-the-Fly" Solution Techniques for Stochastic Petri Nets and Extensions," IEEE Transactions on Software Engineering, vol. 24, no. 10, pp. 889-902, Oct. 1998, doi:10.1109/32.729691
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