"On-the-fly" solution techniques for stochastic petri nets and extensions

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.