Improving the Efficiency of the Proxel Method by Using Individual Time Steps

Discrete stochastic models (DSM) are widely used in various application fields today. Proxel-based simulation can outperform discrete event-based approaches in the analysis of small stiff DSM, which can occur for example in reliability modeling. However, when parallel processes with largely differing speed are involved, the faster process determines the small discretization time step, investing far too much effort into the approximation of the slower process. This paper relieves that problem by using individual time steps for each transition and situation. The key problem is to keep semantic consistency when using different time steps for parallel transitions. However, the preservation of the probability mass in every single simulation time step could be achieved. Experiments show that binary step division in conjunction with appropriate subdivision criteria can outperform the original Proxel method significantly. This increases the applicability of Proxels, by enabling the analysis of larger and therefore more realistic models.