Simulating Markovian stochastic Petri Nets by difference equations with interval parameters

摘要

Fluid modeling is a technique for approximating behavior of stochastic discrete-state systems based on dynamical models with continuous state variables. In this paper, we focus on fluid modeling for Markovian stochastic Petri nets, and propose a method to compute regions including state values that appear with a high probability. This can be seen as the second-order approximation, because the size of each region varies according to the variance of the corresponding state variable. The fluid models are represented by discrete-time dynamical systems with interval parameters, and interval arithmetic is used for computing regions at each time step. We show simulation results on the fluid models and compare the results with the correct solutions obtained by discrete-state analysis on stochastic Petri nets.