Marking optimization of stochastic timed event graphs using IPA

Addresses the marking optimization of stochastic timed event graphs. The transition firing times are generated by random variables with general distribution. The marking optimization problem consists of obtaining a given cycle time while minimizing a p-invariant criterion. Some important properties have been established. The authors also propose a heuristic algorithm. It starts from the optimal solution to the deterministic case and iteratively adds tokens to adequate places as long as the given cycle time is not obtained. Infinitesimal perturbation analysis (IPA) of the average cycle time with respect to the transition firing times is used to identify the adequate places in which the new tokens are added. Numerical results show that the heuristic algorithm provides near optimal solutions