Estimating the mean cycle time for stochastic safe marked graphs

Stochastic safe marked graphs with exponentially distributed firing time of timed transitions are investigated. An approximate method for estimating the mean cycle time is proposed. The method gives a value that tends to be greater than the exact one. It is of polynomial computational complexity. The estimate is much better than the best PERT network upper bound for networks with exponentially distributed durations of activities. The method is compared with the best upper bound for mean cycle time of stochastic marked graphs. The reasons of error of the above two methods are different. Therefore, one of the methods completes the other, and for given stochastic safe marked graphs one can choose the better one from the two estimates. The approximate method can be used for estimating the mean time of stochastic safe marked graphs with NBUE distributed firing times