Estimating completion-time distribution in stochastic activity networks

This paper deals with simulation-based estimation of the probability distribution for completion time in stochastic activity networks. These distribution functions may be valuable in many applications. A simulation method, using importance-sampling techniques, is presented for estimation of the probability distribution function. Separating the state space into two sets, one which must be sampled and another which need not be, is suggested. The sampling plan of the simulation can then be decided after the probabilities of the two sets are adjusted. A formula for the adjustment of the probabilities is presented. It is demonstrated that the estimator is unbiased and the upper bound of variance minimized. Adaptive sampling, utilizing the importance sampling techniques, is discussed to solve problems where there is no information or more than one way to separate the state space. Examples are used to illustrate the sampling plan.