In this article,we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations.For any path in this network,we select all the activities related to this path such that the completion time of the sub-network(only consisting of all the related activities) is equal to the completion time of this path.We use the elapsed time as the supplementary variables and model this sub-network as a Markov skeleton process,the state space is related to the subnetwork structure.Then use the backward equation to compute the distribution of the sub-network's completion time,which is an important rule in project management and scheduling.
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