A new analytical algorithm for computing probability distribution of project completion time - Hou, Zhen-ting; Zhang, Xuan; Kong, Xiang-xing (Journal of Central South University of Technology. Science & technology of mining and metallurgy, 2010)
An analytical algorithm was presented for the exact computation of the probability distribution of the project completion time in stochastic networks, where the activity durations are mutually independent and continuously distributed random variables. Firstly, stochastic activity networks were modeled as continuous-time Markov process with a single absorbing state by the well-know method of supplementary variables and the time changed from the initial state to absorbing state is equal to the project completion time. Then, the Markov process was regarded as a special case of Markov skeleton process. By taking advantage of the backward equations of Markov skeleton processes, a backward algorithm was proposed to compute the probability distribution of the project completion time. Finally, a numerical example was solved to demonstrate the performance of the proposed methodology. The results show that the proposed algorithm is capable of computing the exact distribution function of the project completion time, and the expectation and variance are obtained.