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 continuou...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.展开更多
基金Project(10671212) supported by the National Natural Science Foundation of ChinaProject(20050533036) supported by the Specialized Research Found for the Doctoral Program Foundation of Higher Education of China
文摘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.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.50375126)陕西省教育厅资助科研课题(the research Project of Department of Education of Shannxi Province+1 种基金China under Grant No.05JK312)咸阳师范学院专项科研基金(No.06XSYK211)
