Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (5): 1440-1448.doi: 10.1016/S0252-9602(10)60136-1

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MARKOV SKELETON PROCESS IN PERT NETWORKS

 KONG Xiang-Xing, ZHANG Xuan, HOU Zhen-Ting   

  1. School of Mathematics, Central South University, Changsha 410075, China
  • Received:2008-12-02 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    This work is supported by the National Natural Science Foundation of China (10671212, 10901164, 90820302), the Graduate Research Innovation Projects in Hunan Province (CX2009B020) and the Graduate Degree Thesis Innovation Foundation of Central Sourth University (2009ybfz11).

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Abstract:

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 sub-network 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.

Key words: PERT networks, Markov skeleton process, backward equation

CLC Number: 

  • 05C20
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