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Markov and Markov-Regenerative pert Networks

Author

Listed:
  • V. G. Kulkarni

    (University of North Carolina at Chapel Hill, Chapel Hill, North Carolina)

  • V. G. Adlakha

    (University of Baltimore, Baltimore, Maryland)

Abstract

This paper investigates pert networks with independent and exponentially distributed activity durations. We model such networks as finite-state, absorbing, continuous-time Markov chains with upper triangular generator matrices. The state space is related to the network structure. We present simple and computationally stable algorithms to evaluate the usual performance criteria: the distribution and moments of project completion time, the probability that a given path is critical, and other related performance measures. In addition, we algorithmically analyze conditional performance measures—for example, project completion time, given a critical path—and present computational results. We then study extensions both to resource-constrained pert networks and to a special class of nonexponential pert networks.

Suggested Citation

  • V. G. Kulkarni & V. G. Adlakha, 1986. "Markov and Markov-Regenerative pert Networks," Operations Research, INFORMS, vol. 34(5), pages 769-781, October.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:5:p:769-781
    DOI: 10.1287/opre.34.5.769
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