Estimating the mean completion time of PERT networks with exponentially distributed durations of activities. (English) Zbl 0804.90052

The paper presents an efficient method for estimating the expected duration of a project with exponentially and independently distributed activity times. Since the hypoexponential distribution, being the convolution of exponential distributions, is not preserved under multipliation, the distribution of the maximum of two independent random variables with hypoexponential distributions is proposed to be approximated by a hypoexponential distribution having the same mean and variance.
Though the method tends strongly to overestimate the exact value of the expected project duration, it does not have bounding properties. The accuracy of the method is examined on some simple examples, and the results are encouraging.


90B15 Stochastic network models in operations research
Full Text: DOI


[1] Barlow, R. E.; Proshan, F., Statistical Theory of Reliability and Life Testing Probability Models (1975), Holt: Holt New York
[2] Block, H. W.; Savits, T. H., The IFRA closure problem, Annals Probability, 4, 1030-1032 (1976) · Zbl 0346.60055
[3] Devroye, L. P., Inequalities for the completion times of stochastic PERT networks, Mathematics of Operations Research, 4, 441-447 (1979) · Zbl 0427.90053
[4] Elmaghraby, S. E., The estimation of some network parameters in the PERT model of activity networks: Review and critique, (Slowinski, R.; Weglarz, J., Advances in Project Scheduling (1989), Elsevier: Elsevier Amsterdam), 371-432, Chapter 1, Part III
[5] Kamburowski, J., An upper bound on the expected completion time of PERT networks, European Journal of Operational Research, 21, 206-212 (1985) · Zbl 0569.90047
[6] Kulkarni, V. G.; Adlakha, V. G., Markov and Markov regenerative PRET networks, Operations Research, 34/5, 769-781 (1986) · Zbl 0615.90042
[7] Magott, J.; Skudlarski, K., Combining generalized stochastic Petri nets and PERT networks for the performance evaluation of concurrent processes, (Proc. Third Int. Workshop on Petri Nets and Performance Models. Proc. Third Int. Workshop on Petri Nets and Performance Models, Kyoto, Japan, Dec. 1989 (1989), IEEE Computer Society Press: IEEE Computer Society Press New York), 249-256
[8] Skudlarski, K., Generalized stochastic Petri nets analyzer, Informatyka, 5, 3-6 (1991), (in Polish)
[9] Stoyan, D., Comparison Methods for Queues and Other Stochastic Models (1983), Wiley: Wiley Chichester
[10] Trivedi, K. S., Probability and Statistics with reliability, Queueing and Computer Science Applications (1982), Prentice-Hall: Prentice-Hall Englwwood Cliffs, NJ
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.