Evaluating reliability of stochastic flow networks. (English) Zbl 1134.90326

Fishman, George S.; Shaw, Tien-Yi Danny

Probab. Eng. Inf. Sci. 3, No. 4, 493-509 (1989).

Summary: This paper describes a highly efficient Monte Carlo sampling plan for evaluating the probability that the flow value in a stochastic flow network is greater than or equal to a prespecified level \(d\). A stochastic flow network can characterize communication, transportation, and water or oil distribution systems. The paper first derives lower and upper bounds on the probability of interest and then describes how one can concentrate sampling in a specialized region’ of the arc capacity state space to increase the statistical efficiency of the resulting estimate. The paper also gives expressions for worst-case sample sizes needed to meet specified bounds on variances and coefficients of variation and-illustrates the proposed sampling plan with an example.

MSC:

90B15	Stochastic network models in operations research
90B25	Reliability, availability, maintenance, inspection in operations research

References:

[1]	DOI: 10.2307/2683661 · doi:10.2307/2683661
[2]	DOI: 10.1002/net.3230060208 · Zbl 0339.90017 · doi:10.1002/net.3230060208
[3]	Doulliez, Revue Francaise d’Automatique 6 pp 1972– (1972)
[4]	Bukowski, IEEE Transaclions on Systems 12 pp 538– (1982)
[5]	DOI: 10.1145/355744.355749 · Zbl 1148.65301 · doi:10.1145/355744.355749
[6]	Papadimitriou, Combinatorial optimization (1982)
[7]	Fishman, Operctions Research 34 pp 581– (1986)
[8]	Lee, IEEE Transactions on Reliability 29 pp 24– (1980)
[9]	DOI: 10.1137/0208012 · Zbl 0419.90040 · doi:10.1137/0208012
[10]	Karzanov, Soviet Mathematics Doklady 15 pp 434– (1974)
[11]	DOI: 10.2307/2282952 · Zbl 0127.10602 · doi:10.2307/2282952
[12]	Garey, Computers and intractability: A guide to NP- completeness (1979) · Zbl 0411.68039
[13]	DOI: 10.1016/0020-0190(78)90016-9 · Zbl 0391.90041 · doi:10.1016/0020-0190(78)90016-9