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Evaluate the performance of a stochastic-flow network with cost attribute in terms of minimal cuts

机译：根据最小削减量评估具有成本属性的随机流网络的性能

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摘要

This paper proposes a performance index to measure the quality level of a stochastic-flow network in which each node has a designated capacity, which will have different lower levels due to various partial and complete failures. The performance index is the probability that the maximum flow of the network equals the demand d without exceeding the budget b. A simple algorithm in terms of minimal cuts is first proposed to generate all upper boundary points for (d, b), and then the probability that the maximum flow is less than or equal to d can be calculated in terms of such points. The upper boundary point for (d, b) is a maximal vector representing the capacity of each arc such that the maximum flow of the network under the budget b is d. The performance index can be calculated by repeating the proposed algorithm to obtain all upper boundary point for (d— 1, b). A benchmark example is shown to illustrate the solution procedure.
机译：本文提出了一种性能指标，用于测量随机流网络的质量级别，该网络中的每个节点都有指定的容量，由于各种局部和完全故障，该容量将具有不同的较低级别。性能指标是网络的最大流量等于需求d而不超过预算b的概率。首先提出了一种基于最小割的简单算法来生成（d，b）的所有上边界点，然后可以根据这些点计算最大流量小于或等于d的概率。 （d，b）的上边界点是代表每个弧的容量的最大向量，因此在预算b下网络的最大流量为d。可以通过重复提出的算法以获得（d-1，b）的所有上边界点来计算性能指标。显示了一个基准示例来说明解决程序。

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