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Algorithms for the quickest path problem and the reliable quickest path problem

机译：最快路径问题和可靠最快路径问题的算法

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The quickest path problem consists of finding a path in a directed network to transmit a given amount of items from an origin node to a destination node with minimal transmission time, when the transmission time depends on both the traversal times of the arcs, or lead time, and the rates of flow along arcs, or capacity. In telecommunications networks, arcs often also have an associated operational probability of the transmission being fault free. The reliability of a path is defined as the product of the operational probabilities of its arcs. The reliability as well as the transmission time are of interest. In this paper, algorithms are proposed to solve the quickest path problem as well as the problem of identifying the quickest path whose reliability is not lower than a given threshold. The algorithms rely on both the properties of a network which turns the computation of a quickest path into the computation of a shortest path and the fact that the reliability of a path can be evaluated through the reliability of the ordered sequence of its arcs. Other constraints on resources consumed, on the number of arcs of the path, etc. can also be managed with the same algorithms.
机译：最快的路径问题包括在定向网络中找到一条路径，以便当传输时间取决于弧的遍历时间或提前时间时，以最小的传输时间将给定数量的项目从源节点传输到目标节点。 ，以及沿弧或容量的流率。在电信网络中，电弧通常还具有相关的传输无故障运行概率。路径的可靠性定义为它的弧的操作概率的乘积。可靠性以及传输时间很重要。本文提出了一种算法来解决最快路径问题以及识别可靠性不低于给定阈值的最快路径的问题。该算法既依赖于将最短路径的计算转换为最短路径的计算的网络属性，又依赖于可以通过其弧的有序序列的可靠性来评估路径的可靠性这一事实。对消耗的资源，路径的弧数等的其他约束也可以使用相同的算法进行管理。

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