This study presents algorithms to determine the most reliable routes on stochastic and time-dependent networks. The measure of reliability adopted is the probability of on-time arrival at the destination, given a threshold arrival-time. We propose two distinct algorithms to determine optimal time-adaptive strategy and optimal apriori path on stochastic and time-dependent networks. First, a decreasing order-of-time algorithm is proposed to determine the optimal strategy to the sink from all node and departure-time combinations. Second, a label-correcting, network pruning algorithm is proposed to determine the optimal path between the source and the sink for a given departure-time. The correctness of both the proposed algorithms is proved and their computational complexity expressions are derived. The efficacy of the proposed procedures is demonstrated on large-scale transportation networks. This work has the potential to facilitate wider application of stochastic and time-dependent networks in reliability-based modeling and analysis.

这项研究提出了确定随机和时间相关网络上最可靠路由的算法。给定阈值到达时间，采用的可靠性度量是准时到达目的地的概率。我们提出了两种不同的算法，以确定随机和时间相关网络上的最佳时间自适应策略和最佳先验路径。首先，提出了一种递减的时间顺序算法，用于从所有节点和出发时间组合中确定接收器的最佳策略。其次，提出了一种标签校正网络修剪算法，以确定给定离开时间的源和宿之间的最佳路径。证明了两种算法的正确性，并推导了它们的计算复杂度表达式。所提出的程序的有效性在大规模的运输网络上得到了证明。这项工作有可能促进随机和时间相关网络在基于可靠性的建模和分析中的广泛应用。