Evaluating the reliability of complex technical networks, such as those in energy distribution, logistics, and transportation systems, is of paramount importance. These networks are often represented as multistate flow networks (MFNs). While there has been considerable research on assessing MFN reliability, many studies still need to pay more attention to a critical factor: transmission distance constraints. These constraints are typical in real-world applications, such as Internet infrastructure, where controlling the distances between data centers, network nodes, and end-users is vital for ensuring low latency and efficient data transmission. This paper addresses the evaluation of MFN reliability under distance constraints. Specifically, it focuses on determining the probability that a minimum of $d$ flow units can be transmitted successfully from a source node to a sink node, using only paths with lengths not exceeding a predefined distance limit of $\lambda $. We introduce an effective algorithm to tackle this challenge, provide a benchmark example to illustrate its application and analyze its computational complexity.

翻译：评估复杂技术网络（如能源分配、物流和运输系统中的网络）的可靠性至关重要。这些网络通常被建模为多状态流网络（MFNs）。尽管已有大量关于MFN可靠性评估的研究，但许多研究仍忽视了一个关键因素：传输距离限制。这类约束在实际应用中非常典型，例如在互联网基础设施中，控制数据中心、网络节点与终端用户之间的距离对确保低延迟和高效数据传输至关重要。本文研究了距离约束下MFN的可靠性评估问题，具体聚焦于确定在仅使用长度不超过预定距离限制λ的路径时，能够从源节点成功传输至少d个流量单位的概率。我们提出了一种有效的算法来解决这一挑战，提供了基准示例以说明其应用，并分析了其计算复杂度。