  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.
