Evaluating the transmission distance-constrained reliability for a multi-state flow network

Reliability features in judging the performance of various technical networks (e.g., logistics network and communication network) that can be deemed as a multi-state flow network (MFN). The existing studies dedicate to computing the reliability of an MFN without transmission distance constraint. However, transmission distance is a major concern in some practical applications. For example, there is a strict limit on the transmission distance in a wireless communication network so as to ensure the successful transmission of packets within the allowed delay. This paper, thus, concentrates on the transmission distance-constrained reliability of an MFN, denoting the probability that at least d units of flow can be transmitted from the source to the sink with the transmission distance no larger than a predetermined value D. To reduce the computational complexity, a universal approach is presented to identify and remove redundant edges with no contribution to network reliability. Moreover, a novel model is developed to seek all (D,d)−minimalpaths((D,d)−MPs) based on which an efficient algorithm is put forward to calculate the transmission distance-constrained reliability of an MFN. A large example is discussed to explore the influence of transmission distance on MFN reliability, and a practical case study is provided to demonstrate the utility of the proposed algorithm.