Evaluating the reliability of a novel deterioration-effect multi-state flow network

In a traditional multi-state flow network (MFN), the flow values into and out of any arc are assumed to be equal. In practical application, however, the flow may undergo a loss due to deterioration. For example, electrical power will decrease if the transmission distance is too great. Hence, a novel MFN model called the deterioration-effect MFN (MFNde) is proposed to address this real world problem. A straightforward and simple algorithm based on a novel concept called the deterioration-effect d-minimal path (d-MPde) is presented to evaluate the reliability of an MFNde, which is defined as the probability that at least d units of data can be received by the sink node through the MFNde. The computational complexity of the proposed algorithm is also analyzed. Finally, an example is presented to illustrate how the reliability of an MFNde is calculated using the proposed algorithm.