Abstract
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 (MFN de ) 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-MP de ) is presented to evaluate the reliability of an MFN de , which is defined as the probability that at least d units of data can be received by the sink node through the MFN de . The computational complexity of the proposed algorithm is also analyzed. Finally, an example is presented to illustrate how the reliability of an MFN de is calculated using the proposed algorithm. © 2013 Elsevier Inc. All rights reserved.