Methodology for the reliability evaluation of the novel learning-effect multi-state flow network

Abstract

ABSTRACTIn the traditional multi-state flow networks (MFNs), it is assumed that the flow is fixed in each arc. However, the flow may experience gain after transmission via arcs in many real-life applications; e.g., the infected population size is increased from time to time for a certain period during outbreaks of disease, the number of bit errors is amplified in digital transmission, etc. Hence, a novel network model called the learning-effect MFN (MFNle) is proposed to meet real-world problems. A straightforward and simple algorithm based on minimal path (MP) set is presented here to evaluate MFNle reliability, which is defined as the probability that at least d units of data can be sent from the source node and dout (≥d) units of data exists from the sink node through a single MP in the MFNle. The computational complexity of the proposed algorithm is also analyzed. Finally, an example is given to illustrate how the MFNle reliability is calculated using the proposed algorithm.