A simulation approach with heuristic rules for reliability estimation of two-terminal multi-state networks based on minimal cuts and parallel computations

Both the system reliability and the resilience evaluation of multi-state flow networks (MFNs) play a crucial role in designing and analyzing these networks. The system reliability at level $d$ is the probability of successfully transmitting at least $d$ units of flow. In turn, system resilience allows us to analyze the ability of systems to withstand and bounce back from disruptive events. The paper presents a new simulation approach based on minimal cuts (MCs) and parallel computations to compute the system reliability for all possible non-integer levels. An extension with a time attribute is also considered to investigate the reliability degradation with time. Moreover, it also introduces a novel heuristic that for a given integer $K$ and a state vector $x$, finds an MC for which the capacity under the system state $x$ is the smallest among MCs containing some of $K$ coordinates of $x$ with the smallest capacities. It is also shown how this approach can be used to compute the network resilience at a given time and the system integrated resilience metric is introduced. Numerical experiments are conducted to demonstrate the efficiency and advantages of the presented algorithm.