Reliability Analysis of Interdependent Stochastic-Flow Networks

Network reliability assessment is extremely important for modern complex systems to ensure higher performance in operations and develop effective maintenance plans. Existing literature on network reliability evaluation was primarily focused on single networks and their functioning although the majority of modern systems' networks are interdependent i.e., the failure of one network impacts the failure of other networks as well. Therefore, it is necessary to consider interdependency in network reliability evaluation to design and maintain a high-performance complex system. This paper aims to evaluate the reliability of two interdependent stochastic-flow networks under varying dependencies over specific time horizons. In the proposed framework, the individual network's reliability is estimated using the minimal cut (MC) upper boundary points at level k, which is referred to as k-MC. A simple bridge network is considered for the reliability study. With a given demand of k=3, five upper boundary points are obtained, resulting in a network reliability value of R4 = 0.55233. To observe the dynamic behavior of the network, an exponential distribution is employed, revealing a decreasing trend in the network's reliability over time. Functional dependencies are then created between the source and destination nodes of the two identical networks. The estimated individual network reliability is then utilized to evaluate the partial and complete dependencies on the performance of the complex interdependent system while considering time dependency. It is found that the reliability of an interdependent network decreases more rapidly over time compared to an independent condition. The proposed method is demonstrated with a complex system's network case study analysis. This model can be applied to estimate the reliability of complex systems that are mutually dependent, such as power systems, communication systems, transportation systems, and water distribution systems, while capturing their interdependent behavior, including when they are most vulnerable to disruptions.