Network reliability of a stochastic flow network by wrapping linear programming models into a Monte-Carlo simulation

A stochastic flow network (SFN) serves as a fundamental framework for real-life network-structured systems and various applications. Network reliability NRd d is defined as the probability that an SFN can successfully send at least d units of demand from a source to a terminal. Current analytical algorithms for the network reliability evaluation are classified into an NP-hard problem. This limitation hinders the ability of decision-makers to monitor and manage decisions for an SFN flexibly and immediately. Therefore, this paper develops an algorithm to estimate network reliability by wrapping developed linear programming (LP) models based on minimal paths (MPs) into a Monte-Carlo simulation. The developed LP models present satisfaction of the demand d in the SFN in terms of minimal paths. The effectiveness and efficiency of the proposed algorithm are verified using a series of numerical investigations. Contributions are manifold: (1) an integrated model with the simulation and LP models is provided to estimate network reliability in terms of the MPs, thereby filling a crucial gap in existing research; (2) the scalability and efficiency of the proposed method are shown for the complex SFNs; (3) decision-making capabilities can be provided under real-time reliability predictions.