A path-based simulation approach for multistate flow network reliability estimation without using boundary points

A multistate flow network is useful for the effective and efficient model construction and reliability evaluation of large and complex systems. To evaluate the reliability of a multistate flow network, boundary points for specified demands are generated in the existing path- and cut-based methodologies. Using the boundary points, the system reliability can be calculated using analytical or simulation methodologies. However, evaluating reliability using boundary points is an NP-hard problem. To improve the time efficiency of reliability estimation, a path-based simulation approach without boundary points is proposed in this study, where the minimal path without any cycles is used. The contributions of this study are threefold: First, the proposed path-based simulation complements the cut-based simulation to improve the applicability of reliability estimation for various network topologies. Second, the proposed simulation algorithm presents linear time complexity, whereas conventional boundary-based analytical methodologies or simulations consume exponential/factorial time. Third, the time attribute is included in the proposed simulation approach to analyze the behavior of reliability degradation over time. The experimental results, including those of a case study, indicate that the proposed path-based simulation is more effective and efficient than existing boundary-based approaches, particularly for large and complex systems.