关键词: 多状态网络，随机流量网络，可靠度界，边状态枚举

Abstract: In order to reduce complexity of calculating multi-state network reliability, considering stay probability and effect on network capability when transfering to adjacent state of multimode arc in each intermediate state,an algorithm for calculating multi-state network reliability dynamic bounds based on arc state enumeration was proposed. Firstly, as- suming arcs can be in either of two states: operating or failed, obtained initial reliability upper and lower bounds respec- lively by adding probability of each arc in all intermediate states to probability of operating or failed state. Then, itera- lively enumerated intermediate states in order of decreasing effect to network reliability, and calculated variation value of upper and lower bounds by comparison operation of sets,while it derived a series of decreasing upper bounds and a se- ries of increasing lower bounds simultaneously,guarantecd to enclose the exact reliability value. The algorithm does not require a priori the d-minimal cuts or d-minimal puts of the multi-state network, and can ensure an exact difference be- tween the upper and lower bounds with enumerating fewer network states. Related lemma warrant and example analysis verify correctness and effectiveness of the algorithm.

Key words: Multi state network, Stochasti}flow network, Reliability bound, Arc state enumeration