| Network reliability has always been an important parameter to index the network performance and its importance reflects in network design,maintenance strategy and so on.The definition of expected-path length based on the reliability indicates the average s-t path length with the probability of communication in the network.It is meaningful to analyze the important communication part in the network based on the expected-path length for network design and evaluation.The main conclusions of this paper are as follows:1.As for unreliable-edge model,a two-terminal network reliability model with the expected-path length constraint is proposed.We give definitions of the original graph,the positive and negative s-t paths,the maximal graph,the redundant effective sub-graph and the optimal sub-graph.The optimization problem of finding the maximum reliability sub-graph with expected-path constraint is transformed into the problem of finding the maximal graph.By the rules of deleting redundant efficient sub-graphs,the optimal sub-graph algorithm is designed.2.As for unreliable-vertex model,we give the network a diameter constraint and give the definition of redundant vertexes.The properties of the expected-path function with diameter constraint are discussed.We design an algorithm to transform expected-path constraint into diameter constraint by using the properties of the function. |
