Matrix Analysis Of Reachability Structure In Traffic Network

The discussion of the maximum road width in the traffic network is extended from two vertices to the whole structure on the basis of the study of the matrix standard form. The paper provides theories and practical methods for the improvement of the network reachability and its degree analysis.In the paper, the kinds of reachability notions are defined and charactered firstly in their matrices and graphs. By the discussion of the matrix standard form and its transitive closure, the relation among the maximum partial reachability sets, the standard form of the matrix and its transitive closure are posted and the network partial reachability is based. The standard form provides methods for the improvement of the network reachability.The reachability degree and its matrix character have been done, when the maximum strong component is defined. On the basis of the maximum strong component, the standard form in Fuzzy Matrix is given, and the maximum reachability degree analysis of the network is realized.The equivalent definition of the minimal strong component is given, and it discusses the relation between the standard form and the minimal strong component in the paper. Consequently, the theory is proved that the periodicity of a fuzzy matrix is the least common multiple of periodicity of its minimal strong component. Lastly, the paper studies the periodicity of the minimal strong components and the circularly dominating index.The paper has the aerial traffic network as the background, puts eyes on the whole structure analysis and the maximum reachability degree, and provides methods for the network analysis and its design. The new given concepts and tools not only extend the theory of fuzzy matrix, but also increase the content of fuzzy matrix.