Research On The Analysis And Optimization Of Spatially Embedded Complex Networks And Its Application In The Urban Public Bus Transportation Networks

Real-world complex systems are often consist of multiple components that are connected by a network. The networks inside them undertake the duty of transferring material, information or energy which is necessary for the basic functionality of these systems. Complex network research is a newly uprising research subject in the recent one decade. The basic standing point of the subject is to abstractly depict complex systems by networks which incorporate several specific features of the corresponding systems, and processing the analyzing, modeling and application researches of the systems through the networks. The studies of introducing the spatially embedding or multiple-layer coupling factors, which can be broadly observed in real-world networks, into complex network research recently draw huge interests and attentions from network researchers. In this paper, we present some of our works in the complex network modeling, analyzing and optimization which are related with spatially embedded networks, multiple-layer coupled networks and public bus transportation networks. The works of the paper includes the following five contents.Firstly, a self-organized evolving model for non-growth networks based on internal edge weight adjusting is proposed to explain the power-law (or power-law-like) degree distributions which can be widely observed in real-world networks. Through theoretical analysis and numerical simulation, some network features such as the node strength and the edge weight distributions are studied. The result shows that the network generated by the model possesses power-law (or power-law-like) node strength and degree distributions, exponential edge-weight distribution. And it indicates that the connection density of a network can influence the form of its node strength and degree distributions. Then, spatially embedding fators are introduced into the model. Numerical simulation shows that edge resource limitation and the preference on edge length can also influence the network structure.Secondly, a public bus transportation network representing model which taking account of some spatially embedding factors is proposed. Based on the model, some static network features, such as the degree distribution, the clustering coefficient and the average path length, of the public bus transportation networks of three typical cities in China, namely Beijing, Shanghai and Hangzhou are studied. The result shows that the abundant existence of short-distant-walking station pairs can influence the path length of bus networks in a great way.Thirdly, an analyzing framework for the passenger flow in public bus transportation networks is proposed. The framework consists of two parts. One is a newly proposed parameterized bus transfer computation algorithm. The algorithm takes into account of short-distance-walking station pairs, and it can offer multiple best transfer plans for each of the assigned stations pairs. The second is the defining of some passenger flow indicators for the networks based on the transfer plans offered by the aforementioned algorithm. Through both the analyzing framework and a numerical simulation programe, the distribution of the passenger flow of the public bus transportation network of Hangzhou is studied. The result shows that, very few bus routes which undertake huge amount of passenger flow are main attributes of the congestion in public bus transportation networks.Fourthly, a low time-complexity network path length optimization method, which taking into account path length and utilizing the network flow demand, is proposed. In the method, an assessment indicator for the average path length decrease of adding an edge is used to avoid the frequent time-consuming network path length computation. Then, the validity of the method is tested and proved by a numerical simulation run on some common spatial network models.Lastly, a network model for a kind of broadly existed two-layer coupled networks, namely the base-core two-layer coupled networks, is proposed. Based on the model, the transfer performance of the two-layer network in different situations, such as different network structures, core network sizes, traffic demand patterns and coupling strategies between the base and core networks, are widely studied through a numerical simulation.