Empirical And Simulation Research On The Complex Networks Of Urban Bus-transport Systems

Urban bus-transport systems are key infrastructures of modern cities, and they should be researched deeply. Their still existing defects even after long history evolutions need to be analyzed from a new viewpoint, which Complex Network can provide. This research on urban bus-transport networks (Abbr. BTNs) is carried out by empirical study, theoretical analysis and numerical simulation.The author maps four urban bus-transport systems at the cities of Hangzhou, Nanjing, Beijing & Shanghai in China into BTNs by three methods corresponding to Spaces of the route relation, the stop geographical relation and the bus-transferring relation respectively. 1) Compared with random networks with same sizes, all the considered BTNs have"small world phenomena"with a large clustering coefficient and a small average shortest path length, i.e. only through several steps the passengers can transfer from one bus line to any other bus line, or from one stop to another. 2) The topological BTNs are identified as networks with"positive assortative correlation", which are networks with"pseudo positive assortative correlations"in fact, by some common used measurements, hence Dn n( k ), named the average sum of the nearest neighbor degree of the same degree, is proposed to unveil the BTN's underlying randomly linking correlation. 3) Further, the author uncovers that there is a common stochastic organization law in those topological BTNs identified by Dn n( k ), but their corresponding weighted BTNs (The multi-edges are considered as one's link weight between a pair of vertices.) have positive assortative relations among the adjacent vertices following the power law, i.e. Dn wn( k )∝kβ, whereβ(>1) is constant, which means that a vertex with a larger degree connect preferentially with the others with a large edge-weight degree convergence; therefore, the topological BTNs and the weighted ones have different vertex linking laws, i.e. evolution mechanisms. These facts present qualitative arguments that confirm the importance of the weight and its weighted measurements since the topological measurements can not fully reveal the intrinsic coupling mechanisms among vertices. 4) In the bus-transferring space BTNs, each vertex follows a shifted power-law degree distribution, approaching to an exponential distribution. 5) In the stop geographical space BTNs, every vertex degree distribution has an exponential function form with lower head, and every vertex strength distribution has also an exponential law form but with asymmetric exponents between even and odd strengths. 6) The complementary cumulative distributions of degree and strength are approximate different lines, but they converge to one same line after scaled by their average degree or average strength respectively.Further, the study is focused on the identification and simulation of the evolution law of the real-life BTNs. The statistical results of the four metropolis BTNs in the bus-transferring space show that the networks connectivity does not follow a scale-free degree distribution as most of the other networks do. The shifted power-law mended model proposed at present can analytically reproduce the real-life BTNs with the similar degree distributions tails. Two important ingredients: growth and linear preferential attachment with initial attractor, which are inferred by two facts of preference and random attachment principles in real-life evolutional BTNs, are considered in this model. From the statistical results, we know that in each empirical BTN in the stop geographical space, its vertex degree distribution has an exponential tail and lower head, and its vertex strength distribution has also an exponential law form with asymmetric exponents of even and odd strengths. Those empirical facts imply (infer) that those properties are induced by the constraints of geographical ground with local evolution rules of vertex randomly connected to its near-neighbor vertices as a route walks on stops without self-intersection. A simple model considered those points has been developed, and its simulation results consist with those key findings.The study on the competition and cooperation relations among bus lines is quantitatively presented and the formulas of the measurements of competition and cooperation are given independently. In addition, based on the Nanjing BTN, one model is proposed to simulate its growth process and operation. To explore BTN's competition and cooperation relations led by different correlations by the vertex bus line weights as positive relation, negative relation or mixing relation, many independent numerical simulations have been realized. The simulation results have a theoretical value for optimizing real-life urban bus-transport systems.Finally, it must be claimed that the present study is only at its beginning stage, and the obtained results at present are expected to be verified in a larger scope of samples and more deeply theoretical studies. To unveil the underlying evolution law and to construct more accurate models of real-life BTNs are the author's next goals.