Study Of The Trafficdynamics On Complex Networks

The dissertation studies physical problems of traffic dynamics on complex networks. There are six chapters.In the first chapter, we introduce basic concepts on the topology of complex networks, including terminology and algorithms used in the following chapters, as well as empirical results and theoretical models.In the second chapter, we use generating function formalism to obtain an exact formula of the betweenness centrality in finite components of random networks with arbitrary degree distributions. The formula is confirmed by simulations for Poisson, exponential, and power-law degree distributions. We find that the betweenness centralities for the three distributions are asymptotically power laws with exponent 1.5 and are invariant to the particular distribution parameters if the sizes of the finite components are known. In the third chapter, we introduce basic concepts on the traffic dynamics, including phase transition, performance and robustness.In the fourth chapter, we investigate the percentage of delivering capacities that are actually consumed in a traffic dynamics where the capacities are uniformly assigned over a scale-free network. Theoretical analyses, as well as simulations, reveal that there are a large number of idle nodes under both free and weak congested state of the network. It is worth noting that there is a critical value of effective betweenness to classify nodes in the weak congested state, below which the node has a constant queue size but above which the queue size increases with time. We also show that the consumption ratio of delivering capacities can be boosted to nearly 100% by adopting a proper distribution of the capacities, which at the same time enhances the network efficiency to the maximum for the current routing strategy.In the fifth chapter, we propose a resource distribution strategy to reduce the average travel time in a transportation network given a fixed generation rate. Suppose that there are essential resources to avoid congestion in the network as well as some extra resources. The strategy distributes the essential resources by the average loads on the vertices and integrates the fluctuations of the instantaneous loads into the distribution of the extra resources. The fluctuations are calculated with the assumption of unlimited resources, where the calculation is incorporated into the calculation of the average loads without adding to the time complexity. Simulation results show that the fluctuation integrated strategy provides shorter average travel time than a previous distribution strategy while keeping similar robustness; the strategy is especially beneficial when the extra resources are scarce and the network is heterogeneous and lowly loaded.In the sixth chapter,we study the robustness of several network models subject to edge removal. The robustness is measured by the statistics of network breakdowns, where a breakdown is defined as the destroying of the total connectedness of a network, rather than the disappearance of the giant component. We introduce a simple traffic dynamics as the function of a network topology, and the total connectedness can be destroyed in the sense of either the topology or the function. The overall effect of the topological breakdown and the functional breakdown, as well as the relative importance of the topological robustness and the functional robustness, are studied under two edge removal strategies.