Studies On The Dynamical Properties Of Traffic Processes On Complex Networks

Networks are sets of vertices and edges. There are many kinds of networks in our world and daily life. Some networks play an important role in people's lives, such as the Internet, the communications networks and urban traffic networks. Since the end of last century, complex networks have been considered as an important approach for describing and understanding complex systems.Complex network theory has been extensively researched by many researchers. Today, many networks have been widely studied, such as: the Internet, World Wide Web, wireless telecommunication networks, urban road networks, airline networks, power grids, research collaboration networks, protein-protein interaction networks, and so on. Study of these networks is not only crucial to people's work and life, but also lead to the interdisciplinary development and interaction of statistical physics, applied mathematics, nonlinear dynamics, computer science, sociology, biology and other subjects.The purpose of studying complex networks is to understand the function of the real network system. The characteristics of traffic dynamic processes taking place on networks is a focus of network study. In this paper, we have systematically investigated the dynamics of information traffic on complex networks, including routing strategies, hysteresis phenomena, traffic resource allocation and the optimization routing under the condition of limited resources. The main work for this paper is as follows.Routing strategies based on local and/or global information. In the field of local routing strategy, we proposed a pheromone routing strategy which is based on the local link pheromone density. Comparing with other local strategy, using the pheromone strategy, the system can achieve a larger network capacity. In the field of global routing strategy, we proposed global dynamic routing strategy, global pheromone routing strategy and integrated routing strategy. (I) Global dynamic routing strategy: the path between source and destination is selected in the way that the sum of node queue lengths is minimal. Compared with other global routing strategy, the global dynamic routing can greatly improve the network's transmission efficiency.(II)Global pheromone routing strategy: In the global routing strategy, because the node queue lengths change from time to time, it is computation consuming to update the global dynamic paths. To avoid this situation, we proposed the global pheromone routing strategy. Using the global pheromone routing strategy, the network capacity is slightly smaller than that of using the global dynamic routing strategy. But the global pheromone routing strategy can avoid path updating, so it can save a large amount of computing resources. (III) Integrated routing strategy: In real system, information packets or cars non-homogeneously select destinations. Inspired by this situation, we proposed an integrated routing strategy. In this routing strategy, the information packets or cars use different routing strategies for different destinations. The integrated routing strategy can greatly improve the network's transmission efficiency.The dynamical hysteresis is investigated in constant-density traffic system of the scale-free networks, small-world networks, and lattice grids. With the local-searching strategy, hysteresis persists for the scale-free networks, while it disappears for small-world networks and lattice grids when the handling ability of nodes is higher than a certain threshold. With the global information strategy, hysteresis persists for all the three networks investigated.Optimal traffic resource allocation strategies are studied for complex network systems. The resources are the node's total packet-delivering capacity, the link's total bandwidth and node's buffer. For each resource, the optimal allocation strategies depend on the node's or link's algorithmic betweenness. With the optimal resource allocation strategy, using the shortest path strategy, the network's capacity can achieve the largest.We propose an optimization routing algorithm to improve the traffic flux where each node has a finite buffer and each link has a finite bandwidth. In different network structures, the system can reach a very high flux and the network's capacity when using the optimized routing strategy.