Optimization Of Traffic Congestion And Cascades On Complex Networks

In the past few years, with the rapid development of the information technology such as the Internet, human society has entered the area of complex networks. The impacts of complex networks are prominent and deemed to be far-reaching in human lives. As a new research direction which is called network science, the research of complex networks has been deeply evolved into various fields of science and engi-neering. Furthermore, fruitful progress and remarkable achievements have been made. This graduation design mainly focuses on two important topics in complex networks--the optimization research on traffic congestion and cascading failures, which are both very significant to practical networks in our daily life. The transmission of informa-tion in the communication networks is under the control of the existing communication protocols, meanwhile, the load redistribution of the power girds during the process of cascading failures can not be separated from the calculation of the voltage and current values. The study of the combination of network science and practical engineering is very meaningful. Specifically, this article contains the following three outcomes:(1)Under the real elastic traffic model in communication networks, we propose a more comprehensive concept of resource allocation. Combined with the traffic con-gestion protocol, a convex optimization problem has been established to find the optimal resource allocation strategy while maximizing the traffic performance. To solve this problem, an iterative algorithm has been designed, which can be ef-ficiently embedded into the control of traffic flows. In the last, we prove that the algorithm is theoretically optimal and simulations under the classical complex network models have been made to guarantee the optimal performance.(2)In the cascading failure model proposed by Motter and Lai, we establish two multi-objective combinatorial optimization problems, aiming to identify the effects of links during the propagation of failures while taking the network robustness and operation cost into consideration. Removing links with negative effects can help to defend the cascading failures efficiently, while protecting links with positive effects can be vital to avoid the attacks again during the cascade. We apply one efficient algorithm to identify these two effects of links successfully. This work may be useful for decision makers to take appropriate actions when cascading failures occur.(3)Electrical characteristics are basic elements in power grids, which should be con-sidered when evaluating the performance of grids. In this research, we adopt a newly proposed cascading failure model which integrates the electrical char-acteristics into cascade process. To optimize the robustness of power grids, we propose an optimization problem to design the optimal topology. By using the simulated annealing algorithm, we obtain the best performance of robustness and the corresponding optimal topologies. After investigating the relationship between topological characteristics and the network robustness, some conclu-sions have been drawn. Such work plays an important role in promoting the transformation of network science into network engineering.