复杂网络上的传输：流、干扰与优化
Transport on Complex Networks: Flow, Jamming and Optimization
摘要：
网络上的许多输运过程在很大程度上依赖于底层网络的几何结构，尽管网络结构和输运过程的性质之间的确切关系仍然难以捉摸。在本文中，我们解决这个问题，通过使用数值模型，其中结构和动力学控制系统。我们考虑的信息包的流量，包括驱动，搜索和排队。我们提出了两类网络的广泛模拟的结果;相关的循环无标度网络和不相关的均匀弱簇网络。通过测量不同的动力学变量在自由流制度，我们展示了如何在各个节点（交通噪声）和链接（交通流量）的时间波动的整体统计特性的运输。然后，我们证明了这两个网络类出现在低密度和高密度交通的制度，分别作为最佳交通流的代表拓扑结构。我们还确定了不同的网络几何形状的预堵塞制度的统计指标，并讨论了排队和动态介数的交通拥堵的作用。在不同的网络拓扑结构上，以临界投递率向拥塞交通状态的过渡被研究为具有适当的序参量的相变。我们还解决了几个开放的理论问题有关的网络动力学。
英文摘要：
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics.
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