复杂网络拥塞现象的极小模型
A minimal model for congestion phenomena on complex networks
摘要：
我们研究了复杂网络中交通流的一个极小模型，该模型简单得足以得到解析结果，但具有非常丰富的现象学，呈现出自由流阶段和拥塞阶段之间的连续、不连续以及混合相变，临界点和系统大小的不同标度行为.它由一个具有单范围排斥的移动网络上的随机行走器组成，在这个网络中，粒子只有在移动时才能被摧毁。我们专注于依赖的拓扑结构，以及对交通控制的水平。我们能够获得的过渡曲线和相图在分析水平上的合奏的不相关的网络和数值的单个实例。我们发现，流量控制提高了全局性能，扩大了自由流区域的参数空间中，只有在异构网络。交通控制引入非线性效应，并且超过临界强度，可能以不连续的方式触发拥塞阶段的出现。该模型还再现了在互联网上经验观察到的交通波动的缩放中的交叉，并且，保守的版本可以定性地再现交通网络中的一些程式化的事实。
英文摘要：
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase and a congested phase, critical points and different scaling behaviors in the system size. It consists of random walkers on a queueing network with one-range repulsion, where particles can be destroyed only if they can move. We focus on the dependence on the topology as well as on the level of traffic control. We are able to obtain transition curves and phase diagrams at analytical level for the ensemble of uncorrelated networks and numerically for single instances. We find that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks. Traffic control introduces non-linear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner. The model also reproduces the cross-over in the scaling of traffic fluctuations empirically observed in the Internet, and moreover, a conserved version can reproduce qualitatively some stylized facts of traffic in transportation networks.
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