复杂动态网络上信息输运的统计物理问题研究

The ultimate aim of studying the infoimformation transport on complex networks is to relieve the growing problem of congestion and to enhance the efficiency of communication. Previous statistical physics researches about the imformation transport are carried on static networks, where nodes can not move and links do not change. However, the structures of many real communication systems are dynamically changed. Our project will study the two satistical physics problems about the infoimformation transport on complex networks. One is the phase transition from the free-flow state to jammed state. The other is the average arriving time of packets. In complex dynamic networks, the movement of nodes leads to the change of neighboring nodes in the communication range. Our project will build the movement mode of communication nodes according to the power-law distribution of human movement distances. We will adopt two information routing rules: the random-delivery routing and the distance-based routing. By numerical experiments, we will compare how the two routings affect the information transport capacity of complex dynamic networks. We will give a theoretical derivation about the average arriving time of packets based on Fokker-Planck equation. Furthermore, we can get the analytical expression of critical packet-generating rate according to the queuing theory. Our project aims to provide theoretical references for the enhancement of information transport capacity on complex dynamic systems from the perspective of statistical physics.

研究复杂网络信息输运的最终目标是缓解日益严重的信息堵塞和提高通讯效率。前人关于信息输运的统计物理问题研究都是在静态网络上进行。静态网络中的节点不会发生移动，节点间的连边不会发生变化。但是许多实际通讯系统的结构是在不断变化的。本项目将研究复杂动态网络信息输运中的两个统计物理问题：信息流从自由态到堵塞态的相变以及信息包的平均到达时间。复杂动态网络中，节点的移动会导致其通讯范围内的邻居节点发生变化。本项目将依据人类活动距离的幂律分布特性，建立相应的通讯节点移动模式。本项目将采取两种信息传输的路径规则：随机投递的路由和基于距离的路由。通过数值仿真实验，比较这两种路由对复杂动态网络信息输运能力的影响。此外，本项目将通过福克—普朗克方程，对信息包平均到达时间进行理论推导，进而根据排队论得到临界信息包产生率的解析表达式。本项目的研究旨在从统计物理角度出发，为复杂动态系统中信息输运能力的提高提供理论参考。

研究复杂网络信息输运的最终目标是缓解日益严重的信息堵塞和提高通讯效率。前人关于信息输运的统计物理问题研究都是在静态网络上进行。静态网络中的节点不会发生移动，节点间的连边不会发生变化。但是许多实际通讯系统的结构是在不断变化的。我们针对动态网络上的路由选择问题进行了深入了的研究。我们提出了一种基于距离的路由。相比于前人提出的随机路由，基于距离的路由在很大程度上提高了网络的信息处理能力。此外，我们还提出了一种结合距离和局域信息的自适应路由，该路由极大缩短了信息传输的平均时间。