通信网络中的梯度机制
The Gradient Mechanism in a Communication Network
摘要：
我们研究了在$2-d$通信网络的规则节点和随机分布的集线器的消息传递的梯度机制的效率。网络上的每个集线器都被分配了一些随机选择的容量，容量较低的集线器连接到容量最大的集线器。单个消息在这个网格上传播的平均传播时间，作为枢纽密度的函数绘制，显示出q指数行为。在高枢纽密度，这种分布可以很好地拟合的幂律。我们还研究了当大量的消息同时在随机位置创建，并在网络上向其指定的目的地旅行时，网络的松弛行为。对于这种情况，在没有梯度机制的情况下，网络可以表现出拥塞效应，由于形成的传输陷阱。我们表明，如果枢纽的高介数中心连接的梯度机制，可以实现有效的去拥塞。梯度机制比其他去拥塞方案更不容易形成陷阱。我们还研究了运输陷阱的空间配置，并提出了消除它们的最小策略。
英文摘要：
We study the efficiency of the gradient mechanism of message transfer in a $2-d$ communication network of regular nodes and randomly distributed hubs. Each hub on the network is assigned some randomly chosen capacity and hubs with lower capacities are connected to the hubs with maximum capacity. The average travel time of single messages traveling on this lattice, plotted as a function of hub density, shows q-exponential behavior. At high hub densities, this distribution can be fitted well by a power law. We also study the relaxation behavior of the network when a large number of messages are created simultaneously at random locations, and travel on the network towards their designated destinations. For this situation, in the absence of the gradient mechanism, the network can show congestion effects due to the formation of transport traps. We show that if hubs of high betweenness centrality are connected by the gradient mechanism, efficient decongestion can be achieved. The gradient mechanism is less prone to the formation of traps than other decongestion schemes. We also study the spatial configurations of transport traps, and propose minimal strategies for their elimination.
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