一种大规模无线Ad-Hoc网络路由理论
A Theory of Routing for Large-Scale Wireless Ad-Hoc Networks
摘要：
在这项工作中，我们开发了一个新的理论来分析在大规模的ad-hoc无线网络的路由过程。我们使用的路径积分公式来检查这些类型的网络中不同的路由策略所产生的路径的属性。使用这个理论框架，我们计算的统计分布之间的距离在网络中的任何源到任何目的地，因此，我们能够推导出一个长度参数，这是唯一的每个路由策略。该参数被定义为{ \it有效半径}，有效地对节点所需的路由信息进行编码。分析上述不同路由策略的统计分布，我们得到了实际大规模无线Ad-Hoc网络的三重结果：1）对于任何给定的路由策略，我们获得了网络中所有路径的长度分布，2）我们能够根据其有效半径的演变来识别“好的”路由策略，作为节点的数量，$N$，3）对于任何具有有限有效半径的路由策略，我们证明了在大规模网络中，等价于随机路由策略，并且其传输容量以每秒$Θ(\sqrt{N})$比特米为尺度，从而恢复了Gupta和Kumar（2000）作为单路由大规模无线网络的极限而获得的缩放定律。
英文摘要：
In this work we develop a new theory to analyse the process of routing in large-scale ad-hoc wireless networks. We use a path integral formulation to examine the properties of the paths generated by different routing strategies in these kinds of networks. Using this theoretical framework, we calculate the statistical distribution of the distances between any source to any destination in the network, hence we are able to deduce a length parameter that is unique for each routing strategy. This parameter, defined as the {\it effective radius}, effectively encodes the routing information required by a node. Analysing the aforementioned statistical distribution for different routing strategies, we obtain a threefold result for practical Large-Scale Wireless Ad-Hoc Networks: 1) We obtain the distribution of the lengths of all the paths in a network for any given routing strategy, 2) We are able to identify "good" routing strategies depending on the evolution of its effective radius as the number of nodes, $N$, increases to infinity, 3) For any routing strategy with finite effective radius, we demonstrate that, in a large-scale network, is equivalent to a random routing strategy and that its transport capacity scales as $Θ(\sqrt{N})$ bit-meters per second, thus retrieving the scaling law that Gupta and Kumar (2000) obtained as the limit for single-route large-scale wireless networks.
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