Near-Optimal Load Balancing in Dense Wireless Multi-Hop Networks

E. Hyytia, J. Virtamo
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引用次数: 7

Abstract

We consider the load balancing problem in wireless multi-hop networks. In the limit of a dense network, there is a strong separation between the macroscopic and microscopic scales, and the load balancing problem can be formulated as finding continuous curves ("routes") between all source-destination pairs that minimize the maximum of the so-called scalar packet flux ("traffic load"). In this paper we re-formulate the problem by focusing entirely on the so-called d-flows (vector flow field of packets with a common destination x) and by looking at the equation these flows have to satisfy. The general solution to this equation can be written in terms of a single unknown scalar function, psi(r, x), related to the circulation density of the d-flow, for which function the optimization task can be presented as a problem of variational calculus. In this approach, we avoid completely dealing with systems of paths and calculating the load distribution resulting from the use of a given set of paths. Once the optimal solution for psi(r, x) is found the corresponding paths are obtained as the flow lines of the d-flows. In the example of a unit disk with uniform traffic demands we are able to find a set of paths which is considerably better than any previously published results, yielding a low maximal scalar flux and an extraordinarily flat load distribution. We further illustrate the methodology for a unit square with comparable improvements achieved.
密集无线多跳网络中的近最优负载均衡
研究了无线多跳网络中的负载均衡问题。在密集网络的极限中,宏观和微观尺度之间存在强烈的分离,负载均衡问题可以被表述为在所有源-目的对之间寻找连续曲线(“路由”),使所谓的标量数据包通量(“流量负载”)的最大值最小。在本文中,我们通过完全关注所谓的d流(具有共同目的地x的数据包的矢量流场)并通过观察这些流必须满足的方程来重新表述问题。该方程的通解可以用一个未知标量函数psi(r, x)来表示,该函数与d流的循环密度有关,对于该函数,优化任务可以表现为变分微积分问题。在这种方法中,我们避免了完全处理路径系统和计算由于使用给定路径集而产生的负载分布。一旦找到psi(r, x)的最优解,则得到相应的路径作为d流的流线。在具有均匀流量需求的单元磁盘的示例中,我们能够找到一组路径,这比以前发表的任何结果都要好得多,产生了较低的最大标量通量和非常平坦的负载分布。我们进一步说明了单位平方的方法,取得了类似的改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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