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arXiv cs/0601012cs.ITmath.IT
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无线网络中的产品多商品流

Product Multicommodity Flow in Wireless Networks

Ritesh Madan, Devavrat Shah, Olivier Leveque

摘要:

我们提供了一个紧密的$n$维产品多商品流(PMF)区域的$n$节点的无线网络的近似表征。在信息理论意义上和对于组合干扰模型(例如,协议模型)。这些提供了$n^2$维容量区域的内部近似。这些结果回答了从以前的工作中自然产生的以下问题:(a)$1/\sqrt{n}$在Gupta和Kumar(2000)得到的Protocol干扰模型的标度律中有什么意义?(b)我们可以得到一个紧密的近似“最大可支持流”的节点分布更一般的几何随机分布,流量模型以外的随机选择的源-目的地对,并根据非常一般的假设信道衰落模型?首先,我们建立了随机源-目的地模型本质上是一个一维近似的容量区域,产品多商品流的特殊情况。基于以前的结果,对于由网络和冲突图给出的组合干扰模型,我们将产品多商品流与基础图的谱特性相关联,从而得到计算上界和下界。对于更有趣的随机衰落模型与加性高斯白噪声(AWGN),我们表明,PMF的标度律可以再次严格的频谱特性的适当定义的图形。作为一个含义,我们获得计算效率的上界和下界的PMF的任何无线网络有保证的近似因子。

英文摘要:

We provide a tight approximate characterization of the $n$-dimensional product multicommodity flow (PMF) region for a wireless network of $n$ nodes. Separate characterizations in terms of the spectral properties of appropriate network graphs are obtained in both an information theoretic sense and for a combinatorial interference model (e.g., Protocol model). These provide an inner approximation to the $n^2$ dimensional capacity region. These results answer the following questions which arise naturally from previous work: (a) What is the significance of $1/\sqrt{n}$ in the scaling laws for the Protocol interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a tight approximation to the "maximum supportable flow" for node distributions more general than the geometric random distribution, traffic models other than randomly chosen source-destination pairs, and under very general assumptions on the channel fading model? We first establish that the random source-destination model is essentially a one-dimensional approximation to the capacity region, and a special case of product multi-commodity flow. Building on previous results, for a combinatorial interference model given by a network and a conflict graph, we relate the product multicommodity flow to the spectral properties of the underlying graphs resulting in computational upper and lower bounds. For the more interesting random fading model with additive white Gaussian noise (AWGN), we show that the scaling laws for PMF can again be tightly characterized by the spectral properties of appropriately defined graphs. As an implication, we obtain computationally efficient upper and lower bounds on the PMF for any wireless network with a guaranteed approximation factor.

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