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Explicit Back-Off Rates for Achieving Target Throughputs in CSMA/CA Networks

机译:在CSMA / CA网络中实现目标吞吐量的显式退避速率

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Carrier-sense multiple access/collision avoidance networks have often been analyzed using a stylized model that is fully characterized by a vector of back-off rates and a conflict graph. Furthermore, for any achievable throughput vector θ⃗ , the existence of a unique vector ν⃗ (θ⃗ ) of back-off rates that achieves this throughput vector was proven. Although this unique vector can in principle be computed iteratively, the required time complexity grows exponentially in the network size, making this only feasible for small networks. In this paper, we present an explicit formula for the unique vector of back-off rates ν⃗ (θ⃗ ) needed to achieve any achievable throughput vector θ⃗ provided that the network has a chordal conflict graph. This class of networks contains a number of special cases of interest such as (inhomogeneous) line networks and networks with an acyclic conflict graph. Moreover, these back-off rates are such that the back-off rate of a node only depends on its own target throughput and the target throughput of its neighbors and can be determined in a distributed manner. We further indicate that back-off rates of this form cannot be obtained in general for networks with non-chordal conflict graphs. For general conflict graphs, we nevertheless show how to adapt the back-off rates when a node is added to the network when its interfering nodes form a clique in the conflict graph. Finally, we introduce a distributed chordal approximation algorithm for general conflict graphs, which is shown (using numerical examples) to be more accurate than the Bethe approximation.
机译:经常使用风格化的模型来分析运营商感知的多路访问/冲突避免网络,该模型完全由退避率向量和冲突图来表征。此外,对于任何可达到的吞吐量矢量θ⃗,证明了实现该吞吐量矢量的退避率的唯一矢量ν⃗(θ⃗)的存在。尽管原则上可以迭代地计算该唯一向量,但是所需的时间复杂度在网络规模中呈指数增长,这使得这仅适用于小型网络。在本文中,如果网络具有弦冲突图,我们将为实现任何可实现的吞吐量矢量θ⃗所需的退避率ν⃗(θ⃗)的唯一矢量提供一个明确的公式。此类网络包含许多感兴趣的特殊情况,例如(不均匀)线网络和具有非周期性冲突图的网络。此外,这些退避率使得节点的退避率仅取决于其自身的目标吞吐量和其邻居的目标吞吐量,并且可以以分布式方式确定。我们进一步指出,对于具有非弦冲突图的网络,通常无法获得这种形式的退避率。对于一般的冲突图,我们仍然展示了当一个节点被添加到网络时,如果其干扰节点在冲突图中形成集团,那么如何调整退避率。最后,我们为一般冲突图引入了分布式弦近似算法,该算法显示(使用数字示例)比Bethe逼近更准确。

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