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arXiv 1602.08290cs.NIcs.ITmath.IT
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在CSMA/CA网络中实现目标吞吐量的显式退避率

Explicit back-off rates for achieving target throughputs in CSMA/CA networks

Benny Van Houdt

摘要:

CSMA/CA网络通常使用程式化模型进行分析,该模型完全由退避率向量和冲突图表征。此外,对于任何可实现的吞吐量向量$\vec θ$,证明了实现该吞吐量向量的退避速率的唯一向量$\vec ν(\vec θ)$的存在。虽然这个唯一的向量原则上可以迭代计算,但所需的时间复杂度随着网络规模呈指数级增长,使得这仅适用于小型网络。在本文中,我们提出了一个明确的公式的唯一向量的退避率$\vec ν(\vec θ)$需要实现任何可实现的吞吐量向量$\vec θ$提供的网络具有弦冲突图。这类网络包含了一些特殊的情况,如(非均匀)线网络和网络与非循环冲突图。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。我们进一步表明,这种形式的回退率不能在一般的网络与非弦冲突图。然而,对于一般的冲突图,我们展示了如何适应退避率时,一个节点被添加到网络中时,其干扰节点形成一个集团的冲突图。最后,我们介绍了一个分布式的弦近似算法一般冲突图,这是(使用数值例子)是更准确的Bethe近似。

英文摘要:

CSMA/CA networks have often been analyzed using a stylized model that is fully characterized by a vector of back-off rates and a conflict graph. Further, for any achievable throughput vector $\vec θ$ the existence of a unique vector $\vec ν(\vec θ)$ 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 $\vec ν(\vec θ)$ needed to achieve any achievable throughput vector $\vec θ$ 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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