无线网络中最长队列优先调度下的性能保证
Performance Guarantee under Longest-Queue-First Schedule in Wireless Networks
摘要：
无线网络中的高效链路调度是具有挑战性的。典型的优化算法需要解决一个NP难的子问题。为了应对这一挑战，一个研究流集中在寻找更简单的次优算法，具有低复杂度，但在实践中的高效率。在本文中，我们研究这样的调度算法，最长队列优先（LQF）算法的性能保证。已知当干扰图满足所谓的局部池化条件时，LQF算法实现全容量区域$Λ$。对于一般图$G$，LQF实现（即，稳定）容量区域$σ^*(G) Λ$的一部分，其中$σ^*(G)$是干扰图$G$和$σ^*(G) \leq 1$的总体局部池化因子。稍后已经表明，LQF实现了更大的速率区域$Σ^*(G) Λ$，其中$Σ^ (G)$是对角矩阵。本文的贡献是描述了三个新的可达速率区域，这是大于以前已知的区域。特别地，新的区域包括容量区域的所有极值点，并且通常不是凸的。我们还发现了一个反直觉的现象，其中增加到达率有时可能有助于稳定网络。这一现象可以很好地解释用本文发展的理论。
英文摘要：
Efficient link scheduling in a wireless network is challenging. Typical optimal algorithms require solving an NP-hard sub-problem. To meet the challenge, one stream of research focuses on finding simpler sub-optimal algorithms that have low complexity but high efficiency in practice. In this paper, we study the performance guarantee of one such scheduling algorithm, the Longest-Queue-First (LQF) algorithm. It is known that the LQF algorithm achieves the full capacity region, $Λ$, when the interference graph satisfies the so-called local pooling condition. For a general graph $G$, LQF achieves (i.e., stabilizes) a part of the capacity region, $σ^*(G) Λ$, where $σ^*(G)$ is the overall local pooling factor of the interference graph $G$ and $σ^*(G) \leq 1$. It has been shown later that LQF achieves a larger rate region, $Σ^*(G) Λ$, where $Σ^ (G)$ is a diagonal matrix. The contribution of this paper is to describe three new achievable rate regions, which are larger than the previously-known regions. In particular, the new regions include all the extreme points of the capacity region and are not convex in general. We also discover a counter-intuitive phenomenon in which increasing the arrival rate may sometime help to stabilize the network. This phenomenon can be well explained using the theory developed in the paper.
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