使用Bethe近似的CSMA：调度和效用最大化
CSMA using the Bethe Approximation: Scheduling and Utility Maximization
摘要：
以完全分布式方式解决无线网络上的争用的载波侦听多址接入（Carrier Sense Multiple Access，CSMA）最近获得了很多关注，因为已经证明对CSMA参数的适当控制保证了稳定性方面的最优性（即，调度）和系统范围的效用（即，调度和拥塞控制）。大多数基于CSMA的算法依赖于流行的MCMC（马尔可夫链蒙特卡罗）技术，它使人们能够找到最佳的CSMA参数，通过迭代循环的“模拟和更新”。然而，这种基于模拟的方法往往成为指数缓慢收敛的主要原因，对流/拓扑变化的适应性差。在本文中，我们开发了分布式迭代算法，产生近似解的收敛在多项式时间的稳定性和效用最大化问题。特别是，对于稳定性问题，所提出的分布式算法需要，有点令人惊讶的是，只有一个迭代之间的链接。我们的方法是由贝特近似（由Yedidia，Freeman和Weiss在2005年介绍），使我们能够通过一个特定的多项式大小的非线性系统来表达近似的解决方案。我们的多项式收敛保证来自直接解决非线性系统的分布式方式，而不是多个模拟和更新循环在现有的算法。我们提供的数值结果表明，该算法产生高精度的解决方案和收敛速度比以前的。
英文摘要：
CSMA (Carrier Sense Multiple Access), which resolves contentions over wireless networks in a fully distributed fashion, has recently gained a lot of attentions since it has been proved that appropriate control of CSMA parameters guarantees optimality in terms of stability (i.e., scheduling) and system- wide utility (i.e., scheduling and congestion control). Most CSMA-based algorithms rely on the popular MCMC (Markov Chain Monte Carlo) technique, which enables one to find optimal CSMA parameters through iterative loops of `simulation-and-update'. However, such a simulation-based approach often becomes a major cause of exponentially slow convergence, being poorly adaptive to flow/topology changes. In this paper, we develop distributed iterative algorithms which produce approximate solutions with convergence in polynomial time for both stability and utility maximization problems. In particular, for the stability problem, the proposed distributed algorithm requires, somewhat surprisingly, only one iteration among links. Our approach is motivated by the Bethe approximation (introduced by Yedidia, Freeman and Weiss in 2005) allowing us to express approximate solutions via a certain non-linear system with polynomial size. Our polynomial convergence guarantee comes from directly solving the non-linear system in a distributed manner, rather than multiple simulation-and-update loops in existing algorithms. We provide numerical results to show that the algorithm produces highly accurate solutions and converges much faster than the prior ones.
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