802.11 MAC协议解耦假设的渐近有效性
On the Asymptotic Validity of the Decoupling Assumption for Analyzing 802.11 MAC Protocol
摘要：
802.11 MAC协议的性能评估传统上是基于解耦假设的，该假设假设不同节点处的退避过程是独立的。这种解耦假设是由平均场收敛引起的，并且在渐近意义上（当无线节点的数量趋于无穷大时）在瞬态状态下通常是真实的，但是与普遍的信念相反，在稳态状态下可能不一定成立。这个问题通常与不动点方程解的存在性和唯一性有关;然而，最近也证明了这个条件是不充分的;相反，充分条件是相关常微分方程的全局稳定性。在本文中，我们给出了一个简单的条件，建立了齐次情况下的解耦假设的渐近有效性。我们还讨论了异构和区分服务的情况下，制定了一个新的常微分方程。我们表明，相关的不动点方程的解决方案的唯一性是不够的，我们展示了一种情况下，不动点方程有一个唯一的解决方案，但解耦假设是无效的渐近意义上的平稳制度。
英文摘要：
Performance evaluation of the 802.11 MAC protocol is classically based on the decoupling assumption, which hypothesizes that the backoff processes at different nodes are independent. This decoupling assumption results from mean field convergence and is generally true in transient regime in the asymptotic sense (when the number of wireless nodes tends to infinity), but, contrary to widespread belief, may not necessarily hold in stationary regime. The issue is often related with the existence and uniqueness of a solution to a fixed point equation; however, it was also recently shown that this condition is not sufficient; in contrast, a sufficient condition is a global stability property of the associated ordinary differential equation. In this paper, we give a simple condition that establishes the asymptotic validity of the decoupling assumption for the homogeneous case. We also discuss the heterogeneous and the differentiated service cases and formulate a new ordinary differential equation. We show that the uniqueness of a solution to the associated fixed point equation is not sufficient; we exhibit one case where the fixed point equation has a unique solution but the decoupling assumption is not valid in the asymptotic sense in stationary regime.
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