带宽共享网络中$α$ -公平策略的定性性质
Qualitative properties of $α$-fair policies in bandwidth-sharing networks
摘要：
我们考虑在由Roberts和Massoulié提出的$α$ -公平带宽共享策略（具有$α>0$）下操作的网络的流级模型[《通信系统》15（2000）185-201]。这是一个概率模型，它捕获通信网络中用户或流之间带宽共享的长期方面。我们研究了该模型的瞬态特性以及稳态分布。特别是，对于$α\geq1$，我们得到了在给定的时间范围内的网络中的流的最大数量的界限，通过一个极大不等式来自标准的李雅普诺夫漂移条件。作为推论，我们建立了所有$α\geq1$的全状态空间坍缩性质。对于稳态分布，我们得到明确的指数尾边界上的流的数量，任何$α>0$，依靠一个范数样的李雅普诺夫函数。作为一个推论，我们建立了康等人开发的扩散近似的有效性。19（2009）1719-1780]，在稳定状态下，对于$α=1$的情况和在本地交通条件下。
英文摘要：
We consider a flow-level model of a network operating under an $α$-fair bandwidth sharing policy (with $α>0$) proposed by Roberts and Massoulié [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that captures the long-term aspects of bandwidth sharing between users or flows in a communication network. We study the transient properties as well as the steady-state distribution of the model. In particular, for $α\geq1$, we obtain bounds on the maximum number of flows in the network over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property for all $α\geq1$. For the steady-state distribution, we obtain explicit exponential tail bounds on the number of flows, for any $α>0$, by relying on a norm-like Lyapunov function. As a corollary, we establish the validity of the diffusion approximation developed by Kang et al. [Ann. Appl. Probab. 19 (2009) 1719-1780], in steady state, for the case where $α=1$ and under a local traffic condition.
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