Qualitative properties of $\alpha$-fair policies in bandwidth-sharing networks
Qualitative properties of $\alpha$-fair policies in bandwidth-sharing networks
复制标题
带宽共享网络中$alpha$-公平策略的定性属性
DOI：
10.1214/12-aap915
复制
发表时间：
2011
影响因子：
1.8
通讯作者：
Y. Zhong
中科院分区：
文献类型：
--
作者：
D. Shah;J. Tsitsiklis;Y. Zhong
我们考虑一个网络的流级模型下运行的$\alpha$-公平的带宽共享政策（$\alpha>0$）提出的Roberts和Massouli\'{e} [EQUIPMENT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$\alpha\geq1 $，我们得到了在给定的时间范围内的网络中的流的最大数量的界限，通过一个最大的不等式来自标准的李雅普诺夫漂移条件。作为推论，我们建立了所有$\alpha\geq1 $的全状态空间崩溃性质。对于稳态分布，我们得到明确的指数尾界的流量的数量，任何\alpha>0$，依赖于一个规范的李雅普诺夫函数。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$\alpha=1$的情况并且在局部交通条件下。
We consider a flow-level model of a network operating under an $\alpha$-fair bandwidth sharing policy (with $\alpha>0$) proposed by Roberts and Massouli\'{e} [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 $\alpha\geq1$, 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 $\alpha\geq1$. For the steady-state distribution, we obtain explicit exponential tail bounds on the number of flows, for any $\alpha>0$, 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 $\alpha=1$ and under a local traffic condition.