Network stability under max-min fair bandwidth sharing.
Network stability under max-min fair bandwidth sharing.
复制标题
最大-最小公平带宽共享下的网络稳定性。
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Bramson
中科院分区：
文献类型：
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作者：
M. Bramson
最近有相当大的兴趣在不同的公平带宽共享政策的模型，出现在互联网拥塞控制的背景下的稳定性。这里，我们考虑由Massouli和Roberts [Telecommunication Systems 15（2000）185- 201]引入的连接级模型，其表示网络中存在的随机变化的流的数量。加权$alpha$-fair和加权max-min公平带宽共享策略是针对该模型研究的重要策略之一。在这两种情况下，当到达间隔时间和服务时间是指数分布的稳定性结果是已知的。一般服务时间的部分结果是已知的加权$阿尔法$公平的政策，没有这样的结果是已知的加权最大-最小公平的政策。在这里，我们表明，加权最大-最小公平的政策是稳定的亚临界网络与一般的interarrival和服务分布，后者有$2+delta_1$时刻为一些$delta_1>0$。我们的论点采用了适当的李雅普诺夫函数的加权最大-最小公平的政策。
There has recently been considerable interest in the stability of different fair bandwidth sharing policies for models that arise in the context of Internet congestion control. Here, we consider a connection level model, introduced by Massouli'{e} and Roberts [Telecommunication Systems 15 (2000) 185--201], that represents the randomly varying number of flows present in a network. The weighted $alpha$-fair and weighted max-min fair bandwidth sharing policies are among important policies that have been studied for this model. Stability results are known in both cases when the interarrival times and service times are exponentially distributed. Partial results for general service times are known for weighted $alpha$-fair policies; no such results are known for weighted max--min fair policies. Here, we show that weighted max--min fair policies are stable for subcritical networks with general interarrival and service distributions, provided the latter have $2+delta_1$ moments for some $delta_1>0$. Our argument employs an appropriate Lyapunov function for the weighted max--min fair policy.