网络等弹性和加权$α$公平性
Network iso-elasticity and weighted $α$-fairness
摘要：
当通信网络的容量增加时，自然希望分配的带宽增加以利用该容量。但是，如果在每个网络资源处发生相同的相对容量增加，则希望每个用户看到相同的相对益处也是自然的，因此分配给每个路由的带宽应该保持成比例。我们将对以这种\textit{iso-elastic}方式缩放并且还最大化效用函数的带宽分配感兴趣。效用优化带宽分配已经被频繁地研究，并且效用函数的流行选择是Mo和Walrand \cite{MoWa00}引入的加权$α$ -公平效用函数。由于加权$α$ -公平效用函数具有这种等弹性性质，它们经常被用来形成带宽共享网络的流体模型。在本文中，我们提出的结果表明，在许多设置中，只有效用函数是等弹性加权$α$ -公平的效用函数。因此，如果根据与相对网络变化成比例的网络效用函数来分配带宽，则该效用函数必须是加权的$α$公平效用函数，并且因此，对网络容量和使用的未来相对变化鲁棒的控制协议应当分配带宽，以便最大化加权的$α$公平效用函数。
英文摘要：
When a communication network's capacity increases, it is natural to want the bandwidth allocated to increase to exploit this capacity. But, if the same relative capacity increase occurs at each network resource, it is also natural to want each user to see the same relative benefit, so the bandwidth allocated to each route should remain proportional. We will be interested in bandwidth allocations which scale in this \textit{iso-elastic} manner and, also, maximize a utility function. Utility optimizing bandwidth allocations have been frequently studied, and a popular choice of utility function are the weighted $α$-fair utility functions introduced by Mo and Walrand \cite{MoWa00}. Because weighted $α$-fair utility functions possess this iso-elastic property, they are frequently used to form fluid models of bandwidth sharing networks. In this paper, we present results that show, in many settings, the only utility functions which are iso-elastic are weighted $α$-fair utility functions. Thus, if bandwidth is allocated according to a network utility function which scales with relative network changes then that utility function must be a weighted $α$-fair utility function, and hence, a control protocol that is robust to the future relative changes in network capacity and usage ought to allocate bandwidth inorder to maximize a weighted $α$-fair utility function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
