A Stochastic Network Under Proportional Fair Resource Control - Diffusion Limit with Multiple Bottlenecks
A Stochastic Network Under Proportional Fair Resource Control - Diffusion Limit with Multiple Bottlenecks
复制标题
比例公平资源控制下的随机网络——多瓶颈扩散极限
DOI：
10.1287/opre.1120.1047
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
D. Yao
中科院分区：
文献类型：
--
作者：
H. Ye;D. Yao
我们研究了一个多类随机处理网络，该网络运行在所谓的比例公平分配方案下，遵循首部处理机共享原则。具体地说，每个服务器的容量在需要其服务的作业类之间共享，并且在网络的每种状态下，在每个类的第一个等待作业之间分配，以最大化对数效用函数。我们建立了扩散尺度下网络的限制机制，允许网络中存在多个瓶颈，并放宽了以前研究中所要求的一些条件。我们还确定了其中比例公平分配最小化扩散尺度排队长度的二次代价目标函数的分配方案，并通过反例说明了这种渐近最优性的局限性。
We study a multiclass stochastic processing network operating under the so-called proportional fair allocation scheme, and following the head-of-the-line processor-sharing discipline. Specifically, each server's capacity is shared among the job classes that require its service, and it is allocated, in every state of the network, among the first waiting job of each class to maximize a log-utility function. We establish the limiting regime of the network under diffusion scaling, allowing multiple bottlenecks in the network, and relaxing some of the conditions required in prior studies. We also identify the class of allocation schemes among which the proportional fair allocation minimizes a quadratic cost objective function of the diffusion-scaled queue lengths, and we illustrate the limitation of this asymptotic optimality through a counterexample.