Diffusion Limit of Fair Resource Control -- Stationarity and Interchange of Limits
Diffusion Limit of Fair Resource Control -- Stationarity and Interchange of Limits
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公平资源控制的扩散极限——平稳性与极限互换
DOI：
10.2139/ssrn.2579541
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发表时间：
2015
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
我们研究了一个资源共享网络，其中每个作业需要同时占用一个链路子集（服务器/资源），并且每个链路的容量在需要其服务的作业类之间共享。服务容量在作业类别之间的实时分配由所谓的“比例公平”方案决定，该方案在考虑队列长度和链路容量影子价格的情况下在作业类别之间分配容量。我们证明了通常的交通条件是扩散极限具有平稳分布的充分必要条件。我们还建立了前极限网络的一致稳定性，从而证明了它们的平稳分布的存在性。为了证明两个极限，即时间极限和扩散尺度极限的交换，我们确定了一个有界的工作负荷条件，并证明了它是证明平稳分布及其矩的交换的充分条件。最后一个结果对于扩散极限作为原始网络平稳性能近似值的有效性至关重要。我们给出了一组例子来证明扩散逼近在资源共享网络中的有效性，并讨论了通过著名的Kumar-Seidman/Rybko-Stolyar模型向其他多类网络的扩展。
We study a resource-sharing network where each job requires the concurrent occupancy of a subset of links (servers/resources), and each link’s capacity is shared among job classes that require its service. The real-time allocation of the service capacity among job classes is determined by the so-called “proportional fair” scheme, which allocates the capacity among job classes taking into account the queue lengths and the shadow prices of link capacity. We show that the usual traffic condition is necessary and sufficient for the diffusion limit to have a stationary distribution. We also establish the uniform stability of the prelimit networks, and hence the existence of their stationary distributions. To justify the interchange of two limits, the limit in time and limit in diffusion scaling, we identify a bounded workload condition, and show it is a sufficient condition to justify the interchange for the stationary distributions and their moments. This last result is essential for the validity of the diffusion limit as an approximation to the stationary performance of the original network. We present a set of examples to illustrate justifying the validity of diffusion approximation in resource-sharing networks, and also discuss extensions to other multiclass networks via the well-known Kumar-Seidman/Rybko-Stolyar model.