Stability, Fairness, and Performance: A Flow-Level Study on Nonconvex and Time-Varying Rate Regions
Stability, Fairness, and Performance: A Flow-Level Study on Nonconvex and Time-Varying Rate Regions
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稳定性、公平性和性能：非凸和时变速率区域的流级研究
DOI：
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发表时间：
2009
影响因子：
2.5
通讯作者：
H. Poor
中科院分区：
文献类型：
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作者：
Jiaping Liu;A. Proutière;Yung Yi;M. Chiang;H. Poor
本文研究了效用最大化分配的数据网络的流级稳定性和性能。类似于以前关于流级模型的工作，考虑了具有有限工作负载的外部数据到达。然而，对于许多现实情况的建模，限制资源分配可行性的速率区域可能是非凸的，也可能是时变的。当速率区域固定但非凸时，刻画了一类α-公平分配策略稳定的充要条件，当分配的速率向量集具有连续轮廓时，这些条件重合。当速度域按马尔可夫平稳遍历过程时变时，得到了精确的稳定域。在这两种情况下，稳定区域的大小取决于资源分配策略，特别是取决于α-公平效用最大化中的公平参数α。这与现有的关于固定速率区域和凸速率区域下的稳定性的大量文献形成鲜明对比，在这些文献中，对于许多基于效用的资源分配方案，稳定区域与速率区域重合，与公平参数的值无关。进一步证明，对于在α公平分配下由来自两个不同类别的流组成的网络，在稳定区域和公平参数α之间存在折衷。此外，还研究了这种公平性-稳定性折衷对系统性能的影响，如平均吞吐量和平均流响应时间，并给出了数值实验，说明了新的稳定域和性能与公平性的折衷。
The flow-level stability and performance of data networks with utility-maximizing allocations are studied in this paper. Similarly to prior works on flow-level models, exogenous data arrivals with finite workloads are considered. However, to model many realistic situations, the rate region, which constrains the feasibility of resource allocation, may be either nonconvex or time-varying. When the rate region is fixed but nonconvex, sufficient and necessary conditions are characterized for stability for a class of alpha-fair allocation policies, which coincide when the set of allocated rate vectors have continuous contours. When the rate region is time-varying according to a Markovian stationary and ergodic process, the precise stability region is obtained. In both cases, the size of the stability region depends on the resource allocation policy, in particular, on the fairness parameter alpha in alpha-fair utility maximization. This is in sharp contrast with the substantial existing literature on stability under fixed and convex rate regions, in which the stability region coincides with the rate region for many utility-based resource allocation schemes, independent of the value of the fairness parameter. It is further shown that for networks which consist of flows from two different classes under alpha-fair allocations, there exists a tradeoff between the stability region and the fairness parameter alpha. Moreover, the impact of this fairness-stability tradeoff on the system performance, e.g., average throughput and mean flow response time, is studied, and numerical experiments that illustrate the new stability region and the performance versus fairness tradeoff are presented.