Non-asymptotic end-to-end performance bounds for networks with long range dependent fBm cross traffic
Non-asymptotic end-to-end performance bounds for networks with long range dependent fBm cross traffic
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DOI：
10.1016/j.comnet.2011.07.027
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Amr Rizk;M. Fidler
中科院分区：
文献类型：
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作者：
Amr Rizk;M. Fidler
分数布朗运动(FBM)是一种用于研究自相似和长相关聚集Internet流量的有用模型。对于具有FBM通过业务的单排队系统，已知其近似性能度量分别是渐近的。本文推导了开环FBM交叉业务下串联队列网络中直通流的端到端性能界限。为此，证明了FBM的严格样本路径包络是对以前的近似结果的补充。使用样本路径包络和剩余服务曲线的概念来对在排队系统处调度FBM交叉业务之后的剩余服务进行建模。利用随机网络演算中汇接系统的合成结果，导出了FBM交叉业务下网络中单个流的端到端统计性能界限。我们的发现是，对于串联的n个系统，这些界在(Logn)1/(2-2H)上增长，其中H是交叉流量的Hurst参数。给出了直通和交叉流量的变化性和突发性对网络性能的影响的明确结果。我们的分析对网络规划和服务管理中的基本问题具有直接的影响。
Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent aggregate Internet traffic. Asymptotic, respectively, approximate performance measures are known for single queueing systems with fBm through traffic. In this paper end-to-end performance bounds for a through flow in a network of tandem queues under open-loop fBm cross traffic are derived. To this end, a rigorous sample path envelope for fBm is proven that complements previous approximate results. The sample path envelope and the concept of leftover service curves are employed to model the remaining service after scheduling fBm cross traffic at a queuing system. Using composition results for tandem systems from the stochastic network calculus end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic are derived. The discovery is that these bounds grow in On(logn)1/(2-2H)for n systems in series where H is the Hurst parameter of the cross traffic. Explicit results on the impact of the variability and the burstiness of through and cross traffic on network performance are shown. Our analysis has direct implications on fundamental questions in network planning and service management.