Collaborative Research: Heavy Traffic Limit Models and Control Analysis for Wireless Queuing Systems - incorporating Long-Range Dependence and Heavy Tails

Buche，DMS-060608669Ghosh，DMS-0608634Pipiras，DMS-0608663 研究人员研究了远程依赖和重尾新现象下无线系统中的重流量分析。 这些现象是当前由数据密集型应用（例如多媒体、WWW 和实时交互）驱动的无线系统的特征。 大流量方法是分析接近容量的排队系统的有效方法，产生复杂但易于处理的限制模型，保留实际排队系统的基本特征。 但大多数现有的大流量分析文献（包括无线系统）都是基于短程相关（类马尔可夫）模型和轻尾模型。 仅在重尾的情况下，重点是扩展基于鞅问题的扰动测试函数方法，以显示与预期由稳定 Levy 运动驱动的排队模型的弱收敛。 当还存在远程依赖性特征时，重点是开发基于流量过程的泊松随机测量表示的强大替代方法。 在这种情况下，预计会弱收敛到由分数布朗运动驱动的排队模型。 研究了与无线系统相关的功率控制问题以及极限队列模型的收敛分析。这是针对给定的控制完成的，因为稳定 Levy 运动或分数布朗运动的随机控制分析目前尚未开发。 该项目的重点是分析以多媒体等高容量应用为特征的无线系统。此类系统与越来越多的无线用户（个人和军事）及其对数据密集型应用的需求越来越相关。 例如，军事应用包括在战场环境中使用视频进行会议并向部队提供信息。 个人应用程序包括电影、实时交互和WWW数据。 特别是，分析中使用了已开发方法（即重交通方法）的扩展。 这种方法假设无线系统接近其容量，而实际情况就是这样，应用程序对有限的带宽提出了很高的要求。 这种假设允许获得良好的模型，这些模型保留了实际系统的基本特征，同时易于处理。 这些模型有助于了解设计高效无线网络所需的系统特性。 此外，获得这些模型是为这些新兴应用开发随机控制方法以优化传输队列的资源分配（例如功率）的重要的第一步。

Buche, DMS-060608669Ghosh, DMS-0608634Pipiras, DMS-0608663 The investigators study the heavy traffic analysis inwireless systems under novel phenomena of long-range dependenceand heavy tails. These phenomena are characteristic of currentwireless systems driven by data-intensive applications such asmultimedia, WWW, and real-time interactions. The heavy trafficapproach is a powerful way to analyze queuing systems at nearcapacity, yielding complex, yet tractable limit models thatretain the essential features of the actual queuing system. Butmost of the existing literature on heavy traffic analysis,including wireless systems, is based on short-range dependent(Markovian-like) models and light tails. In the case of heavytails only, the focus is on extending the perturbed test functionmethod, based on the martingale problem, for showing weakconvergence to a queuing model expected to be driven by stableLevy motion. When long-range dependence characteristics are alsopresent, the focus is on developing a powerful alternativeapproach based on the Poisson random measure representation oftraffic processes. In this case, weak convergence to a queuingmodel driven by fractional Brownian motion is expected. Thepower control problem associated with wireless systems is studiedalong with the convergence analysis to the limit queue model. This is done for given controls, as stochastic control analysisfor stable Levy motion or fractional Brownian motion is currentlyundeveloped. The focus of the project is on analyzing wireless systemscharacterized by high capacity applications such as multimedia. Such systems are ever more relevant with an increasing number ofwireless users (personal and military) and their demand fordata-intensive applications. For example, military applicationsinclude the use of video in battlefield settings for conferencingand providing information to troops. Personal applicationsinclude movies, real-time interactions, and WWW data. Inparticular, extensions of a developed approach, the heavy trafficmethod, are used in the analysis. This approach supposes thatthe wireless system is near its capacity, which is the case inpractice where applications make high demands on a limitedbandwidth. This assumption allows obtaining good models thatretain the essential features of the actual system while beingtractable. The models are useful for obtaining an understandingof system characteristics that is needed for the design of anefficient wireless network. Furthermore, obtaining these modelsis an important first step toward developing stochastic controlmethods for these emerging applications to optimize resourceallocations (for example, power) to the queues for transmissions.