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

研究人员研究了新型远程依赖和重尾现象下无线系统的大流量分析。这些现象是当前由多媒体、WWW和实时交互等数据密集型应用驱动的无线系统的特征。大流量方法是一种分析近容量排队系统的有效方法，它产生了复杂但易于处理的极限模型，保留了实际排队系统的基本特征。但是大多数现有的关于大流量分析的文献，包括无线系统，都是基于短程依赖（类马尔科夫）模型和轻尾。仅在重尾的情况下，重点是扩展基于鞅问题的摄动测试函数方法，以显示预期由稳定运动驱动的排队模型的弱收敛性。当远程依赖特性也存在时，重点是开发一种基于交通过程泊松随机度量表示的强大替代方法。在这种情况下，弱收敛到一个由分数布朗运动驱动的排队模型是预期的。研究了无线系统的功率控制问题，并对极限队列模型进行了收敛性分析。这是对给定控制进行的，因为稳定列维运动或分数布朗运动的随机控制分析目前尚未发展。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。这种系统与越来越多的无线用户（个人和军事）以及他们对数据密集型应用的需求更加相关。例如，军事应用包括在战场设置中使用视频进行会议和向部队提供信息。个人应用包括电影、实时交互和WWW数据。特别地，在分析中使用了一种已开发方法的扩展，即繁忙交通方法。这种方法假设无线系统接近其容量，这是实际应用中对有限带宽有高要求的情况。这个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系统的特性，从而设计出高效的无线网络。此外，获得这些模型是为这些新兴应用程序开发随机控制方法以优化传输队列的资源分配（例如，电力）的重要第一步。

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.