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

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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.