Ghosh, DMS-0608634 Pipiras, DMS-0608663
The investigators study the heavy traffic analysis in wireless systems under novel phenomena of long-range dependence and heavy tails. These phenomena are characteristic of current wireless systems driven by data-intensive applications such as multimedia, WWW, and real-time interactions. The heavy traffic approach is a powerful way to analyze queuing systems at near capacity, yielding complex, yet tractable limit models that retain the essential features of the actual queuing system. But most 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 heavy tails only, the focus is on extending the perturbed test function method, based on the martingale problem, for showing weak convergence to a queuing model expected to be driven by stable Levy motion. When long-range dependence characteristics are also present, the focus is on developing a powerful alternative approach based on the Poisson random measure representation of traffic processes. In this case, weak convergence to a queuing model driven by fractional Brownian motion is expected. The power control problem associated with wireless systems is studied along with the convergence analysis to the limit queue model. This is done for given controls, as stochastic control analysis for stable Levy motion or fractional Brownian motion is currently undeveloped.
The focus of the project is on analyzing wireless systems characterized by high capacity applications such as multimedia. Such systems are ever more relevant with an increasing number of wireless users (personal and military) and their demand for data-intensive applications. For example, military applications include the use of video in battlefield settings for conferencing and providing information to troops. Personal applications include movies, real-time interactions, and WWW data. In particular, extensions of a developed approach, the heavy traffic method, are used in the analysis. This approach supposes that the wireless system is near its capacity, which is the case in practice where applications make high demands on a limited bandwidth. This assumption allows obtaining good models that retain the essential features of the actual system while being tractable. The models are useful for obtaining an understanding of system characteristics that is needed for the design of an efficient wireless network. Furthermore, obtaining these models is an important first step toward developing stochastic control methods for these emerging applications to optimize resource allocations (for example, power) to the queues for transmissions.
