This project develops two mathematical methods for the analysis of problems in communications. The first is the large deviations analysis of occupancy models. Occupancy models provide a simple, generic probabilistic construct that has found use in many fields. The proposed large deviations approach is different from and complementary to much of the previous analysis of such models. Motivated by problems from both wired and wireless communications, the research program will develop explicitly computable large deviation asymptotic approximations, and will also develop methods such as importance sampling to provide accurate results even in the non-asymptotic regime. The second topic is the design of stochastic adaptive algorithms for mobile communication. This area of application is narrower in scope, being of particular interest to engineers of next generation, high-rate wireless access systems. However, within that scope, the activities are general and fundamental in nature. The emphasis here is on the development of methods for the analysis of scheduling algorithms in wireless, and on the development of new algorithms. This project will develop mathematical methods for two important areas in modern telecommunication, with an emphasis on a broad university/industrial training of graduate students. A key component of the research program is the joint supervision of graduate students between Bell Labs and Brown University. For the graduate students that are involved, there will be summer internships at Lucent Technologies, which will supplement the more traditional training in a number of ways. Both research areas of focus, namely occupancy models and wireless scheduling, are challenging intellectual problems that are motivated by developing commercial technology. In addition to working with specific industrial mentors, the students also have the opportunity to attend talks, seminars and generally benefit from exposure to a wide variety of current problems and solution methods whose development is in progress. The proposed collaborative research and associated seminar series will help to strengthen the ties between Bell Labs and Brown University, invigorating the intellectual climate at both institutions. The goal of the proposed research is to provide solid, fundamental mathematical foundations for solving problems of current interest, in a framework that will likely be applicable to problems of the future.
