Stochastic Control Problems in Wireless Communications

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ECS-9979250KushnerThe proposal concerns the application of the analytical and numerical methods of modern stochastic control theory to problems in wireless communications. Two broad clases of problems are considered. The first concerns data communications under random connectivity, where the mobile sources are not always available to the transceiver. Little is known about the asociated polling problem. Periods of unavailability of major sources create jumps in the backed up workload, and this jump depends on the polling policy. We are concerned with efficient diffusion approximations that reduce the problem dimension and allow the use of optimal control methods, and ultimately efficient numerical methods. Arbitrary cost functions, general statistical structures and either finite or infinite buffers are of interest, as well as noisy channels, and the use of smart antennas and simultaneous adaptive polling. The main techniques are those of heavy traffic analysis and diffusion approximation, which should shed considerable insight by allowing an approximation of the control problem by a much simpler one of lower dimension for which numerical method are either available or will be developed.The second class of problems concerns the loss of calls due to lack of available frequencies on handover. This is formulated as a control problem, where what one controls are the new entries into the system, somwhat analogous to what is done in the trunk line access/routing problem. Since the loss of calls should be relatively rare and are costly, the theory of large deviations is an appropriate tool. The problems of control within a large deviations context are nonclassical. A new approach to the theory greatly facilitates such analysis to problems such as those arising in wirless, and also provides a basis for numerical methods, an essential component of any "engineering" theory.Key words:Wireless communications, random connectivity, heavy traffic approxima-tions, polling, large deviations, handover losses.