Dr. Chee Wei Tan, from City University of Hong Kong, gave a report of “Wireless Network Optimization by Perron-Frobenius Theory” at F804, New Main Building, Beihang University, on May 16th, 2013.

Abstract: As wireless networks are becoming more heterogeneous and ubiquitous in our life, they are also becoming more difficult to design and manage. How should these large complex wireless net-works be analyzed and designed with clearly-defined fairness and optimality in mind? This talk addresses the following problems: How can we overcome interference to efficiently optimize fair wireless resource allocation, under various stochastic constraints on quality of service demands? Network designs are traditionally divided into layers. How does fairness permeate through layers? Can physical layer innovation be jointly optimized with network layer flow control? While theoretically challenging, we present a nonlinear Perron-Frobenius theory to solve them. Optimality can be characterized analytically by nonlinear positive mappings. More importantly, it provides a systematic way to derive distributed fast algorithms and to evaluate the fairness of resource allocation without increasing complexity. We also highlight how this theory is used to resolve several open problems on algorithms in the wireless networking literature.