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Wanyang Dai
Prof. Wanyang Dai
Nanjing University, China
MIMO Mutual Information Computation and Pareto Optimality of Scheduling Game by Reflecting SDEs
We first introduce a unified system of stochastic differential equations (SDEs) with skew reflections and then prove the existence and uniqueness of its solution in strong or weak sense. Based on this unified system, we derive a generalized mutual information computation formula to determine the signal processing capacity over possible non-Gaussian channels with multi-input multi-output (MIMO) antennas. The channels are proposed to serve multiple competing users (game players) under a Pareto maximal-utility Nash equilibrium resource allocation algorithm (policy) myopically at each time point, which is proven to be an asymptotic Pareto minimal-dual-cost Nash equilibrium policy globally over the whole time horizon. In other words, the policy is fair to all the players and in the meanwhile it is optimal to the whole game system. Furthermore, certain reflecting SDE is proved to be the effective performance model for the scheduling policy both theoretically and numerically. Applications of our studies in intelligent cloud-computing systems for big-data services will also be mentioned.

Wanyang Dai received his Ph.D degree in applied mathematics jointly with industrial engineering and systems engineering from Georgia Institute of Technology, Atlanta, GA, U.S.A., in 1996, where he worked on stochastics and applied probability concerning network performance modeling and analysis, algorithm design and implementation via stochastic diffusion approximation. The breakthrough results and methodologies developed in his thesis were cited, used, and claimed as "contemporaneous and independent" achievements by some other subsequent breakthrough papers that were presented as "45 minute invited talk in probability and statistics" in International Congress of Mathematicians (ICM) 1998, which is the most privilege honor in the mathematical society. The designed finite element-Galerkin algorithm to compute the stationary distributions of reflecting Brownian motions (the weak solutions of general dimensional partial differential equations) is also well-known to the related fields. 

He was a MTS (permanent) in End-to-End Network Architecture Department of AT&T Bell Labs (now called Nokia Bell Labs), Atlanta, GA and Warren, NJ, U.S.A., from 1996-1999, where he was principal investigators and developers of several projects in telecommunication network architecture and design, network performance and financial engineering, operating system and database development to support various intelligent engines/models for strategy planning and big data analysis in a "Plug-in and Play" manner, with some (nowadays called cloud computing) project won "Technology Transfer". 

He is a distinguished professor in Nanjing University, where his research includes stochastic processes related optimization and optimal control, admission/scheduling/routing protocols and performance analysis/optimization for big data oriented cloud computing and the next generation of wireless and wireline communication systems, forward/backward stochastic (ordinary/partial) differential equations and their applications to queueing systems, stochastic differential games, communication networks, financial engineering. His "influential" papers are published in "big name" journals including Operations Research, Journal of Computational and Applied Mathematics, Queueing Systems, Mathematical and Computer Modeling of Dynamical Systems. 

He is Editors-in-Chief of International Journal of Information Engineering, Journal of Advances in Applied Mathematics, editors or members of editorial boards of over 30 international journals ranging from pure mathematics to its applications, General Chairs, invited plenary/keynote speakers, TPC members of over 30 IEEE and international conferences, member/group leader of judge committee in mathematics for National Natural Science Awards of China, Vice Presidents/Directors of probability, statistics, operations research societies. 

He was a visiting scholar in Academy of Mathematics and Systems Science of China, Beijing, China, in 2001, a Long Term Participant of IMA Annual Program of Probability and Statistics in Complex Systems: Financial Engineering, Communication Networks and Genomics in Institute of Mathematics and Its Applications (IMA), Minneapolis, U.S.A., in 2004, a visiting professor in Department of Systems Engineering and Engineering Management in Chinese University of Hong Kong, Hong Kong, China, in 2007.

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