Distributed Game Theoretic Optimization and Management of Multichannel ALOHA Networks

The problem of distributed rate maximization in multi-channel ALOHA networks is considered. First, we study the problem of constrained distributed rate maximization, where user rates are subject to total transmission probability constraints. We propose a best-response algorithm, where each user updates its strategy to increase its rate according to the channel state information and the current channel utilization. We prove the convergence of the algorithm to a Nash equilibrium in both homogeneous and heterogeneous networks using the theory of potential games. The performance of the best-response dynamic is analyzed and compared to a simple transmission scheme, where users transmit over the channel with the highest collision-free utility. Then, we consider the case where users are not restricted by transmission probability constraints. Distributed rate maximization under uncertainty is considered to achieve both efficiency and fairness among users. We propose a distributed scheme where users adjust their transmission probability to maximize their rates according to the current network state, while maintaining the desired load on the channels. We show that our approach plays an important role in achieving the Nash bargaining solution among users. Sequential and parallel algorithms are proposed to achieve the target solution in a distributed manner. The efficiencies of the algorithms are demonstrated through both theoretical and simulation results.Comment: 34 pages, 6 figures, accepted for publication in the IEEE/ACM Transactions on Networking, part of this work was presented at IEEE CAMSAP 201

Stochastic Differential Games and Energy-Efficient Power Control

One of the contributions of this work is to formulate the problem of energy-efficient power control in multiple access channels (namely, channels which comprise several transmitters and one receiver) as a stochastic differential game. The players are the transmitters who adapt their power level to the quality of their time-varying link with the receiver, their battery level, and the strategy updates of the others. The proposed model not only allows one to take into account long-term strategic interactions but also long-term energy constraints. A simple sufficient condition for the existence of a Nash equilibrium in this game is provided and shown to be verified in a typical scenario. As the uniqueness and determination of equilibria are difficult issues in general, especially when the number of players goes large, we move to two special cases: the single player case which gives us some useful insights of practical interest and allows one to make connections with the case of large number of players. The latter case is treated with a mean-field game approach for which reasonable sufficient conditions for convergence and uniqueness are provided. Remarkably, this recent approach for large system analysis shows how scalability can be dealt with in large games and only relies on the individual state information assumption.Comment: The final publication is available at http://www.springerlink.com/openurl.asp?genre=article\&id=doi:10.1007/s13235-012-0068-

Distributed stochastic optimization via matrix exponential learning

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.Comment: 31 pages, 3 figure

The edge cloud: A holistic view of communication, computation and caching

The evolution of communication networks shows a clear shift of focus from just improving the communications aspects to enabling new important services, from Industry 4.0 to automated driving, virtual/augmented reality, Internet of Things (IoT), and so on. This trend is evident in the roadmap planned for the deployment of the fifth generation (5G) communication networks. This ambitious goal requires a paradigm shift towards a vision that looks at communication, computation and caching (3C) resources as three components of a single holistic system. The further step is to bring these 3C resources closer to the mobile user, at the edge of the network, to enable very low latency and high reliability services. The scope of this chapter is to show that signal processing techniques can play a key role in this new vision. In particular, we motivate the joint optimization of 3C resources. Then we show how graph-based representations can play a key role in building effective learning methods and devising innovative resource allocation techniques.Comment: to appear in the book "Cooperative and Graph Signal Pocessing: Principles and Applications", P. Djuric and C. Richard Eds., Academic Press, Elsevier, 201