During the last decade, the number of devices connected to the Internet by Wi-Fi has grown significantly. A high density of both the client devices and the hot spots posed new challenges related to providing the desired quality of service in the current and emerging scenarios. To cope with the negative effects caused by network densification, modern Wi-Fi is becoming more and more centralized. To improve network efficiency, today many new Wi-Fi deployments are under control of management systems that optimize network parameters in a centralized manner. In the paper, for such a cloud management system, we develop an algorithm which aims at maximizing energy efficiency and also keeps fairness among clients. For that, we design an objective function and solve an optimization problem using the branch and bound approach. To evaluate the efficiency of the developed solution, we implement it in the NS-3 simulator and compare with existing solutions and legacy behavior.
The GEE maximization problem can be solved with existing mathematical methods based on the so-called polyblock algorithm @cite_7 . However, this approach is known to converge very slowly when one or more variables are close to zero. While modeling real deployments, we often observed such cases. That is why we use another approach based on the branch-and-bound method that avoids this slow convergence @cite_2 . Although being applied to solve the GEE problem @cite_6 in LTE networks, its applicability for Wi-Fi networks is not straightforward.
@cite_6 @cite_7 @cite_2
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The characterization of the global maximum of energy efficiency (EE) problems in wireless networks is a challenging problem due to their nonconvex nature in interference channels. The aim of this paper is to develop a new and general framework to achieve globally optimal solutions. First, the hidden monotonic structure of the most common EE maximization problems is exploited jointly with fractional programming theory to obtain globally optimal solutions with exponential complexity in the number of network links. To overcome the high complexity, we also propose a framework to compute suboptimal power control strategies with affordable complexity. This is achieved by merging fractional programming and sequential optimization. The proposed monotonic framework is used to shed light on the ultimate performance of wireless networks in terms of EE and also to benchmark the performance of the lower-complexity framework based on sequential programming. Numerical evidence is provided to show that the sequential fractional programming framework achieves global optimality in several practical communication scenarios. This monograph presents a unified framework for energy efficiency maximization in wireless networks via fractional programming theory. The definition of energy efficiency is introduced, with reference to single-user and multi-user wireless networks, and it is observed how the problem of resource allocation for energy efficiency optimization is naturally cast as a fractional program. An extensive review of the state-of-the-art in energy efficiency optimization by fractional programming is provided, with reference to centralized and distributed resource allocation schemes. A solid background on fractional programming theory is provided. The key-notion of generalized concavity is presented and its strong connection with fractional functions described. A taxonomy of fractional problems is introduced, and for each class of fractional problem, general solution algorithms are described, discussing their complexity and convergence properties. The described theoretical and algorithmic framework is applied to solve energy efficiency maximization problems in practical wireless networks. A general system and signal model is developed which encompasses many relevant special cases, such as one-hop and two-hop heterogeneous networks, multi-cell networks, small-cell networks, device-to-device systems, cognitive radio systems, and hardware-impaired networks, wherein multiple-antennas and multiple subcarriers are possibly employed. Energy-efficient resource allocation algorithms are developed, considering both centralized, cooperative schemes, as well as distributed approaches for self-organizing networks. Finally, some remarks on future lines of research are given, stating some open problems that remain to be studied. It is shown how the described framework is general enough to be extended in these directions, proving useful in tackling future challenges that may arise in the design of energy-efficient future wireless networks. This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints; Important discussions of decomposition methods for specially structured problems; A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition. Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint. From the reviews of the first edition: The book gives a good review of the topic. The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it. Mathematical Methods of Operations Research, 49:3 (1999)