Topology control algorithms allow each node in a wireless multi-hop network to adjust the power at which it makes its transmissions and choose the set of neighbors with which it communicates directly, while preserving global goals such as connectivity or coverage. This allows each node to conserve energy and contribute to increasing the lifetime of the network. In this paper, in contrast to most previous work, we consider (i) both the energy costs of communication as well as the amount of available energy at each node, (ii) the realistic situation of varying rates of energy consumption at different nodes, and (iii) the fact that co-operation between nodes, where some nodes make a sacrifice by increasing energy consumption to help other nodes reduce their consumption, can be used to extend network lifetime. This paper introduces a new distributed topology control algorithm, called the Cooperative Topology Control with Adaptation (CTCA), based on a game-theoretic approach that maps the problem of maximizing the network's lifetime into an ordinal potential game. We prove the existence of a Nash equilibrium for the game. Our simulation results indicate that the CTCA algorithm extends the life of a network by more than 50 compared to the best previously-known algorithm. We also study the performance of the distributed CTCA algorithm in comparison to an optimal centralized algorithm as a function of the communication ranges of nodes and node density.
A survey of topology control algorithms can be found in @cite_34 @cite_11 and a survey of the applications of game theory in wireless sensor networks can be found in @cite_8 @cite_14 .
@cite_8 @cite_14 @cite_34 @cite_11
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In a large and complex distributed sensor network, the individual sensor directly communicates only with its neighboring sensors. Despite being restricted to such local communications, the network itself should be self-organizing to maintain certain desirable properties, such as network connectivity and lifetime maximization. Topology control is a technique to determine the optimal transmit parameters for each sensor, such that the network topology has the best possible network performance. In this paper, we investigate a dynamic topology control scheme to improve the network lifetime for wireless sensor networks in the presence of selfish sensors. A non-cooperative game aided topology control approach is developed for designing energy-efficient and energy balanced network topologies dynamically. Each sensor in the topology control game tries to minimize its unwillingness for constructing a connected network according to its residual energy and transmit power. We prove the existence of Nash equilibrium (NE) and demonstrate that the NE is Pareto optimal as well. Specifically, a fully distributed algorithm-topology control with lifetime extension (TCLE)-is proposed to construct dynamic network topologies. The topologies derived by TCLE algorithm can improve the network lifetime significantly as compared with existing algorithms. Simulations demonstrate the efficiency of our TCLE algorithm. * The first tutorial-style book that gives all the relevant theory at the right level of rigor, for the wireless communications engineer. * Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real-word problems. * Contains algorithms and techniques to implement game theory in wireless terminals. Written by leading experts in the field, Game Theory and Learning for Wireless Networks Covers how theory can be used to solve prevalent problems in wireless networks such as power control, resource allocation or medium access control. With the emphasis now on promoting 'green' solutions in the wireless field where power consumption is minimized, there is an added focus on developing network solutions that maximizes the use of the spectrum available. With the growth of distributed wireless networks such as Wi-Fi and the Internet; the push to develop ad hoc and cognitive networks has led to a considerable interest in applying game theory to wireless communication systems. Game Theory and Learning for Wireless Networks is the first comprehensive resource of its kind, and is ideal for wireless communications R&D engineers and graduate students. Samson Lasaulce is a senior CNRS researcher at the Laboratory of Signals and Systems (LSS) at Suplec, Gif-sur-Yvette, France. He is also a part-time professor in the Department of Physics at cole Polytechnique, Palaiseau, France. Hamidou Tembine is a professor in the Department of Telecommunications at Suplec, Gif-sur-Yvette, France. Merouane Debbah is a professor at Suplec, Gif-sur-Yvette, France. He is the holder of the Alcatel-Lucent chair in flexible radio since 2007. The first tutorial style book that gives all the relevant theory, at the right level of rigour, for the wireless communications engineer Bridges the gap between theory and practice by giving examples and case studies showing how game theory can solve real world resource allocation problems Contains algorithms and techniques to implement game theory in wireless terminals Game theory has been used for decades in fields of science such as economics and biology, but recently it was used to model routing and packet forwarding in wireless ad-hoc and sensor networks. However, the clustering problem, related to self-organization of nodes into large groups, has not been studied under this framework. In this work our objective is to provide a game theoretical modeling of clustering for ad-hoc and sensor networks. The analysis is based on a non-cooperative game approach where each sensor behaves selfishly in order to conserve its energy and thus maximize its lifespan. We prove the Nash Equilibria of the game for pure and mixed strategies, the expected payoffs and the price of anarchy corresponding to these equilibria. Then, we use this analysis to formulate a clustering mechanism (which we called Clustered Routing for Selfish Sensors--CROSS), that can be applied to sensor networks in practice. Comparing this mechanism to a popular clustering technique, we show via simulations that CROSS achieves a performance similar to that of a very popular clustering algorithm. This study considers an integrated topology control and routing problem in wireless sensor networks (WSNs), which are employed to gather data via use of sensors with limited energy resources. We employ a hierarchical topology and routing structure with multiple sinks and devise a topology control scheme via usable energy fraction at the sensors. We develop and examine three different mathematical models whose solutions prescribe clusterhead and sink locations and data routing from sensors to sinks in a period of a deployment cycle. We develop a heuristic solution algorithm which provides very small optimality gaps for the models. The approach utilizes two types of solution representations, a combination of multiple neighborhoods, and objective value-based cut inequalities for improving the evaluation of candidate solutions. We present extensive numerical test results and analysis of the models and the solution approach. We determine that our proposed model, which minimizes average energy usage and the range of remaining energy distribution at the sensors, captures important characteristics of topology control and routing integration in WSN design and exhibits significantly better performance than our benchmark models and a well-known protocol HEED in extending network lifetime.