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Optimization theory and game theory provide a suite of tools that are flexible in modelling various network systems, and a rich series of equilibrium solution concepts and convergent algorithms. In this thesis, we view network protocols as distributed algorithms achieving the corresponding network equilibria, and study wireless network design and control in optimization and game-theoretic frameworks.
Specifically, we first take a holistic approach and design an overall framework for the protocol architecture in ad hoc wireless networks. The goal is to integrate various protocol layers into a unified framework, by regarding them as distributed computations over the network to solve some optimization problem. Our current theory integrates three functions--congestion control, routing and scheduling--in transport, network and link layers into a coherent framework. These three functions interact through and are regulated by congestion price so as to achieve a global optimality, even in a time-varying environment. This framework is promising to be extended to provide a mathematical theory for network architecture, and to allow us to systematically carry out cross-layer design.
We then develop a general game-theoretic framework for contention control. We define a general game-theoretic model, called random access game, to study the contention/interaction among wireless nodes, and propose a novel medium access method derived from carrier sensing multiple access with collision avoidance in which each node estimates its conditional collision probability and adjusts its persistence probability or contention window, according to a distributed strategy update mechanism achieving the Nash equilibrium of random access game. This results in simple dynamics, controllable performance objectives, good short-term fairness, low collision, and high throughput. As wireless nodes can estimate conditional collision probabilities by observing consecutive idle slots between transmissions, we can decouple contention control from handling failed transmissions. This also opens up other opportunities such as rate adaptation to channel variations. In addition to providing a general and systematic design methodology for medium access control, the random access game model also provides an analytical framework to understand the equilibrium properties such as throughput, loss and fairness, and dynamic properties of different medium access protocols and their interactions.
Finally, we conclude this work with some suggestions for future research.