In the last few years, there has been a large body of literature on congestion control based on optimization and control theories. This paper provides an overview of optimization flow control starting from the first original papers, and traces the development in a unified framework, from unicast to multicast, from theory to algorithms to implementation issues. The optimal congestion control problem is formulated, both for unicast and multicast. Decentralized theoretical solutions are derived by applying duality theory. Based on these results, actual generic algorithms and implementations are proposed for solving these problems in a distributed way. Some alternative methods not based on duality theory are also reviewed. Finally the complementary problem of choosing suitable utility functions in the optimization problem is addressed. (c) 2005 Elsevier B.V. All rights reserved.
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