| Convex optimization techniques have found important applications in communications and signal processing. Recently, there has been a surge in research activities that apply the latest development in convex optimization to the design and analysis of communication systems. This research focuses on how to apply optimization techniques on both massive content distribution in high-speed Internet core, and cross-layer design in wireless ad hod networks.;One of the important trends is that the Internet will be used to transfer content on more and more massive scale. Collaborative distribution techniques such as swarming and parallel download have been invented and effectively applied to end-user file-sharing or media-streaming applications, but mostly for improving end-user performance objectives. We consider the issues that arise from applying these techniques to content distribution networks for improving network objectives, such as reducing network congestion. In particular, we formulate the problem of how to make many-to-many assignment from the sending nodes to the receivers and allocate bandwidth for every connection, subject to the node capacity and receiving rate constraints. The objective is to minimize the worst link congestion over the network, which is equivalent to maximizing the distribution throughput, or minimizing the distribution time. The optimization framework allows us to jointly consider server load balancing, network congestion control, as well as the requirement of the receivers. We develop a special, diagonally-scaled gradient projection algorithm, which has a faster convergence speed, and hence, better scalability with respect to the network size than a standard subgradient algorithm. We provide both a synchronous algorithm and a more practical asynchronous algorithm.;However, on the negative side, swarming traffic has made capacity shortage in the backbone networks a genuine possibility, which will be more serious with fiber-based access. The second problem addressed is how to conduct massive content distribution efficiently in the future network environment where the capacity limitation can equally be at the core or the edge. We propose a novel peer-to-peer technique as a main content transport mechanism to achieve efficient network resource utilization. The technique uses multiple trees for distributing different file pieces, which at the heart is a version of swarming. In this chapter, we formulate an optimization problem for determining an optimal set of distribution trees as well as the rate of distribution on each tree under bandwidth limitation at arbitrary places in the network. The optimal solution can be found by a distributed algorithm. The results of the chapter not only provide stand-alone solutions to the massive content distribution problem, but should also help the understanding of existing distribution techniques such as BitTorrent or FastReplica.;The joint optimal design of congestion control and wireless MAC-layer scheduling problem in multi-hop wireless networks has become a very active research area in the last few years. We solve this problem using a column generation approach with imperfect scheduling. We point out that the general subgradient algorithm has difficulty in recovering the time-share variables and experiences slower convergence. We first propose a two-timescale algorithm that can recover the optimal time-share values. Most existing algorithms have a component, called global scheduling, which is usually NP-hard. We apply imperfect scheduling and prove that if the imperfect scheduling achieves an approximation ratio rho, then our algorithm converges to a sub-optimum of the overall problem with the same approximation ratio. By combining the idea of column generation and the two-timescale algorithm, we derive a family of algorithms that allow us to reduce the number of times the global scheduling is needed. |
