Distributed resource allocation in networked systems using decomposition techniques

Abstract: The Internet and power distribution grids are examples of ubiquitous systems that are composed of subsystems that cooperate using a communication network. We loosely define such systems as networked systems. These systems are usually designed by using trial and error. With this thesis, we aim to fill some of the many gaps in the diverse theory of networked systems. Therefore, we cast resource allocation in networked systems as optimization problems, and we investigate a versatile class of optimization problems. We then use decomposition methods to devise decentralized algorithms that solve these optimization problems.The thesis consists of four main contributions: First, we review decomposition methods that can be used to devise decentralized algorithms for solving the posed optimization problems. Second, we consider cross-layer optimization of communication networks. Network performance can be increased if the traditionally separated network layers are jointly optimized. We investigate the interplay between the data sending rates and the allocation of resources for the communication links. The communication networks we consider have links where the data transferring capacity can be controlled. Decomposition methods are applied to the design of fully distributed protocols for two wireless network technologies: networks with orthogonal channels and network-wide resource constraints, as well as wireless networks using spatial-reuse time division multiple access. Third, we consider the problem of designing a distributed control strategy such that a linear combination of the states of a number of vehicles coincide at a given time. The vehicles are described by linear difference equations and are subject to convex input constraints. It is demonstrated how primal decomposition techniques and incremental subgradient methods allow us to find a solution in which each vehicle performs individual planning of its trajectory and exchanges critical information with neighbors only. We explore various communication, computation, and control structures. Fourth, we investigate the resource allocation problem for large-scale server clusters with quality-of-service objectives, in which key functions are decentralized. Specifically, the problem of selecting which services the servers should provide is posed as a discrete utility maximization problem. We develop an efficient centralized algorithm that solves this problem, and we propose three suboptimal schemes that operate with local information.