Optimal resource management is a crucial task in a plethora of scientific fields, including wireless communication and electric power networks, where it ensures efficient operation and user satisfaction. The pressing need to modernize the aging power grid has culminated to a vision encouraging interaction of the end users with the grid through demand response, which amounts to electricity end users adapting their power consumption in response to pricing schemes varying over time (e.g., every hour or day). By the same token, delivering data, voice, and video seamlessly over wireless networks with the quality-of-service demanded by today's multimedia applications requires optimal link-adaptive allocation of the available resources, e.g., power, to the different network nodes and layers. This thesis develops algorithms for (a) scheduling of demand response in the smart power grid, and (b) cross-layer wireless network design.
First, demand response is considered in a multiple-residence setup. The utility company adopts a cost function representing the cost of providing energy to end users. Each residential end user has a base load, two types of adjustable loads, and possibly a storage device. The first load type must consume a specified amount of energy over the scheduling horizon, but the consumption can be adjusted across different slots. Charging a plug-in hybrid electric vehicle is an example. The second type does not entail a total energy requirement, but operation away from a user-specified level results in user dissatisfaction. The research issue amounts to minimizing the electricity provider cost plus the total user dissatisfaction, subject to the individual constraints of the loads. The problem can be solved by a distributed subgradient method. The utility company and the end users exchange information through the Advanced Metering Infrastructure (AMI)---a two-way communication network---in order to converge to the optimal amount of electricity production and the optimal power consumption schedule. The algorithm finds near-optimal schedules even when AMI messages are lost, which can happen in the presence of malfunctions or noise in the communications network. The algorithm amounts to a subgradient iteration with outdated Lagrange multipliers, for which convergence results of wide scope are established.
Next, attention is turned to an energy consumption scheduling problem for a single residential end user, but with an added complexity. Each adjustable load is interruptible in the sense that the load can be either operated (resulting in nonzero power consump- tion), or not operated (resulting in zero power consumption). The task amounts to minimizing the cost of electricity plus user dissatisfaction, subject to individual load consumption constraints. The resulting problem is nonconvex, but it is shown to have zero duality gap if a continuous-time horizon is considered. This opens up the possibility of using Lagrangian dual algorithms without loss of optimality in order to come up with efficient demand response scheduling schemes.
As regards wireless networking, the challenge is to jointly optimize application-level rates, routes, link capacities, power consumption, and power allocation across frequency tones, neighboring terminals, and fading states. The physical layer is interference-limited, whereby network terminals treat interference as noise. Provably convergent algorithms yield (near-)optimal end-to-end rates, multicommodity flows, link capacities, and average powers. These design variables are obtained offline, and are subsequently used for control during network operation. Moreover, physical layer power allocation algorithms that are seamlessly integrated into layered architectures are developed using successive convex approximations.