"To sense" or "not to sense" in energy-efficient power control games

A network of cognitive transmitters is considered. Each transmitter has to decide his power control policy in order to maximize energy-efficiency of his transmission. For this, a transmitter has two actions to take. He has to decide whether to sense the power levels of the others or not (which corresponds to a finite sensing game), and to choose his transmit power level for each block (which corresponds to a compact power control game). The sensing game is shown to be a weighted potential game and its set of correlated equilibria is studied. Interestingly, it is shown that the general hybrid game where each transmitter can jointly choose the hybrid pair of actions (to sense or not to sense, transmit power level) leads to an outcome which is worse than the one obtained by playing the sensing game first, and then playing the power control game. This is an interesting Braess-type paradox to be aware of for energy-efficient power control in cognitive networks.Comment: Proc. of the 2nd International Conference on Game Theory for Network (GAMENETS), 201

OPTIMIZATION AND EQUILIBRIUM MODELING FOR RENEWABLE ENERGY: FOCUS ON WASTEWATER-TO-ENERGY APPLICATIONS

This dissertation presents three novel optimization models for sustainable wastewater management. The Blue Plains Advance Wastewater treatment plant (AWTP) operated by the District of Columbia Water and Sewer Authority (DC Water) is used as a case study. The application to the Blue Plains AWTP is presented to illustrate the usefulness of the model and how wastewater treatment plants (WWTPs), solid waste disposal plants, community management groups can actively and positively participate in energy and agricultural markets. Besides the conversion of the solid end products into biogas and electricity via digesters, WWTP can also produce Class B biosolids for land application or Class A biosolids for use as fertilizer. Chapter 1 introduces the Blue Plains case study and other important aspects of wastewater management. The first problem, discussed in Chapter 2, is a multi-objective, mixed-integer optimization model with an application to wastewater-derived energy. The decisions involve converting the amount of solid end products into biogas, and/or electricity for internal or external purposes. Three objectives; maximizing total value, minimizing energy purchased from external sources and minimizing carbon dioxide equivalent (CDE) emissions were presented via an approximation to the Pareto optimal set of solutions. The second type of problem is a stochastic multi-objective, mixed-integer optimization model with an application to wastewater-derived energy and is presented in Chapter 3. This model considers operational and investment decisions under uncertainty. We also consider investments in solar power and processing waste from outside sources for revenue and other benefits. The tradeoff decision between operational and investment costs and CDE emissions are presented. The third type of optimization model is a stochastic mathematical program with equilibrium constraints (MPEC) for sustainable wastewater management and is presented in Chapter 4. This two-level optimization problem is a stochastic model with a strategic WWTP as the upper-level player. The lower-level players represent the fertilizer, natural gas, compressed natural gas (CNG) and electricity markets. All the lower-level players are price-takers. Chapter 5 considers a comparison of the three optimization models discussed above and highlights differences. Chapter 6 provides conclusions, contributions, and potential future directions

Stackelberg games for energy-efficient power control in wireless networks

International audienceThis paper addresses the power control problem in wireless networks where transmitters choose their control policy freely and selfishly in order to maximize their individual energy­ efficiency. In this framework, two new scenarios are studied in details: 1. a scenario where a fraction of the transmitters can observe the power levels of the other transmitters while the latter have no sensing capabilities; 2. a scenario where the observation structure is triangular, that is, the k th transmitter can observe the k-1 th transmitters (which corresponds to a multi-level hierarchical game). In both scenarios the equilibrium analysis (existence, uniqueness, determination, efficiency) is conducted. In scenario 1, it is proved that the game outcome Pareto dominates the one obtained when no transmitters can sense the others. Taking the sensing cost into account, a simple condition under which being a follower (namely a transmitter who senses) is better than a leader is provided. Interestingly, the existence of an optimum fraction of cognitive transmitters in terms of sum utility is proved in the case where the sensing cost is neglected. In scenario 2, it is proved analytically that knowing more leads to a better utility and the game outcome Pareto dominates the solution with no sensing. The derived results are illustrated by numerical results and provide some insights on how to deploy cognitive radios in heterogeneous networks in terms of sensing capabilities