With the advancement of communication networks, a great number of multicast applications such as multimedia, video and audio communications have emerged. As a result, energy efficient multicast in wireless networks is becoming increasingly important in the field of Information and Communications Technology (ICT). According to the study by Gartner and Environmental Protection Agency (EPA) report presented to United State Congress in 2007,energy consumption of ICT nodes accounts for 3% of the worldwide energy supply and is responsible for 2% of the global Carbon dioxide (CO2) emission. However, several initiatives are being put in place to reduce the energy consumption of the ICT sector in general. A review of related literature reveals that existing approaches to energy efficient multicast are largely evaluated using a single metric and while the single metric is appropriate for effective performance, it is unsuitable for measuring efficiency adequately. This thesis studied existing coded packet methods for energy efficiency in ad hoc wireless networks and investigates efficiency frontier, which is the expected minimum energy within the minimum energy multicast framework. The energy efficiency performance was based on effective evaluation and there was no way an inefficient network could reach a level of being an efficiency frontier. Hence, this work looked at the position of how true efficiency evaluation is obtained when the entire network under examination attains their efficiency frontiers using ratios of weighted outputs to weighted inputs with multiple variables. To address these challenges and assist network operators when formulating their network policies and performing network administrations, this thesis proposed novel approaches that are based on Data Envelopment Analysis (DEA) methodology to appropriately evaluate the efficiency of multicast energy and further minimizes energy transmission in ad hoc wireless networks without affecting the overall network performance. The DEA, which was used to study the relative efficiency and productivity of systems in Economic and Operational Research disciplines, is a non-parametric method that relies on linear programming technique for optimization of discrete units of observation called the decision making units (DMUs)
