Abstract

The main focus of this research is directed towards fairness in a dynamic network. Two specific applications are mathematically formulated: heating, ventilation, and air conditioning (HVAC), and code division multiple access (CDMA). In the first problem, namely, fair power allocation for temperature regulation of a multi-unit building, the temperature of each unit is described by a discrete-time dynamic equation. The formulation considers the effect of outside temperature and heat transfer between the adjacent rooms. Temperature regulation is then described as a constrained optimization problem, where the objective is to maintain the temperature of each unit within a prescribed thermal comfort zone with a limited amount of power. An optimal control strategy is presented to minimize the maximum mutual temperature difference between different units (long-term fairness) while maintaining the temperature of each unit in the comfort zone or close to it at all times, as much as possible (short-term fairness). Simulations demonstrate the effectiveness of the proposed control strategy in regulating the temperature of every unit in a building. Regarding the second application, an optimization-based fair reverse-link rate assignment strategy is proposed for fair resource allocation in a CDMA network. The network is modeled in a star topology, where the nodes represent either the base station (BS) or access terminals (ATs). The BS at every instant computes the fair rate for each AT by minimizing the maximum disparity in users' rates. Then, the BS sends a single bit to all ATs at every instant. It is shown that if each AT could compute a specific variable, called the coordinating variable, it can find its fair rate, which means the decision-making strategy is distributed. The proposed method is computationally efficient, and simulations confirm its efficacy in different scenarios.