Optimal placement of a relay node with controllable mobility in wireless networks considering fairness

Since the capacity of a wireless link depends on the distance between its transmitter and receiver nodes, the optimal placement of nodes in the wireless network is important to improve the system efficiency. We study this issue in this paper considering a wireless network that consists of multiple nodes that do not have controllable mobility and a relay node that has controllable mobility. We model the capacity of a wireless link between node and relay node as a function of the distance between them. We then formulate the optimization problem that aims at maximizing the weighted throughput of a node that achieves the lowest weighted throughput among all nodes. Unfortunately, the problem is inherently non-convex, which is in general difficult to solve. However, in this paper, we develop the algorithm for the optimal placement of the relay node based on duality theories in optimization. We also show that the optimal position of the relay node obtained by our algorithm is in fact the weighted max-min fair position.