In this paper, we propose a mathematical model with the aim to give guidelines for the dimensioning of fixed WiMAX bandwidth provisioning service to residential customers. Our proposal relies on the modeling of a CAC policy associated to a priority-based bandwidth sharing strategy. Both mechanisms aim to satisfy Quality of Service constraints while maximizing the gain of the system. But unlike in Khemiri et al. (Optimal call admission control for an IEEE 802.16 wireless metropolitan area network. In: International Conference on Network Control and Optimization, 2007, accepted), we do not necessarily seek here for an optimal CAC policy. We rather consider a coordinate convex CAC policy, whose mathematical modeling leads to a tractable analytical resolution. We chose the Guaranteed Minima (GM) policy, which consists in reserving a specified amount of bandwidth for each traffic class. The remaining bandwidth is shared between all traffic classes. The purpose of the paper is to determine, using an analytical model and a heuristic approach, the nearly-optimal sizes of the GM reservation thresholds associated to each type of connection. The main concern here is to propose simple and robust computational methods, which can be easily and efficiently used to dimension a realistic WiMAX network.