In this paper, we propose a mathematical model with the aim to give guidelines for the dimensioning of 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 , 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.