Abstract-Admission control algorithms must ensure that, when a new QoS resource reservation is accepted, reservations already present in the system continue having their QoS guarantees honored. In this paper we consider different approaches to compute the aggregated allocated capacity in WiMAX networks and, based on their limitations, propose the EDiophantine solution. The mathematical foundations for the designed approach are provided along with the performance improvements to be expected, both in accuracy and computational terms, as compared to three alternatives of increasing complexity. Finally, the different solutions considered are evaluated with OPNET's WiMAX simulator in a realistic scenario.