The paper considers the connection admission control (CAC), which is a key resource management procedure, and proposes a solution to the problem based on modelling and control methodologies. The CAC problem will be formulated as an optimal control problem subject to a set of constraints. As a matter of fact, the proposed controller, modelling the CAC mechanism, computes the above-mentioned control variables so that (i) a set of proper constraints, which model the quality of service (QoS) requirements ( link availability, blocking probability and dropping probability), are respected and (ii) a proper performance index, which models the exploitation degree of the available bandwidth, is maximized. The proposed CAC successfully compares with other CACs proposed in the literature, and in particular significantly extends the upper limit of the accepted traffic rate.