In this paper we propose an admission control algorithm which is suitable for real time traffic in a sink-tree network in which per-aggregate resource management is in place. Every flow specifies its leaky-bucket parameters and a required delay bound, and the algorithm admits a new flow if a guarantee can be given that the delay bound for every established flow is not exceeded. The algorithm is based on a formula, derived through Network Calculus, that relates the worst-case delay of a single flow to the transmission rate provisioned for the aggregate and to the leaky-bucket parameters of flows at the ingress of the network. We describe the algorithm and the employed data structures, and we evaluate its complexity.