An call admission control (CAC) algorithm for probabilistic services scheduled by an EDF scheduler was presented. The connections with similar quality of service (QoS) constraints as an aggregate traffic class were considered. The algorithm differs from others in that it is derived from the analysis of per-class QoS metrics. It was found that due to strict coupling between the deadline violation probability and the delay bound, the QoS metrics that an EDF scheduler actually gurantees have an asymptotic ordering property, which provides a serious implication for the design and control of EDF networks. The investigation on robust admission control mechanisms were being conducted to support long-range dependent processes with infinite variances.