In this paper, we focus on the quantitative Quality of Service (QoS) guarantee in a Differenciated Services (DiffServ) domain that can be granted to an Expedited Forwarding (EF) ?ow in terms of end-to-end delay. This study shows that delays much smaller than the deterministic bound can be guaranteed with probabilities close to one. An admission control derived from these results is then proposed, providing a probabilistic QoS guarantee to EF flows.