Earliest deadline first (EDF) has become one of the most promising scheduling schemes for providing quality-of-service (QoS) differentiation over high speed networks. In this paper, we study the deadline violation (loss) probability at an EDF scheduling switch. An analytical framework based on the dominant time scale (DTS) has been developed for estimating the deadline violation probabilities of the aggregated traffic and the individual flows. This enables us to determine whether a given flow can meet its deadline with the required loss probability. As shown by simulations using real network traffic, the asymptotic approximations developed in this paper are accurate enough to predict the real metrics. The framework can serve as the basis for the design of call admission control (CAC) mechanisms which are targeted to provide statistical guarantees on transmission delays and/or loss.