The IEEE 802.11e Enhanced Distributed Channel Access (EDCA) is designed to provide differentiated services without real hard performance guarantees, such as bandwidth and delay bounds in wireless LANs. In this paper we design a measurement-assisted, model-based call admission control (MM-CAC) scheme to support guaranteed QoS in the EDCA. For this purpose, we first develop an accurate analytical model of the legacy IEEE 802.11 DCF under non-saturation conditions; then using this model, we define the concept of equivalent number of competing entities, to convert a heterogeneous (multi-class) EDCA network into an equivalent homogeneous network and study traffic classes in isolation. Our analytical model is then invoked to decide to admit a new flow or reject it with much little computational complexity as compared to a fully fledged EDCA model. Numerical results validate our model and analysis, and simulations demonstrate the effectiveness of our MM-CAC scheme.