Extensive research addressing IEEE 802.11e enhanced distributed channel access (EDCA) performance analysis, by means of analytical models, exist in the literature. Unfortunately, the currently proposed models, even though numerous, do not reach this accuracy due to the great number of simplifications that have been done. Particularly, none of these models considers the 802.11e contention free burst (CFB) mode which allows a given station to transmit a burst of frames without contention during a given transmission opportunity limit (TXOPLimit) time interval. Despite its influence on the global performance, TXOPLimit is ignored in almost all existing models. To fill in this gap, we develop in this paper a new and complete analytical model that (i) reflects the correct functioning of EDCA, (ii) includes all the 802.11e EDCA differentiation parameters, (iii) takes into account all the features of the protocol, and (iv) can be applied to all network conditions, going from nonsaturation to saturation conditions. Additionally, this model is developed in order to be used in admission control procedure, so it was designed to have a low complexity and an acceptable response time. The proposed model is validated by means of both calculations and extensive simulations.