This paper presents the first comprehensive model of the 802.1laa intra-access category prioritization under saturated condition. We propose a 3D Markov chain to model the system and analyze several important QoS metrics, including throughput, delay, and frame drop ratio. The accuracy of our model is verified by extensive simulations. The results show that the 802.1laa can provide a finer grained prioritization between individual audio and video streams in throughput and delay. However, advanced physical layer techniques are necessary in providing QoS support in a large-scale WiFi network.