IEEE 802.11e standard defines two access modes to provide Quality of Service support for 802.11-based Wireless LANs: Enhanced Distributed Channel Access and HCF Controlled Channel Access (HCCA). Only HCCA can guarantee bandwidth per flow which is suitable for various multimedia application requirements. However, the reference scheme HCCA is designed without awareness of variable bit rate (VBR) transmission. Several enhancement techniques have been proposed to address the VBR problem, but there are few research results for a model to capture the characteristics of HCCA. In this paper, an analytical model for the expected packet waiting time is proposed. The model can capture the system behavior per session leading to suitable admission control process for VBR support. The proposed model has been validated using the Network Simulator. The results confirm that the reference admission control scheme with mean data rate acceptance cannot guarantee the required bound on waiting time. Using the model, suitable parameters can be investigated for admission control with VBR support. The model can also be applied with polling based technologies, such as WiMAX.