This paper presents a performance analysis for the bandwidth allocation in IEEE 802.16 broadband wireless access (BWA) networks considering the packet-level quality-of-service (QoS) constraints. Adaptive Modulation and Coding (AMC) rate based on IEEE 802.16 standard is used to adjust the transmission rate adaptively in each frame time according to channel quality in order to obtain multiuser diversity gain. To model the arrival process and the traffic source we use the Batch Markov Arrival Process (BMAP), which enables more realistic and more accurate traffic modelling. We determine analytically different performance parameters, such as average queue length, packet dropping probability, queue throughput and average packet delay. Finally, the analytical results are validated numerically.