In this paper performance of dynamic bandwidth allocation in broadband wireless networks under dynamic arrival process and channel SNR is evaluated using queuing analysis framework. Adaptive modulation and coding 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 multi-user diversity gain. Arrival process is considered to be discrete-time Markov chain which is modeled by the Markov Modulated Poisson Process (MMPP) as the traffic source. Quality of service parameters are evaluated under several allocated bandwidths to a single queue in the case of two scenarios: 1) different arrival traffic intensity, and 2) different channel quality. As expected, dynamic bandwidth allocation according to channel variations improves quality of service parameters.