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In this paper, we propose an adaptive bandwidth framework for supporting multiple classes of multimedia services with different quality of service (QoS) requirements in the next generation of wireless cellular networks. The framework combines the following components: (i) a threshold-based bandwidth allocation policy. (ii) an efficient threshold-type call admission control (CAC) algorithm, and (iii) a bandwidth adaptation algorithm (BAA). The framework can be modeled as a multi-dimensional Markov chain, and therefore, a product form solution is provided. The QoS metrics - new call blocking probability, handoff call dropping probability, and degradation probability are derived. The analytical results are supported by simulation and show that this work improves the service quality by minimizing the handoff call dropping probability.