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Bandwidth is an extremely valuable and scarce resource in a wireless network. Therefore, efficient bandwidth management is necessary in order to provide high quality service to users with different requirements in a multimedia wireless/mobile network. In this paper, we propose an on-line bandwidth reservation algorithm that adjusts bandwidth reservations adaptively based on existing network conditions. The most important contribution of our work is an adaptive algorithm that is able to resolve conflicting performance criteria - bandwidth utilization, call dropping and call blocking probabilities. Our algorithm is quite flexible, is responsive to current traffic conditions in cellular networks, and tries to strike the appropriate performance balance between contradictory requirements for QoS sensitive multimedia services.