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Efficient bandwidth allocation strategy with simultaneous fulfillment of QoS requirement of a user in a mobile cellular network is still a critical and an important practical issue. We explore the problem of finding the reservation schedule that would minimize the amount of time for which bandwidth has to be allocated in a cell while meeting the QoS constraint. With the knowledge about the arrival and residence time distribution of a user in a cell, the above problem can be optimally solved using a dynamic programming based approach in polynomial time. To be able to use the solution, we provide a mechanism for constructing the arrival/residence time distribution based on the measurement of hand-off events in a cell. The above solution allows us to propose an optimal time based bandwidth reservation and call admission scheme. By being scalable and distributed, the proposed scheme justifies for practical implementation. Simulations results are also presented to show the effectiveness of the scheme to achieve the target QoS level and optimal bandwidth utilization.