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This paper proposes a new method of bandwidth sharing policy which dynamically adjusts the bandwidth among the different services within the cell with changing network traffics. The proposed method, called min-max fairness scheme, exhibits good performances in cellular network applications where bandwidth is at a premium such as in multimedia communications. The improved efficiency of the scheme is achieved by considering the online and the offline services in different ways as well as using a strategy of temporary borrowing the reserved bandwidth for offline services. The scheme distributes the bandwidth among the services as evenly as possible and guarantees the minimum bandwidth to all the services besides maintaining the quality of service at various traffic loads. Simulation results are presented to confirm the superior performance compared with other recent existing schemes.