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We explore an approach for bandwidth allocation for the centralized MAC protocol employed by DOCSIS (data over cable service interface specification) compliant cable networks. The proposed approach is based on the statistics of the source traffic models. It aims at achieving low excess bandwidth while still offering delays that are acceptable from the point of view of the application's QoS requirements. The access and total delays as well as the excess bandwidth are our performance metrics. Computer programs were used to compute the performance metrics for a system servicing two applications with different QoS requirements. The selected applications are an Internet video game, which is delay sensitive, and data transfer, which is delay tolerant. The performance metrics were computed for different offered loads. Results show our approach yields QoS complying delays while achieving high bandwidth utilization.