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The appearance of increased-bandwidth applications with quality-of-service (QoS) requirements has brought about the emergence of multi-service access networks. Data Over Cable Service Interface Specification (DOCSIS) networks are intended to support high quality audio, video, and interactive services over Internet protocol (IP) flows within a Hybrid Fiber/Coax (HFC) network context. In order to support large amount of users and demanded QoS for such applications, a careful management of resources is needed. In this paper we propose a centralized bandwidth allocation scheme for the return path of DOCSIS networks. The proposed scheme takes advantage of the application's traffic characteristics to minimize the bandwidth dedicated to control signals and achieve high bandwidth utilization. At the same time, the proposed approach complies with the QoS requirements of the serviced applications. The performance of our bandwidth allocation approach was evaluated using computer simulation. The performance metrics used are the average packet delay, data throughput, and number of users supported. Results are obtained for networks with a single service as well as for a mixed service scenario. As shown by the results, our approach achieves high bandwidth utilization, and still complies with the delay constraints imposed by the user applications. It increases the system capacity as compared to reference approaches.