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Ethernet passive optical networks (EPONs) have emerged as one of the most promising access network technologies. Propelled by rapid price declines in fiber optics and Ethernet components, these architectures combine the latest in optical and electronic advances and are poised to become the dominant means of delivering gigabit broadband connectivity to homes over a unified single platform. As this technology matures, related quality of service (QoS) issues are becoming a key concern. This paper proposes a novel dynamic scheduling algorithm, termed hybrid granting protocol (HGP), to support different QoS in EPON. Specifically, the proposed dynamic scheduling algorithm minimizes packet delay and jitter for delay and delay-variation sensitive traffic (e.g., voice transmissions) by allocating bandwidth in a grant-before-report (GBR) fashion. This considerably improves their performance without degrading QoS guarantees for other service types. Detailed simulation experiments are presented to validate the effectiveness of the proposed algorithm.