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Quality-of-service (QoS) support in Ethernet passive optical networks is a crucial concern. We propose a new dynamic bandwidth allocation (DBA) algorithm for service differentiation that meets the service-level agreements (SLAs) of the users. The proposed delay-aware (DA) online DBA algorithm provides constant and predictable average packet delay and reduced delay variation for the high- and medium-priority traffic while keeping the packet loss rate under check. We prove the effectiveness of the proposed algorithm by exhaustive simulations.