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We propose an optical line terminal (OLT) centric dynamic bandwidth allocation (DBA) scheme based on individual requests from service queues in optical network units (ONUs) for a quality-of-service (QoS) aware Ethernet passive optical network (EPON). The goal is to provide fairness for allocating bandwidth among different service classes based on their service level agreements (SLAs). The proposed DBA scheme makes use of the excess bandwidth of lightly loaded queues to meet the bandwidth demand of heavily loaded queues. To implement this scheme, an effective polling mechanism is incorporated to solve the idle period problem. In addition, to reduce the scheduling overhead, the DBA scheme utilizes a novel different cycle policy which involves selective bandwidth allocations to different service classes based on their delay bounds. We conduct detailed simulation experiments and compare the results with the well-known interleaved polling with adaptive cycle time (IPACT) algorithm that utilizes strict priority policy.