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While the backbone networks have experienced substantial changes in the last decade; the access networks have not changed much. Recently, passive optical networks (PONs) seem to be ready for commercial deployment in access networks due to the maturity of a number of enabling technologies, long distance and reduced maintenance. Among PON technologies, the Ethernet PON (EPON) presently being standardized by the IEEE 802.3ah Ethernet in the first miles (EFM) task force is most attractive because of its high speed, low cost, familiarity, interoperability and low overhead. In this paper, we propose a novel bandwidth guarantee polling (BGP) scheme that will allow the upstream bandwidth to be shared based on the service level agreement (SLA) between each subscriber and the operator. It is able to provide bandwidth guarantee for premium subscribers according to the SLAs while providing best-effort service to other subscribers. The analytical and simulation results prove that the proposed scheme does best in what it is designed to do compared to another well-known scheme that has not considered providing differentiated services. With business customers preferring premium services with guaranteed bandwidth and residential users preferring low-cost best effort services, our scheme could benefit both groups of subscribers as well as the operators.