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Ethernet-based passive optical network (EPON) technology is being considered as a promising solution for next-generation broadband access networks due to the convergence of low-cost Ethernet equipment and low-cost fiber infrastructures. A major feature for this new architecture is the use of a shared transmission media between all users; hence, medium access control arbitration mechanisms are essential for the successful implementation of EPON: i.e., to ensure a contention-free transmission and provide end users with equal access to the shared media. We propose to use the multipoint control protocol defined by the IEEE 802.3ah task force to arbitrate the transmission of different users, and we present different dynamic bandwidth allocation (DBA) algorithms to allocate bandwidths effectively and fairly between end users. These DBA algorithms are also augmented to support differentiated services, a crucial requirement for a converged broadband access network with heterogeneous traffic. We show that queueing delays under strict bandwidth allocation algorithms result in an unexpected behavior for certain traffic classes, and we suggest the use of DBA with appropriate local queue management to alleviate this inappropriate behavior. We conduct detailed simulation experiments to study the performance and validate the effectiveness of the proposed protocols.