Fiber based access networks can deliver performance that can support the increasing demands for high speed connections. One of the new technologies that has emerged in recent years is Ethernet Passive Optical Networks. The key features of this approach are the simplicity of the architecture and compatibility with existing Ethernet based local area networks. To make Ethernet Passive Optical Networks (EPONs) a fully functional part of the telecommunication system, support for classes of traffic with different Quality of Service (QoS) requirements is mandatory. Much research has been done on the optimal bandwidth allocation algorithms that would have the capability of supporting Differentiated Services (DiffServ) in EPONs. This thesis proposes that the access control mechanism should be centralized and performed by the Optical Line Terminal (OLT). It is shown that this approach can give greater flexibility to adjust to changing traffic conditions, can simplify the structure of the Optical Network Units, and can allow the easy adoption of Service Level Agreements. This thesis introduces a novel EPON simulator that allows testing of various types of bandwidth allocation algorithms. It is possible to evaluate the allocation mechanism under different traffic conditions and with network configurations that closely resemble real systems. New algorithms are presented based on a paradigm of centralized access control. Simulation results showed that they offer good performance and support for the DiffServ architecture.