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Gigabit-Ethernet passive optical networks (Gigabit EPONs) are expected to be an attractive solution for next-generation high speed access networks. Since the network topology of EPON is point-to-multipoint (multiple ONUs are connected to one OLT), a media access control called dynamic bandwidth allocation (DBA) algorithm is an important factor for determining the performance of EPON. This paper proposes a new DBA scheme, D-CRED, which can achieve a higher utilization of EPON, and discusses how the scheme can be applied to the quality of service capability. The first part of this paper focuses on efficiency. The authors argue that in order to achieve higher efficiency, unused slot and cycle shrinkage must be eliminated. D-CRED can overcome this problem by introducing a dynamic queue threshold technique. Through computer simulations, the authors confirm that D-CRED can achieve a higher efficiency: approximately a 6.4% higher utilization compared with a scheme based on literature, and 99% utilization of the theoretical maximum utilization. The latter part of this paper covers quality of service issues. The authors propose a new concept, satisfaction based allocation, for fair allocation on the basis of D-CRED, and discuss how this concept is extended to the weighted fair allocation of EPON.