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This paper investigates an application-oriented bandwidth allocation scheme to ensure fairness among queues with diversified quality-of-serice (QoS) requirements in EPONs. Formerly, differentiated services (DiffServ) were suggested to be used in EPON so as to provision some queues with higher QoS over others. However, owing to the coarse granularity, DiffServ can hardly facilitate any particular QoS profile of an application in EPONs. In this paper, we define application utilities to quantify users' quality-of-experience (QoE) as a function of network layer QoS metrics. Then, we formulate the fair resource allocation issue into a utility max-min optimization problem, which is quasiconcave over queues' delayed traffic and dropped traffic. Utilizing the quasiconvex property, we propose to employ the bisection method to solve the optimization problem. The optimal value can be achieved by proper bandwidth allocation and queue management in EPONs. Detailed implementation of the proposed algorithm is discussed, and simulation results show that our proposed scheme can ensure fairness and guarantee QoS with fine granularity.