In this paper we discuss optical network unit (ONU) based traffic prediction in Ethernet passive optical networks (EPONs). The technique utilizes least-mean-square polynomial regression for the estimation of incoming traffic and adaptive least-mean-squares filtering for the estimation of the EPON cycle duration. Given these estimates, the ONU successfully predicts its bandwidth requirements at the next available transmission opportunity and communicates this prediction, rather than its actual buffer occupancy, to the optical line terminal (OLT). The proposed scheme is assessed via simulations and it is demonstrated that a delay improvement of 30% can be achieved without modifying the dynamic bandwidth assignment process at the OLT. In addition, we further explore aspects of traffic prediction combined with a max-min fair bandwidth redistribution scheme at the OLT. Initial results show that the combination of the ONU-based prediction and the OLT-based fair bandwidth redistribution further improves the delay.