In this paper, a design alternative for guaranteeing short-term QoS in the E-PON (Ethernet-Passive Optical Network) OLT (Optical Line Terminal) node is studied. A scheduling algorithm called Short-term QoS Deficit Round Robin (SQ-DRR) is proposed to guarantee tunable deterministic QoS constraints for multimedia applications over E-PON. The major appealing aspect of the scheduler is that it guarantees delay constraint for short-term aggregate burst traffic violating pre-contracted descriptors at the same time without loosing long-term fairness. We then evaluate the scheduler performance with and without admission control scheme under non-stationary long-range dependence (LRD) traffic. The simulation results indicate that the SQ-DRR performs well in dynamic burst traffic conditions.