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In this paper, we present a new service scheme, Periodic GATE Optimization (PGO) for long-reach passive optical networks. PGO is based on a previously proposed service scheme where the optical line terminal (OLT) generates multiple threads to poll the bandwidth requests of the optical network units (ONUs). In PGO, OLT periodically builds an ILP formulation by using the collected requests of the ONUs, and solves the model for the overloaded ONUs. Based on the outputs, it determines how to credit the ONUs until the next ILP formulation whenever they are overloaded. We evaluate the performance of PGO by simulation, and show that it introduces further decrease in average packet delay until the heavy loads. Average queue length at the ONUs is also shortened by PGO. The results imply that PGO achieves these enhancements without increasing the packet drop probability. In the paper, we also present the quality-of-service (QoS) aware version of PGO, namely PGO-QoS. PGO-QoS consists of two modules such as intra-ONU scheduling where the dequeuing proportion of the QoS classes is determined and reported to OLT, and dynamic bandwidth allocation module where mostly PGO runs. We evaluate the performance of PGO-QoS for each QoS class and for the overall network in terms of average packet delay, average queue size, and packet drop probability under different scenarios. Based on the simulation results, PGO-QoS is shown to introduce further decrease in delay, queue length, and packet loss probability for the high priority class requests that are granted by multithread polling in Long-Reach PON.