Abstract-Next generation Passive Optical Network (PON) technology has been evolving to consolidate the metro and access networks in order to offer enhanced capacity, high split ratio and reduced deployment cost per subscriber. However, transmission of the signals to long distances up to 100km leads to increased propagation delay whereas high split ratio may lead to long cycle times resulting in large queue occupancies and long packet delays. In this article, we present a delay-constrained admission control mechanism and adapt this scheme to our previously proposed bandwidth allocation technique, namely Periodic GATE Optimization (PGO). We call this new scheme Delay-Constrained Periodic GATE Optimization (DC-PGO). DC-PGO is designed to run for multiple service classes as it inherits the advantages of PGO by periodically building and solving an ILP formulation at the OLT in order to obtain the appropriate credit values for the overloaded ONUs. At the ONU side, DC-PGO runs an admission control scheme before pushing the arriving packets in the sub-queues. The admission control scheme uses statistical information consisting of the local data at the ONU and the previously received GATE messages from the OLT. Through simulations, we show that DC-PGO enhances the performance of multi-threaded polling in longreach Ethernet PON when packets of differentiated service classes arrive with pre-specified delay requirements.