This work investigates void filling (idle periods) in long-reach Ethernet passive optical networks. We focus on reducing grant delays and hence reducing the average packet delay. We introduce a novel approach called parallel void thread (PVT), which allocates bandwidth grants during voids baseless of bandwidth requests. We introduce three different grant sizing schemes for PVT, namely void extension, count controlled batch void filling, and size controlled batch void filling. The proposed approaches canbe integrated with almost all of the previously reported dynamic bandwidth allocation schemes. Unlike other void filling schemes, PVT is less sensitive to the differential distance between optical network units and can work very well in the case of limited differential distances. We have analytically investigated the packet delay and derived a bound condition for PVT to outperform the other competitors. We support our work with extensive simulation study considering bursty traffic with long range dependence for both the single-class and differentiated services (DiffServ) scenarios. Numerical results show delay reduction up to 35% compared with the non-void filling scheme for the single-class scenario. For DiffServ traffic, PVT achieves delay reduction up to 80% for expedited forward traffic, 52% for assured forward traffic, and 56% for best effort traffic. © 2015 OSA.