Network-on-Chip (NoC) is a preferred communication medium for massively parallel platforms. Fixed-priority based scheduling using virtual-channels is one of the promising solutions to support real-time traffic in on-chip networks. Most of the existing works regarding priority-based NoCs use a flit-level preemptive scheduling. Under such a mechanism, preemptions can only happen between the transmissions of successive flits but not during the transmission of a single flit. In this paper, we present a modified framework where the non-preemptive region of each NoC packet increases from a single flit. Using the proposed approach, the response times of certain traffic flows can be reduced, which can thus improve the schedulability of the whole network. As a result, the utilization of NoCs can be improved by admitting more real-time traffic. Schedulability tests regarding the proposed framework are presented along with the proof of the correctness. Additionally, we also propose a path modification approach on top of the non-preemptive region based method to further improve schedulability. A number of experiments have been performed to evaluate the proposed solutions, where we can observe significant improvement on schedulability compared to the original flit-level preemptive NoCs.This work is an extended version of the paper presented at RTCSA 2016 (Liu et al. 2016).