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Along with the rapid development and deployment of real-time wireless network (RTWN) technologies in a wide range of applications, effective packet scheduling algorithms have been playing a critical role in RTWNs for achieving desired Quality of Service (QoS) for real-time sensing and control, especially in the presence of unexpected disturbances. Most existing solutions in the literature focus either on static or dynamic schedule construction to meet the desired QoS requirements, but have a common assumption that all wireless links are reliable. Although this assumption simplifies the algorithm design and analysis, it is not realistic in real-life settings. To address this drawback, this paper introduces a novel reliable dynamic packet scheduling framework, called RD-PaS. RD-PaS can not only construct static schedules to meet both the timing and reliability requirements of end-to-end packet transmissions in RTWNs for a given periodic network traffic pattern, but also construct new schedules rapidly to handle abruptly increased network traffic induced by unexpected disturbances while minimizing the impact on existing network flows. The functional correctness of the RD-PaS framework has been validated through its implementation and deployment on a real-life RTWN testbed. Extensive simulation-based experiments have also been performed to evaluate the effectiveness of RD-PaS, especially in large-scale network settings.