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Video on demand (VoD) is one of the most important services for many network operators that deploy and operate optical access networks. It is crucial to design next generation optical access networks that can guarantee a high quality VoD service. In this paper, we address this challenging issue and focus on the worst-case playback delay (WPD), which cannot be guaranteed by Internet-based video streaming, and has not been well addressed previously in optical access networks. Specifically, we first propose an integrated Gigabit Passive Optical Network (GPON) and Wavelength Division Multiplexing PON (WDM PON) architecture. With the proposed architecture, an optical line terminal (OLT) can broadcast popular videos through GPON and deliver other videos through WDM-PON, while the optical network units (ONUs) can conduct patching for their end users. We then elaborate on two minimum-WPD schemes. In the first one, we assume that the video broadcast schedule is fixed at the OLT and develop an optimal patching scheme at each ONU such that the WPD is minimized. In the second one, we consider coordinated OLT broadcast scheduling and ONU patching. A heuristic algorithm which can achieve near-optimal WPD is proposed for coordinated OLT broadcast scheduling and ONU patching. Simulation results confirm the superiority of the proposed schemes over the existing ones in terms of both worstcase and average delay performance.