Hybrid optical and wireless technology integrations have been considered as one of the most promising candidates for the next generation broadband access networks for quite some time. The integration scheme provides the bandwidth advantages of the optical networks and mobility features of the wireless networks for Subscriber Stations (SSs). It also brings economic efficiency to the network providers particularly in rural area where the existing wired telecommunication infrastructures such as Digital Subscriber Line (DSL), Cable Modem (CM), T-l/E-I networks or fibre deployments are either costly or unreachable. For successful integration of the optical and wireless technologies there are some technical issues which need to be addressed efficiently in order to provide End-to-End (ETE) and diverse Quality of Service (QoS) for various service classes. This paper investigates the possible challenging issues for the integrated structure of the Time Division Multiplexing and Wavelength Division Multiplexing Ethernet Passive Optical Networks (TDM EPON and WDM EPON) with the Worldwide Interoperability for Microwave Access and Wireless Fidelity (WiMAX and Wi-Fi) networks. To reduce the ETE delay and provide the QoS for diverse service classes, we have compared six existing upstream scheduling mechanisms in two levels which are distributed on Access Points (APs) from Wi-Fi domain and Base Stations (BSs) from WiMAX domain. Performance evaluations of the existing scheduling techniques for three popular service classes (Quad-play) have been studied which show the strong impact of using the efficient up-link scheduler in converged scenario. We have also proposed a dynamic scheduling algorithm for optical and wireless integration scheme, which is under the implementation and evaluation process.