Optical and wireless technology integration has been proposed as one of the most promising nominees for the next-generation broadband access networks for quite some time. Integration scheme merges the high-speed and high-capacity of the optical networks with the low-cost, wide-coverage and mobility features of the wireless counterparts for the Subscriber Stations (SSs). It is also financially viable for the telecommunication service providers, particularly in the rural area where the development of optical infrastructure or expansion of the existing telecommunication solutions such as Digital Subscriber Line (DSL), Cable Modem (CM) or T-1/E-1 networks are either too costly or unreachable. In order to successfully integrate the two technologies, there are some technical concerns in terms of Architectural aspects, Physical Layer features and Media Access Control (MAC) related issues, which need to be addressed efficiently in order to provide the smooth end-to-end (e2e) integration. This paper is mainly focused upon the analysis of the key topics in MAC-related issues such as E2E wavelength/bandwidth requests and allocations over the converged scenario. It proposes an Inter-channel and Intra-channel Dynamic Wavelength/Bandwidth Allocation (IIDWBA) algorithm where the hybrid Passive Optical Network (PON) acts as a back haul technology for the wireless counterpart. The proposed algorithm works in three phases, namely, Initialisation, Intra-channel bandwidth allocations and Inter-channel bandwidth allocations and is capable of allocating wavelength/bandwidth efficiently and effectively over the converged scenario. Performance of the proposed algorithm is evaluated through conducted simulation scenarios under different simulation parameters, traffic patterns and load values. According to the captured results, IIDWBA algorithm shows a better performance when it is compared to the scenario in which it has not been employed.