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Access networks contribute a significant portion of the energy consumption of the telecom network. In this study, the authors propose a distributed bandwidth allocation signalling framework for a green hybrid Fibre-Wireless (Fi-Wi) access network, which is based on the convergence of ethernet passive optical network and third-generation partnership project-long-term evolution-advanced technologies. According to the proposed framework, the Fi-Wi network is deployed by pairing joint optical network unit-base station (ONU-BS) nodes. An ONU-BS that is experiencing light load from the end-users sends a SLEEP signal to the optical line terminal (OLT), and switches to the stand-by mode whereas its BS module forwards the traffic to the peer ONU-BS. The peer ONU-BS keeps buffering the requests destined to the sleeping ONU-BS, and sends REPORTs for the corresponding packets to the OLT. Through simulations, the authors generate various traffic profiles, and show that the proposed framework provides significant amount of energy savings at the ONUs when compared with regular operation mode. Furthermore, the simulation results also show that average packet delay and average packet loss do not increase significantly by utilising the active ONU-BS devices whereas their corresponding peers are sleeping.