Integration of Ethernet passive optical network (EPON) and WiMAX technologies is viewed as a great solution for next-generation broadband access networks. In the systems adopting this strategy, weighty bandwidth allocation schemes are fundamental to fulfil the quality of service (QoS) and fairness requirements of different traffic classes. Existing proposals to overcome the bandwidth allocation problem in EPON/WiMAX networks dismiss collaboration between the self-interested EPON and WiMAX service providers (WSPs). This study presents a novel EPON-based semi-dynamic bandwidth allocation (S-DBA) method that shows points of interest in the integration process. In the proposed algorithm depending on the auction process, the optical line terminal runs an auction to adequately post the optical network unit bandwidth that distributes the most elevated bidders based on the measurement of the accessible bandwidth. Simulation results demonstrate massive upgrades compared with fair sharing using dual-service-level agreements, `limited service' interleaved polling with adaptive cycle time methods, bandwidth allocation strategy using Stackelberg game, and bandwidth allocation strategy using coalition game regarding the quality of service parameters such as throughput and time delay. This will be extremely helpful for optical system upgrading and improvement with minimal effort.