Relay-based cooperative wireless networks have been widely considered one of the cost-effective solutions to meet the demands in future wireless networks. In order to maximize the overall sum-rate while maintaining proportional fairness among users, we investigate different resource allocation algorithms in two-way relay networks with analog network coding (ANC) protocol and time division broadcast (TDBC) protocol. The algorithms investigated are different from traditional proportional fairness schemes in terms of fairness and computational complexity as we have applied Access Proportional Fairness (APF) and Minimum Rate Proportional Fairness (MRPF) along with load balancing at the relays. A MATLAB simulation has been performed and simulation results show the effectiveness of these algorithms.