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The provision of very high data rates in a ubiquitous and fair manner throughout the service area is a great challenge for 4G and beyond-4G wireless networks. Towards that end, the deployment of fixed relays by the operators has become an accepted radio access network concept in various standardization activities including LTE-A and 802.16m. In this paper, we present a fair resource allocation scheme that can significantly reduce the co-channel interference and improve spectrum utilization in OFDMA-based multi-cellular networks enhanced by fixed relays. The major goal is to obtain an effective throughput-fairness trade-off through the combination of dynamic resource allocation, in-cell routing, traffic diversity, and history of users' past service. The proposed scheme achieves substantial fairness, throughput, and latency improvements in comparison to the reference schemes as well as to another scheme proposed, earlier by the authors. Numerical results indicate that the proposed scheme provides an almost ubiquitous high-data-rate service to users, irrespective of their locations (including cell-edge users), with a minimal sacrifice in the overall network throughput.