In multi-hop wireless mesh networks, the end-to-end throughput decays exponentially with the increase in hop counts. This is mainly due to the increase in successive spatial contentions. As a result, flows with longer hops suffer from bandwidth starvation and fair link access disparities along the path towards the gateway. In this paper, we first develop a theoretical reference model that can be used to measure throughput disparities among contending flows. Second, we introduce a fair access rate (FAR) algorithm, based on the end-to-end blocking probabilities of contending flows, that will offset throughput disparities. Finally, we simulate FAR over a set of 802.11s-based network topologies with different aggregate blocking probabilities. The performance of FAR, in terms of its throughput and fairness index, has been evaluated and compared with the performance of the default algorithm used in 802.11s.