We propose a novel stochastic radio-resource-allocation strategy that achieves long-term fairness considering backhaul and air-interface capacity limitations. The base station (BS) is powered only with a finite battery that is recharged by an energy harvester. The energy harvesting is also taken into account in the proposed resource-allocation strategy. The constrained scenario is often found in remote rural areas where the backhaul connection is limited, and the BSs are fed with solar panels of reduced size. Our results show that the proposed scheme achieves higher fairness among the users and provides greater worst user rate and sum rate if an average backhaul constraint is considered.