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The multi-access scheme of 802.11 wireless networks imposes difficulties in achieving predictable service quality in multi-hop networks. In such networks, the residual capacity of wireless links should be estimated for resource allocation services such as flow admission control. In this paper, we propose an accurate and non-intrusive method to estimate the residual bandwidth of an 802.11 link. Inputs from neighboring network activity measurements and from a basic collision detection mechanism are fed to the analytical model so that the proposed algorithm calculates the maximum allowable traffic level for this link. We evaluate the efficiency of the method via OPNET simulations, and show that the percent estimation error is significantly lower than two other prominent estimation methods, bounded only between 2.5-7.5%. We also demonstrate that flow admission control is successfully achieved in a realistic WMN scenario. Flow control through our proposed algorithm keeps the unsatisfied traffic demand bounded and at a negligibly low level, which is less than an order of magnitude of the other two methods.