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The task of estimating path available bandwidth is difficult but paramount for QoS routing in supporting bandwidth-demanding traffic in multirate and multihop wireless ad hoc networks. The multirate capability and the impact of background traffic has not been carefully studied for the problem of estimating path available bandwidth in prior works. In this paper, we develop a theoretical model for estimating the available bandwidth of a path by considering interference from both background traffic and traffic along the path. We show that the clique constraint widely used to construct upper bounds does not hold any more when links are allowed to use different rates at different time. In our proposed model, traditional clique is coupled with rate vector to more properly characterize the conflicting relationships among links in wireless ad hoc networks where time-varying link adaption is used. Based on this model, we also investigate the problem of joint optimization of QoS routing and link scheduling. Several routing metrics and a heuristic algorithm are proposed. The newly proposed conservative clique constraint performs the best among the studied metrics in estimating available bandwidth of flows with background traffic.