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Supporting real-time multimedia communication over multi-hop wireless mesh networks is a challenging problem, considering the necessity of intelligent allocation of shared wireless medium amongst different nodes within the network while ensuring the desired level of quality of service (QoS). Many existing cross-layer design approaches that are aiming for an integrated operation of the different protocol layers often either not consider the network functions as a whole or rely on mechanisms that provide global network information. There is certainly a need for developing distributed and scalable algorithms for optimal utilization of system resources and providing the end-to-end QoS. In this paper, we utilize the general network utility maximization (GNUM) framework that tackles the cross-layer design problem in a systematic manner. More specifically by incorporating contention based IEEE 802.11 MAC protocol, we developed an optimal joint congestion-contention control scheme that maximize network throughput while at the same time providing end-to-end QoS for multimedia traffic. The proposed algorithm distributedly calculates the optimal solution by means of exchanging prices between the source and the network links, and hence fully scalable to large networks. Our results reveal the tradeoffs between QoS requirement and rate allocation, and ultimately provide guidelines for how the medium access and transport layer parameters should be selected in order to guarantee QoS for the application. The proposed algorithm can be easily generalized into other multi-hop wireless ad hoc networks.