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Wireless mesh networks (WMNs) have attracted increasing attention from the research community as a high-performance and low-cost solution to last-mile broadband Internet access. In WMNs, admission control is deployed to efficiently control different traffic loads and prevent the network from being overloaded. This paper introduces a distributed admission control scheme for WMNs, namely, routing on cliques admission control (RCAC). In particular, we propose an analytical model to compute the appropriate acceptance ratio and guarantee that the packet loss probability (PLP) in the network does not exceed a threshold value. The model also allows computing end-to-end delay to process flow requests with delay constraints. RCAC achieves scalability since it partitions the network into cliques, and only clique heads (CHs) are involved in the admission-control procedure. Using extensive simulations, we demonstrate that our RCAC achieves high resource utilization by providing lower blocking probabilities in a dynamic traffic-load environment while satisfying quality-of-service (QoS) constraints in terms of PLP and end-to-end delay. Moreover, we show that a contention access (CA) enforced with our RCAC outperforms the mesh deterministic access (MDA).