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Wireless local area networks (WLANs) have risen in popularity for in-car networking systems that are designed to make driving safer. Wireless mesh networks (WMNs) are widely deployed to expand the coverage of high-speed WLANs and to support last-mile connectivity for mobile users anytime and anywhere at low cost. Many recent measurement studies have shown that the traffic arrival process in wireless networks exhibits the bursty and correlated nature. A new analytical model is developed in this paper as a cost-effective performance tool to investigate the quality-of-service (QoS) of the WMN that interconnects multiple WLANs in the presence of bursty and correlated traffic. After validating its accuracy via extensive simulation experiments, the analytical model is then used to investigate the performance of the hybrid wireless networks.