The rapid growth of wireless LAN-enabled devices over recent years has generated a successful framework for wireless data accessing. It seems viable to expand the framework as part of last mile solution for mobile users to access data services. Therefore, in this paper, we further focus on Quality of Service (QoS) and timeliness issues for supporting advanced multimedia applications in such environments. A bridging model, named Q-Bridge, is proposed in the paper for layer-2 access points to exhibiting QoS and real-time packet scheduling capabilities in the last mile configuration. The model explicitly applies the imprecise computation technique. That is, each bridged packet can be logically divided into two portions: a mandatory portion and an optional portion. The mandatory portions must be scheduled to transmit by their deadlines while the optional portions can be chopped to meet their deadlines or QoS requirements. By taking advantage of this model and the scheduling algorithms we devised, wireless data services can benefit from QoS and timeliness guarantees provided by access points supporting Q-Bridge at the last mile.