Smart home gateway has to process different types of network traffic generated from several devices in an optimal way to meet their QoS requirements. However, the fluctuation of network traffic distributions results in packets concurrency. Current QoS-aware scheduling methods in the smart home networks do not consider concurrent traffic in their scheduling solutions. This paper presents an analytic model for a QoS-aware scheduling optimization of concurrent smart home network traffic with mixed arrival distributions and using probabilistic queuing disciplines. We formulate a hybrid QoS-aware scheduling problem for concurrent traffics in smart home network, and propose an innovative queuing design based on the auction economic model of game theory to provide a fair multiple access over different communication channels/ports. Our experiments show the proposed solution achieves an improvement of 14% of packets that meet their required delay and 57% of delay for different number of concurrent flows in the system.