Smart home gateway has to process different types of network traffic generated from several devices in an optimal way to meet their Quality-of-Service (QoS) requirements. However, the fluctuation of network traffic distributions results in packets concurrency. Current QoS-aware scheduling methods in smart home networks do not consider concurrent traffic in their scheduling solutions. This article 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 traffic in smart home network, propose an innovative queuing design based on the auction economic model of the game theory to provide a fair multiple access over different communication channels/ports, and design an applicable model to implement auction game on both sides; traffic sources and the home gateway, without changing the structure of the IEEE 802.11 standard. 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.