IoT gateways aim to meet the deadlines and QoS needs of packets from as many IoT devices as possible, though this can lead to a form of congestion known as the Massive Access Problem (MAP). While much work was conducted on predictive or reactive scheduling schemes to match the arrival process of packets to the service capabilities of IoT gateways, such schemes may use substantial computation and communication between gateways and IoT devices. This paper proves that the recently proposed “Quasi-Deterministic-Transmission-Policy (QDTP)” traffic shaping approach which delays packets at IoT devices, substantially alleviates the MAP: QDTP does not increase overall end-to-end delay and reduces gateway queue length. We then introduce the Adaptive Non-Deterministic Transmission Policy (ANTP) that requires only one packet buffer at the gateway, offering substantial QoS improvement over FIFO scheduling.