Networks such as LTE-M, NB-IoT, LoRa and SigFox are being deployed for massive IoT communications. However, the Aloha protocols used for the media access are inefficient when the network size is high. As a result, a Distributed Queuing (DQ) algorithm is being proposed to replace the conventional access schemes because of its superior network performance. In this paper, we study the algorithm with no prior consideration of any underlying technology at the physical layer. We perform a steady-state analysis of the algorithm in a network where the traffic is composed of periodic and urgent packets. It was found that for high traffic from the network all the nodes were taking part in each contention. Nevertheless, for better performance in terms of access delay and packet drop rate, it was preferable to operate the algorithm in the small traffic interval. Moreover, the downlink traffic has been observed to have a significant impact on the stability of the algorithm.