Congestion is one of the main problems in networks such as the internet that has been studied by many researchers. Since the fast development in computer networks and the increase of demands on network resources such as bandwidth allocation and buffer spaces, congestion control becomes a crucial task. In this paper, we introduce a dynamic random early drop (DRED) discrete-time queue analytical model to deal with network congestion incipiently. We compare the proposed analytical model with the original DRED algorithm with reference to packet loss probability, average queue length, throughput, and average queuing delay. The experimental results clearly show that when the traffic load increases, DRED router buffer drops packets on a higher rate than the proposed analytical model, which consequently degrades the throughput performance. Furthermore, the packet loss rate for the proposed analytical model is often stable is not affected with the increase of the traffic loads, and thus stabilise the throughput performance.