Understanding the end-to-end packet delay dynamics of the Internet is of crucial importance since it directly affects the QoS (Quality of Services) of various applications, and it enables us to design an efficient congestion control mechanism. In our previous studies, we have measured round-trip time of the Internet, and have modeled its dynamics by the ARX (Auto-Regressive eXogenous) model using system identification. As input and output data for the ARX model, we have used the packet inter-departure time from a source host and the corresponding round-trip time variation measured by the source host. In the current paper, for improving the model accuracy, we instead use the packet transmission rate from the source host and the average round-trip time measured by the source host. Using input and output data measured in working LAN and WAN environments, we model the round-trip time dynamics by determining coefficients of the ARX model using system identification. Through numerical examples, we show that in LAN environment, the round-trip time dynamics can be accurately modeled by the ARX model. We also show that in WAN environment, the round-trip time dynamics can be accurately modeled when the bottleneck link is shared by a small number of users.