The wireless LAN (WLAN) system based on IEEE802.11 uses multiple transmission rates to obtain improved communication quality according to the communication environment. Furthermore, the range of use of wireless LAN is rapidly expanding in daily life, and it has become an important infrastructure for safe and secure life. However, because the dynamic change in transmission rate depends on variation in the communication environment, it is difficult to implement this transmission rate model in typical simulators, making it impossible to sufficiently simulate the real environment using the existing transmission rate model. To address this issue, this study first evaluates the characteristics of transmission rate over the multi-rate environment using real machines. We then propose a transmission rate model for the multi-rate environment based on the experimental results. In this study, we show a transmission rate model using an advection-diffusion equation. Note that there is an effort to use Wi-Fi systems at the time of disaster. Our proposed model is useful for the design and the operation of such Wi-Fi systems. Next, our simulation results confirm that the proposed transmission rate model can replicate the performance achieved in the actual environment.