This paper aims at designing a congestion and priority solution for Ethernet congestion management. Following the popular approach that uses a cooperation of an Additive Increase and Multiplicative Decrease (AIMD) based rate limiter and Explicit Congestion Notification (ECN) active queue management to combat congestions in Ethernet, the proposal considers differentiated AIMD settings for rate limiters to achieve congestion control differentiation for traffic of different priorities. We illustrate that while the operations of AIMD and ECN are independent, by using different AIMD settings, we can achieve differentiated control of bandwidth utilization. We develop a control theoretic analytical model to study the effectiveness of our proposed method. Moreover, we implement our proposed method in OMNET++ simulator to conduct simulation experiments. Our analytical and simulation results both indicate the effectiveness of bandwidth ratio differentiation.