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With the proliferation of multicast service in the Internet, much attention has been put upon multicast congest control. Multicast traffic poses new challenges to the design of Internet congestion control protocols and system stability analysis. In this paper, we focus on the feedback-based sessions rate control problem on the combination of unicast and multirate multicast traffic architecture networks. Firstly, fairness problem is discussed in detail and reasonable consumption strategy is proposed. Scaling functions are adaptively adjusted based on relationship of session rates. Secondly, in the case of link capacities available for feedback-based unicast and multicast sessions, stability analysis of closed loop system under the modified rate mechanism is made based on Lyapunov stable theory. Finally, the simulations demonstrate the effectiveness and goodness of reasonable consumption strategy.