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Recent advances in scalable video coding have paved the way for the development of flexible and adaptive media streaming applications. In order to support rate adaptation, 3GPP Packet-Switched Streaming Service (PSS) has specified a feedback mechanism that includes transmitting information about the status of the client buffer. This paper presents a novel Multiple Virtual Client Buffer Feedback (MVCBF) mechanism, which includes information about multiple media times each of which corresponding to a different set of sub-streams in scalable media streaming. Moreover, a new rate adaptation method is presented that a) assigns different requirements for the buffering time to the different sets of sub-streams, b) observes the media time variation at sub-stream level, and c) efficiently changes the operation point to maintain the required buffering time in priority order. Simulation results show that the proposed MVCBF-based rate adaptation algorithm outperforms the traditional PSS compliant rate adaptation method in the overall throughput by quickly adapting the operation point to the varying network resources and avoiding unnecessary bouncing between operation points.