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This paper addresses the problem of the transmission of scalable video streams to a set of heterogeneous clients through a common bottleneck channel. The packet scheduling policy is typically crucial in such systems that target smooth media playback at all the receivers. In particular, the playback delays and the transmission strategy for the packets of the different layers have to be chosen carefully. When the same video is sent simultaneously to multiple clients that subscribe to different parts of the stream, the playback delay cannot be jointly minimized for all the clients. We therefore propose delay optimization strategies along with low complexity solutions for a fair distribution of the delay penalty among the different receivers. Once the delays are selected, we show that there exists a unique scheduling solution that minimizes the buffer occupancy at all the receivers. We derive an algorithm for computing the optimal sending trace, and we show that optimal scheduling has to respect the order of the packets in each media layer. Interestingly enough, solving both delay and buffer optimization problems sequentially leads to a jointly optimal solution when the channel is known. We finally propose a simple rate adaptation mechanism that copes with unexpected channel bandwidth variations by controlling the sending rate and dropping layers when the bandwidth becomes insufficient. Experimental results shows that it permits to reach close to optimal performances even if the channel knowledge is reduced. Rate adaptation provides an interesting alternative to conservative scheduling strategies, providing minor and controllable quality variations, but with a higher resulting average quality.