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Overlay multicast has been proposed for implementing multicast routing in the application layer as a practical alternative to IP multicast. A technical challenge for overlay multicast is that the dynamic multicast members can make data delivery unreliable. In this paper, we focus this issue in the context of live media streaming by exploring how to construct a stable multicast tree that minimizes the negative effect of frequent member departures on an overlay tree. For the problem, we study two layout for the tree nodes, namely, the bandwidth-ordered tree and the time-ordered tree. We propose a distributed switching tree algorithm that minimizes the failure effect among tree nodes and conduct a stochastic analysis on their properties regarding reliability and tree depth.