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Receiver adaptation layered multicast video has been proposed to address the issue of network bandwidth heterogeneity in multiparty video communication over networks. An important issue in this approach is how to conduct layer adaptation to achieve the "optimal level" of subscription to maximize the perceived video quality at receivers while utilizing bandwidth efficiently. In the paper, optimal layers are typically determined by congestion signals fed back from networks. This approach implies that instantaneous congestion is a key parameter; however, in random traffic, such an implication somewhat under-estimates other parameters. In order to investigate the performance of "layer adaptation" in random traffic for improving the network based multi party video communication system, in this paper we present an analytical studying of the issue of receiver layer adaptation for layered video transmission. In this work, we use the notion of congestion probability as a partial and indirect measure of the perceived layered video quality at a receiver. The system's efficiency under a given receiver layer adaptation scheme is also defined and used as a metric to study the performance of a receiver layer adaptation scheme. Through the analysis, we determine the optimal receiver layer adaptation scheme, which maximizes the system efficiency while providing best sustainable video quality to a receiver. We show that the greedy receiver layer adaptation scheme is indeed optimal if the traffic generated by various layers of a layered video as well as the cross traffic are constant. However, in a more realistic setting where layered video traffic or the cross traffic varies over the time, the greedy receiver layer adaptation scheme is in general not optimal. To verify our theory, we conduct simulations.