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Periodic broadcast protocols enable efficient streaming of highly popular media files to large numbers of concurrent clients. Most previous periodic broadcast protocols, however, assume that all clients can receive at the same rate, and also assume that reception bandwidth is not time-varying. In this article, we first develop a new periodic broadcast protocol, Optimized Heterogeneous Periodic Broadcast (OHPB), that can be optimized for a given population of clients with heterogeneous reception bandwidths and quality-of-service requirements. The OHPB protocol utilizes an optimized segment size progression determined by solving a linear optimization model that takes as input the client population characteristics and an objective function such as mean client startup delay. We then develop a generalization of the OHPB linear optimization model that allows optimal server bandwidth allocation among multiple concurrent OHPB broadcasts, wherein each media file and its clients may have different characteristics. Finally, we propose complementary client protocols employing work-ahead buffering of data during playback, so as to enable more uniform playback quality when the reception bandwidth is time-varying.