A method for reducing output traffic bursts in a streaming media cache includes receiving a request from a first client system for a stream of media data, the stream of media data including a first streaming media data packet and a second streaming media data packet, receiving a request from a second client system for the stream of media data, receiving the first streaming media data packet from an upstream server, the first streaming media data packet including a delivery time, determining a first modified delivery time for the first streaming media data packet, determining a second modified delivery time for the first streaming media data packet, the first modified delivery time different from the second modified delivery time, modifying the first streaming media data packet with the first modified delivery time to form a first modified first streaming media data packet, modifying the first streaming media data packet with the second modified delivery time to form a second modified first streaming media data packet, outputting the first modified first streaming media data packet to the first client system at the first modified delivery time, and outputting the second modified first streaming media data packet to the second client system at the second modified delivery time.