Methods and systems for processing streams of media data. The system may allow for the demultiplexing (110) of a multiple multi-program transport stream ("MPTS") into a single program transport stream ("SPTS"). The system also provides a data structure for storing a program that facilities the rapid positioning at a desired time within the program during playback. In addition, the system when recording a program time processes time discontinuities so that positioning based on time during playback can occur rapidly. The system also allows a live television broadcast to be paused indefinitely in way that will not use up all system storage and will allow the most recent broadcast to be available for playback.