Minimizing Average Startup Delay of Periodic VOD Broadcasting Schedules

Consider a video consisting of a sequence of fixedsize pages to be transmitted over c broadcast channels such that a page fits in a slot of a channel. In Shifted Harmonic Windows scheduling, page i must be scheduled at least once in any consecutive i+m−1 slots for some integer m ≥ 1, to ensure continuous display of successive pages by the viewer, starting at the m slot boundary after tuning in. As m is increased, the maximum startup delay for Shifted Harmonic Windows schedules approaches the well-known general lower bound on the maximum startup delay, 1/(e − 1). We first derive a tight lower bound, which is lower than 1/(e − 1), on the average startup delay of periodic schedules. This settles one of the longstanding open problems about the optimal average performance of periodic broadcasting schedules. We then show that the average startup delay of Shifted Harmonic Windows schedules cannot approach this lower bound. Using a new framework called Harmonic Block Windows scheduling with a parameter b (≥ 1), we present a scheduling algorithm which generates schedules whose average startup delays approach the lower bound as b is increased. EDICS: 5-STRM