Optimally scheduling video-on-demand to minimize delay when server and receiver bandwidth may differ
William Evans, David G. Kirkpatrick · 2004
Abstract We establish tight bounds on the intrinsic cost (eitherminimizing delay d for fixed server and receiver band-widths, or minimizing server bandwidth for fixed delay and receiver bandwidth) of broadcasting a movie oflength m over a channel of bandwidth S in such a waythat a receiver (with bandwidth R), starting at an ar-bitrary time t, can download the movie so that it canbegin playback after a delay of at most d time units.Our bounds are realized by a simple abstract protocol that partitions the movie into a fixed numberof segments, partitions the server bandwidth into an equivalent number of equal bandwidth subchannels, andbroadcasts each segment repeatedly on its own subchannel. This protocol can be implemented as a concrete dis-crete protocol in which movie information is packaged into discrete fixed length packets using only a modestoverhead (measured in terms of increased delay or server bandwidth).Our primary contribution is a lower bound on the required delay that applies in a very general modelof communication. This lower bound matches the behaviour of our abstract protocol in the limit as thenumber of segments approaches infinity. We are also able to relate its behaviour to arbitrary protocols thathave a fixed number of segments. 1 Introduction Suppose we broadcast a movie using bandwidth S(measured in units of movie bandwidth). A person may tune their television, which can receive any R/S fractionof the bandwidth, to this channel at any time in order to watch the movie. We would like to minimize the delaybetween when they tune to the channel and when they can start watching the movie. Let m be the length of themovie (in minutes). We can certainly guarantee a delay of at most m minutes simply by repeatedly broadcastingthe movie back-to-back (as long as