The decoding time is neglected for two reasons. First, this gives a tighter bound. Second, as decoding and playing are pipelined in most players, rendering will start immediately af- ter the first few frames are decoded, which takes a very short time. If we use D ch to denote the play duration of each chunk and T r i,j to denote the time at which the AP receives the re- quest for chunk j from client i, then for j > 1 we can get