Optimal smoothing for guaranteed service

We consider the transmission of variable bit rate (VBR) video over a networ k offering a guaranteed service such as ATM VER or the guaranteed service o f the IETF, The guaranteed service requires that the flow accepted by the n etwork has to be conforming with a traffic envelope sigma; in return, it re ceives a service guarantee expressed by a network service curve beta, Funct ions sigma and beta are derived from the parameters used for setting up the reservation, for example, from the T-SPEC and R-SPEC fields used with the resource reservation protocol (RSVP), In order to satisfy the traffic envel ope constraint, the output of the encoder is fed to a smoother, possibly wi th some look-ahead, The resulting stream is transported by the network; at the destination, the decoder waits for an initial playback delay and reads the stream from the receive buffer. We consider the problem of whether ther e exists one optimal strategy at the smoother which minimizes the playback delay and the receive buffer size, given the traffic envelope sigma and the service curve beta, We show that there does exist such an optimal smoothin g, and give an explicit representation for it. We also obtain a simple expr ession for the smallest playback delay and playback buffer size which dan b e achieved over all possible smoothing and playback strategies, We show tha t the computation of optimal smoothing and minimum playback delay do not de pend on the past, We show that separate delay equalization is optimal in th e constant bit rate (CBR) case, but not otherwise. We also apply the theory to the analysis of which T-SPEC should be requested by a source-destinatio n pair, given some playback delay and buffer constraint, and given the path characteristics advertised in RSVP PATH messages.