Extremal shape-controlled traffic patterns in high-speed networks

We consider a variable bit-rate connection with a deterministically shaped random traffic process, as specified by communications networking standards . Regarding randomness, we assume no restricted model other than the natura l requirement that the process be stationary and ergodic, Given only the sh ape parameters, we consider the open problem of determining the maximum ser vice bandwidth required to achieve a given bound on the probability that th e packet-transfer delay exceeds a certain threshold. The shape parameters t ogether with a probabilistic bound on packet-transfer delay define a variab le bit-rate "channel;" an equivalent problem is to determine the "capacity" of this channel. To this end, we consider a queue with a constant service rate and a shaped arrival process and obtain tight bounds on queue occupanc y and queueing delay. In particular, we describe that traffic pattern (amon g all stationary-ergodic and deterministically constrained arrival processe s) which achieves the probabilistic bound.