The asymptotics of cell loss ratio (CLR) in the regime of large buffers are exponential and can be characterized by two parameters, the asymptotic constant and asymptotic decay rate. This result is very general, provided that the arrival process does not possess long-range dependence. As for the long-range dependent case (or equivalently, when the increment of the traffic process is self-similar), the CLR decreases with the buffer size sub-exponentially, and the two parameters are no longer adequate to capture this phenomenon. Recent results from the literature show that for self-similar traffic models the tail of the stationary queue length distribution is Weibullian. Using these results, this paper proposes an algorithm for estimating the CLR in real time based on buffer measurements, which works for both the long-range- and the short-range-dependent case. For this purpose, the notion of state-space representation of a single-server queue is introduced, and Bayesian regression analysis is applied to estimate the state variable of that system. Our approach does not require any models describing the statistics of the traffic other than the asymptotic behaviour of the CLR. We describe how our method can be applied to VP bandwidth control by using results from simulation experiments. Copyright © 1999 John Wiley & Sons, Ltd.