The asymptotics of cell loss ratio (CLR) in the regime of large bu!ers 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 tra$c process is self-similar), the CLR decreases with the bu!er size sub-exponentially, and the two parameters are no longer adequate to capture this phenomenon. Recent results from the literature show that for self-similar tra$c 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 bu!er 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 tra$c other than the asymptotic behaviour of the CLR. We describe how our method can be applied to VP bandwidth control by using results from simulation experiments.If the actual cell loss performance of an ATM output bu!er could be determined in real time, the rate of the server (that is, the VP bandwidth) could be adjusted such that the cell loss would be smaller than a pre-determined threshold. In Reference 6, Shioda and Saito presented a method for estimating the cell loss ratio in real time, and applied it to VP bandwidth estimation and call admission control. They utilized the large deviation result of Glynn and Whitt, that the CLR decays exponentially as the bu!er size increases. In this case the CLR (in the regime of large bu!ers) is characterized by two parameters, the so-called asymptotic constant and the asymptotic decay rate . As a result, an algorithm for estimating these coe$cients on an on-line basis from the bu!er measurement was proposed.The objective of this paper is to develop an algorithm (by reformulating the method proposed in Reference 6) for real-time VP bandwidth estimation, which works also in the case of longrange-dependent tra$c.The inherent correlations of a long-range-dependent stochastic process decay hiperbolically as the lag increases. As a result, the autocorrelation function is non-summable. This non-summability captures the intuition behind long-range dependence, namely, that while high-lag correlations are all individually small, the cumulative e!ect is of importance and gives rise to features which are drastically di!erent from those of the more conventional, i.e. short-range-dependent processes. The latter are characterized by an exponential decay of the correlations, resulting in a summable autocorrelation function.For long-range-dependent tra$c, the asymptotics for the queue length distributions are no longer exponential. Du$eld and O'Connell generalized the results o...