Real-time cell loss ratio estimation and its applications to ATM traffic controls

The asymptotics of cell-loss ratio (CLR) in the regime of large buffers are characterized by two parameters, the asymptotic constant and asymptotic decay rate. Both parameters can be expanded in powers of one minus the link utilization (heavy traffic expansion). Thus, once the coefficients in this expansion are obtained, the CLR can be very easily estimated from the measured link utilization by using CLR asymptotics. This paper proposes an algorithm for estimating these coefficients in real time. For this purpose, the notion of state-space representation for a single-server queue is introduced: the elements of the state vector are the coefficients in the expansion of the asymptotic constant and asymptotic decay rate. Bayesian regression analysis is applied to estimate the state vector based on the buffer measurement. Our approach does not require any models describing the statistics of the traffic other than the asymptotic behavior of the CLR in the regime of large buffers. In addition, it allows us to estimate the effective bandwidth of the aggregated process easily, so it is applicable to a wide range of ATM traffic control methods, such as connection admission control and VP bandwidth control. We describe how this method of CLR estimation will be applied to connection admission control and VP bandwidth control by using results from simulation experiments.