Evaluating the queue distribution of an ATM multiplexer with multiple time scale arrivals

For an ATM multiplexer we develop a recursive asymptotic expansion method for approximating the queue length distribution and investigate the radius of convergence of the queue asymptotic expansion series. The analysis focuses on "small" to "moderate" buffer sizes under the conditions of strictly stable multiple time scale arrivals. For a class of examples we analytically determine the radius of convergence using methods of linear operator theory. We also give general sufficient conditions under which the radius converges to zero; this shows roughly what situations have to be avoided for the proposed method to work well. We combine the asymptotic expansion method with the EB approximation, and give an approximation procedure for the buffer probabilities for all buffer ranges. The procedure is tested on extensive numerical examples. We suggest this procedure for efficient admission control in ATM networks.