Computational methods for performance evaluation of an ATM multiplexer supporting bursty traffic

An asynchronous transfer mode (ATM) multiplexer supporting a number of bursty sources is modeled as a discrete time, single server queuing system with an infinite buffer. The probability generating function (PGF) method is used to analyze the queuing behavior. The PGF method requires the determination of a large number of boundary values, and hence the roots of the characteristic equation. An iterative algorithm for evaluating the roots is proposed. The algorithm is decomposable when the arrival process is a superposition of elemental processes. Conditions for all the roots to be real are established. A set of equations to recursively compute the moments of the queue length is derived. The proposed methods are used to evaluate the performance of an ATM multiplexer supporting either voice or video traffic