Computational methods for performance evaluation of a statistical multiplexer supporting bursty traffic

A statistical multiplexer supporting a number of bursty sources is modeled as a discrete time, single server queueing system with an infinite buffer. The probability generating function (PGF) method is used to analyze the queueing 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 to evaluate the characteristic roots is proposed. When the arrival process is a superposition of independent processes, a decomposition approach is used to reduce the state space involved in the computational algorithm. Additionally, the computational algorithm is made efficient through the establishment of conditions under which all the roots are either real or nonnegative real numbers. A set of equations to recursively compute the moments of the queue length are established. Sample applications of the computational methods to evaluate the performance of a multiplexer supporting voice and video sources, modeled by two-state Markov and L-state MMPP processes, respectively, demonstrate the viability of the proposed methods.