Efficient solution of multiple server queues with application to the modeling of ATM concentrators

This paper introduces a method for obtaining the steady state probabilities in G^[X]/D/C/K type queues. The solution method is more efficient than other known techniques in terms of both time and space requirements. The method is an extension of the MBH technique used to solve single server queues, It is shown that this method allows one to perform a parametric study quickly and efficiently by building on already existing results. The solution technique is used to evaluate the performance of concentrators used in ATM networks where low speed lines are connected to higher speed ones, e.g., 150 Mb/s lines to a 620 Mb/s or 1.2 Gb/s line. The concentrator is equipped with a finite capacity buffer, and is modeled as a synchronous multiple server queue with finite buffer. The concentrator is fed by a discrete batch Markov arrival process (D-BMAP) which is capable of capturing the traffic characteristics of a broad range of applications. The paper derives the probability of cell loss introduced by the concentrator buffering, and considers the effect of the buffer size as well as the line speeds on this measure