Transient Diffusion Approximation for M/G/m system

Abstract

We investigate a transient diffusion approximation by diffusion process with elementary return boundary for the number of customers in the M/G/m system. We formulate and solve the forward diffusion equation with variable coefficient, whose solution is a transient approximation to queue size distribution. Numerical examples show that these diffusion approximation results are quite accurate for all traffic cases. It is shown that stationary approximation by Kimura is obtained from our transient diffusion approximation.