A Diffusion Approximation to the Multi-Server Queue

Exact solutions to queueing problems with customer interarrival times and customer service times drawn from arbitrary (generalized) distributions have not been found. We are, therefore, much interested in good quality approximate solutions to such problems. This paper presents a methodology for obtaining (approximately) the distribution of the number of customers in a multiserver queue for which both the customer interarnval and customer service times are drawn from arbitrary distributions. The approximation is based on the theory of diffusion, depends only on the means and variances of the interarnval and service time distributions, and as the numeric examples attest is of very good quality when the queueing system is heavily loaded. The approximate solution is obtained via a very simple computational procedure, so that good quality approximate solutions to such problems can be easily produced.