In queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation (sometimes called heavy traffic limit theorem[1] or diffusion approximation) involves the matching of a queueing model with a diffusion process under some limiting conditions on the model's parameters. The first such result was published by John Kingman, who showed that when the utilisation parameter of an M/M/1 queue is near 1, a scaled version of the queue length process can be accurately approximated by a reflected Brownian motion.[2]