Heavy traffic approximation

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]

  1. ^ Halfin, S.; Whitt, W. (1981). "Heavy-Traffic Limits for Queues with Many Exponential Servers" (PDF). Operations Research. 29 (3): 567. doi:10.1287/opre.29.3.567.
  2. ^ Kingman, J. F. C.; Atiyah (October 1961). "The single server queue in heavy traffic". Mathematical Proceedings of the Cambridge Philosophical Society. 57 (4): 902. Bibcode:1961PCPS...57..902K. doi:10.1017/S0305004100036094. JSTOR 2984229.