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heavy traffic approximation
In queueing theory, a discipline within the mathematical theory of probability, a heavy traffic approximation (sometimes heavy traffic limit theorem or diffusion approximation) is 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.
==Heavy traffic condition ==
Heavy traffic approximations are typically stated for the process ''X''(''t'') describing the number of customers in the system at time ''t''. They are arrived at by considering the model under the limiting values of some model parameters and therefore for the result to be finite the model must be rescaled by a factor ''n'', denoted
::
::with ''ρ'' representing the traffic intensity and ''s'' the number of servers. Traffic intensity and the number of servers are increased to infinity and the limiting process is a hybrid of the above results. This case, first published by Halfin and Whitt is often known as the Halfin–Whitt regime〔 or quality-and-efficiency-driven (QED) regime.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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