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Heavy traffic approximation
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<p>In <a href="/facts/Queueing_theory/8NDl56EM">queueing theory</a>, a discipline within the mathematical <a href="/facts/Probability_theory/mFBn51rE">theory of probability</a>, a heavy traffic approximation (sometimes called heavy traffic limit theorem or diffusion approximation) involves the matching of a queueing model with a <a href="/facts/Diffusion_process/n7u5hjKX">diffusion process</a> under some <a href="/facts/Limit_(mathematics)/j8JBhj4e">limiting</a> conditions on the model's parameters. The first such result was published by <a href="/facts/John_Kingman/fh6KUPkC">John Kingman</a>, who showed that when the utilisation parameter of an <a href="/facts/M%2fM%2f1_queue/eTkKX6Ro">M/M/1 queue</a> is near 1, a scaled version of the queue length process can be accurately approximated by a <a href="/facts/Reflected_Brownian_motion/Wb4Knnzv">reflected Brownian motion</a>. </p>