Editing Queueing theory (section)

=== Heavy traffic/diffusion approximations ===
{{Main|Heavy traffic approximation}}
In a system with high occupancy rates (utilisation near 1), a heavy traffic approximation can be used to approximate the queueing length process by a [[reflected Brownian motion]],<ref>{{Cite journal | last1 = Chen | first1 = H. | last2 = Whitt | first2 = W. | doi = 10.1007/BF01149260 | title = Diffusion approximations for open queueing networks with service interruptions | journal = [[Queueing Systems]]| volume = 13 | issue = 4 | page = 335 | year = 1993 | s2cid = 1180930 }}</ref> [[Ornstein–Uhlenbeck process]], or more general [[diffusion process]].<ref>{{Cite journal | last1 = Yamada | first1 = K. | title = Diffusion Approximation for Open State-Dependent Queueing Networks in the Heavy Traffic Situation | doi = 10.1214/aoap/1177004602 | journal = The Annals of Applied Probability | volume = 5 | issue = 4 | pages = 958–982 | year = 1995 | jstor = 2245101| doi-access = free }}</ref> The number of dimensions of the Brownian process is equal to the number of queueing nodes, with the diffusion restricted to the non-negative [[orthant]].