Reflected Brownian motion

In probability theory, reflected Brownian motion (or regulated Brownian motion,[1][2] both with the acronym RBM) is a Wiener process in a space with reflecting boundaries.[3] In the physical literature, this process describes diffusion in a confined space and it is often called confined Brownian motion. For example it can describe the motion of hard spheres in water confined between two walls.[4]

RBMs have been shown to describe queueing models experiencing heavy traffic[2] as first proposed by Kingman[5] and proven by Iglehart and Whitt.[6][7]

  1. ^ Dieker, A. B. (2011). "Reflected Brownian Motion". Wiley Encyclopedia of Operations Research and Management Science. doi:10.1002/9780470400531.eorms0711. ISBN 9780470400531.
  2. ^ a b Cite error: The named reference harrison-book was invoked but never defined (see the help page).
  3. ^ Veestraeten, D. (2004). "The Conditional Probability Density Function for a Reflected Brownian Motion". Computational Economics. 24 (2): 185–207. doi:10.1023/B:CSEM.0000049491.13935.af. S2CID 121673717.
  4. ^ Faucheux, Luc P.; Libchaber, Albert J. (1994-06-01). "Confined Brownian motion". Physical Review E. 49 (6): 5158–5163. doi:10.1103/PhysRevE.49.5158. ISSN 1063-651X.
  5. ^ Kingman, J. F. C. (1962). "On Queues in Heavy Traffic". Journal of the Royal Statistical Society. Series B (Methodological). 24 (2): 383–392. doi:10.1111/j.2517-6161.1962.tb00465.x. JSTOR 2984229.
  6. ^ Iglehart, Donald L.; Whitt, Ward (1970). "Multiple Channel Queues in Heavy Traffic. I". Advances in Applied Probability. 2 (1): 150–177. doi:10.2307/3518347. JSTOR 3518347. S2CID 202104090.
  7. ^ Iglehart, Donald L.; Ward, Whitt (1970). "Multiple Channel Queues in Heavy Traffic. II: Sequences, Networks, and Batches" (PDF). Advances in Applied Probability. 2 (2): 355–369. doi:10.2307/1426324. JSTOR 1426324. S2CID 120281300. Retrieved 30 Nov 2012.