Wiener process with reflecting spatial boundaries
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]
^ Dieker, A. B. (2011). "Reflected Brownian Motion". Wiley Encyclopedia of Operations Research and Management Science . doi :10.1002/9780470400531.eorms0711 . ISBN 9780470400531 .
^ a b Cite error: The named reference harrison-book
was invoked but never defined (see the help page ).
^ 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 .
^ 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 .
^ 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 .
^ 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 .
^ 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 .