The Annals of Applied Probability

Reflected Brownian Motion in an Orthant: Numerical Methods for Steady-State Analysis

J. G. Dai and J. M. Harrison

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This paper is concerned with a class of multidimensional diffusion processes, variously known as reflected Brownian motions, regulated Brownian motions, or just RBM's, that arise as approximate models of queueing networks. We develop an algorithm for numerical analysis of a semimartingale RBM with state space $S = \mathbb{R}^d_+$ (the nonnegative orthant of $d$-dimensional Euclidean space). This algorithm lies at the heart of the QNET method for approximate two-moment analysis of open queueing networks.

Article information

Ann. Appl. Probab., Volume 2, Number 1 (1992), 65-86.

First available in Project Euclid: 19 April 2007

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Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 65U05 65P05 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Brownian system model reflected Brownian motion stationary distribution numerical analysis open queueing networks performance analysis


Dai, J. G.; Harrison, J. M. Reflected Brownian Motion in an Orthant: Numerical Methods for Steady-State Analysis. Ann. Appl. Probab. 2 (1992), no. 1, 65--86. doi:10.1214/aoap/1177005771.

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