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February, 1992 Reflected Brownian Motion in an Orthant: Numerical Methods for Steady-State Analysis
J. G. Dai, J. M. Harrison
Ann. Appl. Probab. 2(1): 65-86 (February, 1992). DOI: 10.1214/aoap/1177005771


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.


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J. G. Dai. J. M. Harrison. "Reflected Brownian Motion in an Orthant: Numerical Methods for Steady-State Analysis." Ann. Appl. Probab. 2 (1) 65 - 86, February, 1992.


Published: February, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0786.60107
MathSciNet: MR1143393
Digital Object Identifier: 10.1214/aoap/1177005771

Primary: 60J70
Secondary: 60K30 , 65P05 , 65U05 , 68M20

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

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 1 • February, 1992
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