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October, 1991 Stochastic Discrete Flow Networks: Diffusion Approximations and Bottlenecks
Hong Chen, Avi Mandelbaum
Ann. Probab. 19(4): 1463-1519 (October, 1991). DOI: 10.1214/aop/1176990220


Diffusion approximations for stochastic congested networks, both open and closed, are described in terms of the networks' bottlenecks. The approximations arise as limits of functional central limit theorems. The limits are driven by reflected Brownian motions on the nonnegative orthant (for open networks) and on the simplex (for closed ones). The results provide, in particular, invariance principles for Jackson's open queueing networks, Gordon and Newell's closed networks and some of Spitzer's finite particle systems with zero-range interaction.


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Hong Chen. Avi Mandelbaum. "Stochastic Discrete Flow Networks: Diffusion Approximations and Bottlenecks." Ann. Probab. 19 (4) 1463 - 1519, October, 1991.


Published: October, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0757.60094
MathSciNet: MR1127712
Digital Object Identifier: 10.1214/aop/1176990220

Primary: 60F17
Secondary: 60F15 , 60G99 , 60J70 , 60K25 , 60K30 , 60K35 , 90B10 , 90B15 , 90B22 , 90B30 , 90C35 , 93B99

Keywords: bottlenecks , diffusion approximations , Flow networks , fluid approximations , heavy traffic , Oblique reflection , Queueing networks , reflected Brownian motions on the orthant and on the simplex , sample path analysis

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 4 • October, 1991
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