The Annals of Probability

Stochastic Discrete Flow Networks: Diffusion Approximations and Bottlenecks

Hong Chen and Avi Mandelbaum

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Abstract

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.

Article information

Source
Ann. Probab., Volume 19, Number 4 (1991), 1463-1519.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990220

Digital Object Identifier
doi:10.1214/aop/1176990220

Mathematical Reviews number (MathSciNet)
MR1127712

Zentralblatt MATH identifier
0757.60094

JSTOR
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 90B10: Network models, deterministic 60F15: Strong theorems 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G99: None of the above, but in this section 90B15: Network models, stochastic 90B22: Queues and service [See also 60K25, 68M20] 90B30: Production models 90C35: Programming involving graphs or networks [See also 90C27] 93B99: None of the above, but in this section

Keywords
Flow networks bottlenecks fluid approximations diffusion approximations sample path analysis queueing networks heavy traffic oblique reflection reflected Brownian motions on the orthant and on the simplex

Citation

Chen, Hong; Mandelbaum, Avi. Stochastic Discrete Flow Networks: Diffusion Approximations and Bottlenecks. Ann. Probab. 19 (1991), no. 4, 1463--1519. doi:10.1214/aop/1176990220. https://projecteuclid.org/euclid.aop/1176990220


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