Stochastic Systems

Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach

Anton Braverman, J. G. Dai, and Masakiyo Miyazawa

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Abstract

In the seminal paper of Gamarnik and Zeevi [17], the authors justify the steady-state diffusion approximation of a generalized Jackson network (GJN) in heavy traffic. Their approach involves the so-called limit interchange argument, which has since become a popular tool employed by many others who study diffusion approximations. In this paper we illustrate a novel approach by using it to justify the steady-state approximation of a GJN in heavy traffic. Our approach involves working directly with the basic adjoint relationship (BAR), an integral equation that characterizes the stationary distribution of a Markov process. As we will show, the BAR approach is a more natural choice than the limit interchange approach for justifying steady-state approximations, and can potentially be applied to the study of other stochastic processing networks such as multiclass queueing networks.

Article information

Source
Stoch. Syst., Volume 7, Number 1 (2017), 143-196.

Dates
Received: August 2015
First available in Project Euclid: 26 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1495785619

Digital Object Identifier
doi:10.1214/15-SSY199

Mathematical Reviews number (MathSciNet)
MR3663340

Zentralblatt MATH identifier
1370.60162

Keywords
Stochastic processing networks single class networks multiclass networks stationary distributions heavy traffic approximation interchange of limits reflecting Brownian motions SRBM

Rights
Creative Commons Attribution 4.0 International License.

Citation

Braverman, Anton; Dai, J. G.; Miyazawa, Masakiyo. Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach. Stoch. Syst. 7 (2017), no. 1, 143--196. doi:10.1214/15-SSY199. https://projecteuclid.org/euclid.ssy/1495785619


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