Translator Disclaimer
2017 Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach
Anton Braverman, J. G. Dai, Masakiyo Miyazawa
Stoch. Syst. 7(1): 143-196 (2017). DOI: 10.1214/15-SSY199

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.

Citation

Download Citation

Anton Braverman. J. G. Dai. Masakiyo Miyazawa. "Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach." Stoch. Syst. 7 (1) 143 - 196, 2017. https://doi.org/10.1214/15-SSY199

Information

Received: 1 August 2015; Published: 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60162
MathSciNet: MR3663340
Digital Object Identifier: 10.1214/15-SSY199

JOURNAL ARTICLE
54 PAGES


SHARE
Vol.7 • No. 1 • 2017
Back to Top