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 Stochastic Systems > Vol. 7 (2017) open journal systems 


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

Anton Braverman, Cornell University
J.G. Dai, Cornell University
Masakiyo Miyazawa, Tokyo University of Science


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.

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

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

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