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

By Anton Braverman, Jim G. Dai, Masakiyo Miyazawa. 2015

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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.

Subfields: Management Information Systems, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e2263780d71474303dabe829437299daacf0f8b5