- Stoch. Syst.
- Volume 7, Number 1 (2017), 143-196.
Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach
In the seminal paper of Gamarnik and Zeevi , 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.
Stoch. Syst., Volume 7, Number 1 (2017), 143-196.
Received: August 2015
First available in Project Euclid: 26 May 2017
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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. Stoch. Syst. 7 (2017), no. 1, 143--196. doi:10.1214/15-SSY199. https://projecteuclid.org/euclid.ssy/1495785619