Heavy traffic approximation for the stationary distribution of a generalized Jackson network: the BAR approach. (English) Zbl 1370.60162

Summary: In the seminal paper of D. Gamarnik and A. Zeevi [Ann. Appl. Probab. 16, No. 1, 56–90 (2006; Zbl 1094.60052)], 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.


60K25 Queueing theory (aspects of probability theory)
60J65 Brownian motion
90B22 Queues and service in operations research
90B15 Stochastic network models in operations research


Zbl 1094.60052
Full Text: DOI arXiv Euclid