×

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.

MSC:

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

Citations:

Zbl 1094.60052
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid