Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic

2023/04/04 by Dai, J. G., Glynn, Peter, Xu, Yaosheng
#60J27 #60K25 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2304.01499

Abstract

We prove that under a multi-scale heavy traffic condition, the stationary distribution of the scaled queue length vector process in any generalized Jackson network has a product-form limit. Each component in the product form follows an exponential distribution, corresponding to the Brownian approximation of a single station queue. The ``single station'' can be constructed precisely and its parameters have a good intuitive interpretation.

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