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

J. G. Dai; Peter Glynn; Yaosheng Xu

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arXiv · 2304.01499

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

J. G. Dai·Peter Glynn·Yaosheng Xu

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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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BibTeX RIS

J. G. Dai, Peter Glynn, Yaosheng Xu. 2023-04-04. Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic. https://arxiv.org/abs/2304.01499

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