Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic
J. G. Dai, Peter Glynn, Yaosheng Xu
Published: 2023/4/4
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.