Asymptotic Product-Form Steady State for Generalized Jackson Networks in Multiscale Heavy Traffic

We prove that under a multiscale 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.

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2023.0184.