Uniform Moment Bounds for Generalized Jackson Networks in Multiscale Heavy Traffic

We establish uniform moment bounds for steady-state queue lengths of generalized Jackson networks (GJNs) in multiscale heavy traffic as recently proposed by Dai et al. in 2023. Uniform moment bounds lay the foundation for further analysis of the limit stationary distribution. Our result can be used to verify the crucial moment state space collapse (SSC) assumption in Dai et al. in 2023 to establish a product-form limit of GJN in the multiscale heavy traffic regime. Our proof critically utilizes the Palm version of the basic adjoint relationship (BAR) as developed in Braverman et al. in 2024. Funding: X. Chen acknowledges support from the National Natural Science Foundation of China [Grant 72171205] and the Science, Technology and Innovation Commission of Shenzhen Municipality [Grant RCYX20210609103124047].