State space collapse for multi-class queueing networks under SBP service policies

In Braverman et al. [ 3 ], the authors justify the steady-state diffusion approximation of a multiclass queueing network under static buffer priority policy in heavy traffic. A major assumption in [ 3 ] is the moment state space collapse (moment-SSC) property of the steady-state queue length. In this paper, we prove that moment-SSC holds under a corresponding state space collapse condition on the fluid model. Our approach is inspired by Dai and Meyn [ 8 ], which was later adopted by Budhiraja and Lee [ 4 ] to justify the diffusion approximation for generalized Jackson networks. We will verify that the fluid state space collapse holds for various networks.