“…Recent years have seen a growing use of the generator comparison approach of Stein's method to establish rates of convergence for steady-state diffusion approximations of Markov chains. One very active area has been the study of queueing and service systems; see, for example, Gurvich (2014a), Stolyar (2015), Braverman et al (2016Braverman et al ( , 2020Braverman et al ( , 2021, Ying (2016Ying ( , 2017, Braverman and Dai (2017), Dai and Shi (2017), Huang and Gurvich (2018), Feng and Shi (2018), Liu and Ying (2019), and Braverman (2020). In the typical setup, one considers a parametric family of continuous-time Markov chains (CTMCs) {X(t)} taking values in some discrete state space.…”