  This paper provides a recipe for deriving calculable approximation errors of
mean-field models in heavy-traffic with the focus on the well-known load
balancing algorithm -- power-of-two-choices (Po2). The recipe combines Stein's
method for linearized mean-field models and State Space Concentration (SSC)
based on geometric tail bounds. In particular, we divide the state space into
two regions, a neighborhood near the mean-field equilibrium and the complement
of that. We first use a tail bound to show that the steady-state probability
being outside the neighborhood is small. Then, we use a linearized mean-field
model and Stein's method to characterize the generator difference, which
provides the dominant term of the approximation error. From the dominant term,
we are able to obtain an asymptotically-tight bound and a nonasymptotic upper
bound, both are calculable bounds, not order-wise scaling results like most
results in the literature. Finally, we compared the theoretical bounds with
numerical evaluations to show the effectiveness of our results. We note that
the simulation results show that both bounds are valid even for small size
systems such as a system with only ten servers.
