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

Beyond Scaling: Calculable Error Bounds of the Power-of-Two-Choices Mean-Field Model in Heavy-Traffic