  In this note, we apply Stein's method to analyze the steady-state
distribution of queueing systems in the traditional heavy-traffic regime.
Compared to previous methods (e.g., drift method and transform method), Stein's
method allows us to establish stronger results with simple and template proofs.
In particular, we consider discrete-time systems in this note. We first
introduce the key ideas of Stein's method for heavy-traffic analysis through a
single-server system. Then, we apply the developed template to analyze both
load balancing problems and scheduling problems. All these three examples
demonstrate the power and flexibility of Stein's method in heavy-traffic
analysis. In particular, we can see that one appealing property of Stein's
method is that it combines the advantages of both the drift method and the
transform method.
