In this note, we apply Steins 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), Steins 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 Steins 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 Steins method in heavy-traffic analysis. In particular, we can see that one appealing property of Steins method is that it combines the advantages of both the drift method and the transform method.
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