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This paper presents asymptotic properties of the Erlang-C formula in aspectrum of many-server limiting regimes. Specifically, we address an importantgap in the literature regarding its limiting value in critically loaded regimesby studying extensions of the well-known square-root safety staffing rule usedin the Quality-and-Efficiency-Driven (QED) regime.

Some Asymptotic Properties of the Erlang-C Formula in Many-Server Limiting Regimes