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

TL;DR

This paper investigates the asymptotic behavior of the Erlang-C formula in various many-server regimes, focusing on its limits in critically loaded conditions and extending the square-root staffing rule used in QED regimes.

Contribution

It provides new insights into the limiting properties of the Erlang-C formula in critically loaded regimes and extends the square-root safety staffing rule for these scenarios.

Findings

Erlang-C formula's limiting value in critically loaded regimes analyzed

Extensions of the square-root safety staffing rule developed

Asymptotic properties characterized across multiple regimes

Abstract

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