Scaled control in the QED regime

TL;DR

This paper develops asymptotic analysis for large many-server systems with admission control in the QED regime, providing new approximations and insights for system dimensioning and performance optimization.

Contribution

It introduces scaled admission control in the QED regime, deriving limits and corrected approximations for performance measures in Markovian models.

Findings

QED limits for stationary performance measures identified

Corrected QED approximations generalized for various models

Optimality gaps for staffing and dimensioning established

Abstract

We develop many-server asymptotics in the QED regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with this scaled control, we identify the QED limits for two stationary performance measures. We also derive corrected QED approximations, generalizing earlier results for the Erlang B, C and A models. These results are useful for the dimensioning of large systems equipped with an active control policy. In particular, the corrected approximations can be leveraged to establish the optimality gaps related to square-root staffing and asymptotic dimensioning with admission control.