Staffing many-server systems with admission control and retrials

TL;DR

This paper advances the theoretical understanding of staffing in large many-server systems with admission control and retrials, using asymptotic analysis in the QED regime to refine staffing rules and improve service level management.

Contribution

It develops new many-server asymptotics in the QED regime for models with admission control and retrials, refining the square-root staffing principle.

Findings

Refined asymptotic formulas for staffing in systems with admission control and retrials

Enhanced accuracy of staffing rules in the QED regime

Insights into queue behavior with retrials and admission constraints

Abstract

In many-server systems it is crucial to staff the right number of servers so that targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are hard to solve. During the last decade, a powerful many-server asymptotic theory has been developed to solve such problems and optimal staffing rules are known to obey the square-root staffing principle. This paper develops many-server asymptotics in the so-called QED regime, and presents refinements to many-server asymptotics and square-root staffing for a Markovian queueing model with admission control and retrials.