Optimality gaps in asymptotic dimensioning of many-server systems

TL;DR

This paper derives bounds on the difference between true optimal solutions and QED-based asymptotic solutions in many-server systems, enhancing understanding of their accuracy and applicability.

Contribution

It generalizes previous bounds for classical systems and applies them to systems with threshold control, advancing asymptotic dimensioning methods.

Findings

Derived bounds for optimality gaps in many-server systems

Generalized earlier results to broader system classes

Applied bounds to systems with threshold control

Abstract

The Quality-and-Efficiency-Driven (QED) regime provides a basis for solving asymptotic dimensioning problems that trade off revenue, costs and service quality. We derive bounds for the optimality gaps that capture the differences between the true optimum and the asymptotic optimum based on the QED approximations. Our bounds generalize earlier results for classical many-server systems. We also apply our bounds to a many-server system with threshold control.