Critically loaded multi-server queues with abandonments, retrials, and time-varying parameters

TL;DR

This paper develops adjusted fluid and diffusion models for critically loaded multi-server queues with abandonments and retrials, improving their accuracy in performance estimation under complex, time-varying conditions.

Contribution

It introduces a methodology to modify existing fluid and diffusion models, enhancing their accuracy for analyzing critically loaded queues with abandonments and retrials.

Findings

Adjusted models significantly improve estimation accuracy

Numerical experiments validate the effectiveness of the proposed methodology

Models are applicable to time-varying multi-server queue systems

Abstract

In this paper, we consider modeling time-dependent multi-server queues that include abandonments and retrials. For the performance analysis of those, fluid and diffusion models called "strong approximations" have been widely used in the literature. Although they are proven to be asymptotically exact, their effectiveness as approximations in critically loaded regimes needs to be investigated. To that end, we find that existing fluid and diffusion approximations might be either inaccurate under simplifying assumptions or computationally intractable. To address that concern, this paper focuses on developing a methodology by adjusting the fluid and diffusion models so that they significantly improve the estimation accuracy. We illustrate the accuracy of our adjusted models by performing a number of numerical experiments.