Fluid Models of Many-server Queues with Abandonment

TL;DR

This paper develops measure-valued fluid models for large many-server queues with customer abandonment, providing a first-order approximation of system dynamics and performance metrics.

Contribution

It introduces a novel measure-valued fluid model framework for queues with abandonment, establishing existence, uniqueness, and approximation results.

Findings

Fluid model solutions serve as the limit for large systems.

First-order performance approximations are derived from the fluid model.

The model captures residual service and patience times effectively.

Abstract

We study many-server queues with abandonment in which customers have general service and patience time distributions. The dynamics of the system are modeled using measure- valued processes, to keep track of the residual service and patience times of each customer. Deterministic fluid models are established to provide first-order approximation for this model. The fluid model solution, which is proved to uniquely exists, serves as the fluid limit of the many-server queue, as the number of servers becomes large. Based on the fluid model solution, first-order approximations for various performance quantities are proposed.