Fluid models of many‐server queues with abandonment

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 a first‐order approximation for this model. The fluid model solution, which is proved to uniquely exist, 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.