Long Time Limits of Fluid Models for Many-Server Queues with Abandonment via Nonlinear Volterra Equations

In this paper, we study the fluid limit of many-server queues with abandonment (with traffic intensity $\lambda \in [1,\infty )$) via a class of nonlinear Volterra equations. For a broad class of service time distributions, we establish the asymptotic behavior of the solutions to the class of nonlinear Volterra equations, which in turn implies the large time behavior of the fluid limit of the many-server queues with abandonment.