Existence and uniqueness of a fluid model for many-server queues with abandonment

In this paper, we establish a new (direct) proof for existence and uniqueness of the fluid model for Gt/GI/N+GIGt/GI/N+GI queues proposed recently by Kang and Ramanan under mild conditions on the arrival, service and patience time distributions. In particular, the existence of the fluid model is established directly from the fluid model itself. Then main technique here is the application of two non-linear functional integral equations, one of which is of Volterra type.