Well-Posedness and Sensitivity Analysis of a Fluid Model for Multiclass Many-Server Queues with Abandonment Under Global FCFS Discipline

In this paper, under mild conditions on the arrival, service, and patience time distributions, we establish the well-posedness of the fluid model of a multiclass many-server queueing model with differentiated service and patience times operated under the global FCFS service discipline. In particular, the well-posedness of the fluid model is established through the study of the existence and uniqueness of fixed points of a certain functional map of Volterra type. In addition, by showing a local Lipschitz property of this functional map as a functional of the initial data to the fluid model, we also perform a sensitivity analysis on the fluid model.