  Fluid models have become an important tool for the study of many-server
queues with general service and patience time distributions. The equilibrium
state of a fluid model has been revealed by Whitt (2006) and shown to yield
reasonable approximations to the steady state of the original stochastic
systems. However, it remains an open question whether the solution to a fluid
model converges to the equilibrium state and under what condition. We show in
this paper that the convergence holds under a mild condition. Our method builds
on the framework of measure-valued processes developed in Zhang (2013), which
keeps track of the remaining patience and service times.
