  This work considers a many-server queueing system in which customers with
i.i.d., generally distributed service times enter service in the order of
arrival. The dynamics of the system is represented in terms of a process that
describes the total number of customers in the system, as well as a
measure-valued process that keeps track of the ages of customers in service.
Under mild assumptions on the service time distribution, as the number of
servers goes to infinity, a law of large numbers (or fluid) limit is
established for this pair of processes. The limit is characterised as the
unique solution to a coupled pair of integral equations, which admits a fairly
explicit representation. As a corollary, the fluid limits of several other
functionals of interest, such as the waiting time, are also obtained.
Furthermore, in the time-homogeneous setting, the fluid limit is shown to
converge to its equilibrium. Along the way, some results of independent
interest are obtained, including a continuous mapping result and a maximality
property of the fluid limit. A motivation for studying these systems is that
they arise as models of computer data systems and call centers.
