Asymptotic approximations of many-server queues

Many-server queues arise in a variety of applications, including call centers and computer data systems. We show how a Markovian description of the system leads naturally to a measure-valued representation. Under an appropriate (Halfin-Whitt) asymptotic scaling we identify the functional strong law and functional central limits of these processes.  The latter, in particular, gives rise to a functional SDE with memory.  Our framework is quite general and, for example, allows for the incorporation of abandonments.