  In many-server systems it is crucial to staff the right number of servers so
that targeted service levels are met. These staffing problems typically lead to
constraint satisfaction problems that are hard to solve. During the last
decade, a powerful many-server asymptotic theory has been developed to solve
such problems and optimal staffing rules are known to obey the square-root
staffing principle. This paper develops many-server asymptotics in the
so-called QED regime, and presents refinements to many-server asymptotics and
square-root staffing for a Markovian queueing model with admission control and
retrials.
