  A multi-class single-server queueing model with finite buffers, in which
scheduling and admission of customers are subject to control, is studied in the
moderate deviation heavy traffic regime. A risk-sensitive cost set over a
finite time horizon $[0,T]$ is considered. The main result is the asymptotic
optimality of a control policy derived via an underlying differential game. The
result is the first to address a queueing control problem at the moderate
deviation regime that goes beyond models having the so called pathwise
minimality property. Moreover, despite the well known fact that an optimal
control over a finite time interval is generically of a nonstationary feedback
type, the proposed policy forms a stationary feedback, provided $T$ is
sufficiently large.
