  We consider the problem of staffing large-scale service systems with multiple
customer classes and multiple dedicated server pools under joint
quality-of-service (QoS) constraints. We first analyze the case in which
arrival rates are deterministic and the QoS metric is the probability a
customer is queued, given by the Erlang-C formula. We use the Janssen-Van
Leeuwaarden-Zwart bounds to obtain asymptotically optimal solutions to this
problem. The second model considered is one in which the arrival rates are not
completely known in advance (before the server staffing levels are chosen), but
rather are known via a probability distribution. In this case, we provide
asymptotically optimal solutions to the resulting stochastic integer program,
leveraging results obtained for the deterministic arrivals case.
