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We consider the problem of staffing large-scale service systems with multiplecustomer classes and multiple dedicated server pools under jointquality-of-service (QoS) constraints. We first analyze the case in whicharrival rates are deterministic and the QoS metric is the probability acustomer is queued, given by the Erlang-C formula. We use the Janssen-VanLeeuwaarden-Zwart bounds to obtain asymptotically optimal solutions to thisproblem. The second model considered is one in which the arrival rates are notcompletely known in advance (before the server staffing levels are chosen), butrather are known via a probability distribution. In this case, we provideasymptotically optimal solutions to the resulting stochastic integer program,leveraging results obtained for the deterministic arrivals case.

Staffing Large Service Systems Under Arrival-rate Uncertainty