Staffing large-scale service systems with distributional uncertainty

This paper analyzes a staffing level problem for large-scale single-station queueing systems. The system manager operates an Erlang-C queueing system with a quality-of-service constraint on the probability that a customer is queued. However, in this model, the arrival rate is uncertain in the sense that even the arrival-rate distribution is not completely known to the manager. Rather, the manager has an estimate of the support of the arrival-rate distribution and the mean. The goal is to determine the number of servers needed to satisfy the quality-of-service constraint. Two cases are explored. First, the constraint is enforced on an overall delay probability, given the probability that different feasible arrival-rate distributions are selected. In the second case, the constraint has to be satisfied by every possible distribution. For both problems, asymptotically optimal solutions are developed based on Halfin–Whitt type scalings.