Staffing for many-server systems facing non-standard arrival processes

Arrival processes to service systems often display (i) larger than anticipated fluctuations, (ii) a time-varying rate, and (iii) temporal correlation. Motivated by this, we introduce a specific non-homogeneous Poisson process that incorporates these three features. The objective is to develop a staffing rule for a many-server system facing such an arrival process. So as to obtain approximations for its performance, we first consider the situation of the arrival process being fed into the corresponding infinite-server system. Using the square-root staffing principle leads to a staffing rule that acknowledges the three features. After a slight rearrangement of servers over the time slots, we succeed to stabilize system performance even under highly varying and strongly correlated conditions. We fit the arrival stream model to real data from an emergency department and demonstrate (by simulation) the performance of the novel staffing rule.