  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 resulting arrival process
is fed into an infinite-server system, which is then used as a proxy for its
many-server counterpart. This leads to a staffing rule based on the square-root
staffing principle 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.
