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 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.

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