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

TL;DR

This paper introduces a new staffing rule for many-server systems with complex, correlated, and time-varying arrival processes, validated through real data and simulations, improving system stability under challenging conditions.

Contribution

It develops a non-homogeneous Poisson process model capturing key arrival features and proposes a staffing rule that stabilizes performance in highly variable, correlated environments.

Findings

The new model accurately fits real emergency department data.

The staffing rule stabilizes system performance under high variability.

Simulation confirms improved stability with the proposed approach.

Abstract

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.