Refined square-root staffing for call centers with impatient customers

In call centers it is crucial to staff the right number of agents so that the targeted service levels are met. These staffing problems typically lead to constraint satisfaction problems that are hard to solve. During the last decade, a beautiful asymptotic theory has been developed to solve such problems for large call centers operating in the quality-and-efficiency-driven (QED) regime. In this asymptotic regime, optimal staffing rules are known to obey the square-root staffing principle. This paper presents refinements to this principle that take into account the effect of impatient customers and work well for small systems.