We study large-scale service systems with multiple customer classes and many statistically identical servers. The following question is addressed: How many servers are required (staffing) and how does one match them with customers (control) to minimize staffing cost, subject to class-level...

The literature on many-server approximations provides significant simplifications toward the optimal capacity sizing of large-scale monopolists, but falls short of providing similar simplifications for a competitive setting in which each firm's decision is affected by its competitors' actions....