Dimensioning large-scale membership services

Motivated by workforce planning problems in health care, professional, warranty, and repair services, we propose modeling service centers that are exclusively dedicated to fixed client constituencies as closed multiserver queueing systems, a framework we refer to as membership services. We provide fluid and diffusion approximations of the number of users within the membership who are requesting service. The approximations are obtained via many-server limit theorems, where the limiting regime assumptions of each theorem correspond to a particular staffing strategy a manager might employ. Accordingly, we propose staffing rules designed to meet a certain desired performance criterion. In particular, when the objective is to minimize the staffing size subject to a constraint on the probability of delay for a service-requesting customer, we suggest staffing rules inspired by the so-called quality-and efficiency-driven ( QED), or Halfin-Whitt, limiting regime. Numerical evaluations of our proposed QED scheme indicate that, although justified for large systems, the staffing rule performs well for memberships of all sizes.