Service-level differentiation in call centers with fully flexible servers

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 quality-of-service constraints? We tackle this question by characterizing scheduling and staffing schemes that are asymptotically optimal in the limit, as system load grows to infinity. The asymptotic regimes considered are consistent with the efficiencydriven (ED), quality-driven (QD), and quality-and-efficiency-driven (QED) regimes, first introduced in the context of a single-class service system. Our main findings are as follows: (a) Decoupling of staffing and control, namely, (i) staffing disregards the multiclass nature of the system and is analogous to the staffing of a single-class system with the same aggregate demand and a single global quality-of-service constraint, and (ii) class-level service differentiation is obtained by using a simple idle-server-based threshold-priority (ITP) control (with state-independent thresholds); and (b) robustness of the staffing and control rules: our proposed single-class staffing (SCS) rule and ITP control are approximately optimal under various problem formulations and model assumptions. Particularly, although our solution is shown to be asymptotically optimal for large systems, we numerically demonstrate that it performs well also for relatively small systems.