Customer Scheduling in Large Service Systems Under Model Uncertainty

Scheduling in the context of many-server queues has received considerable attention. When there are multiple customer classes and many servers, it is common to make simplifying assumptions that result in a “low-fidelity” model, potentially leading to model misspecification. However, empirical evidence suggests that these assumptions may not accurately reflect real-world scenarios. Although relaxing these assumptions can yield a more accurate “high-fidelity” model, it often becomes complex and challenging, if not impossible, to solve. In this paper, we introduce a novel approach for decision makers to generate high-quality scheduling policies for large service systems based on a simple and tractable low-fidelity model instead of its complex and intractable high-fidelity counterpart. At the core of our approach is a robust control formulation, wherein optimization is conducted against an imaginary adversary. This adversary optimally exploits the potential weaknesses of a scheduling rule within prescribed limits defined by an uncertainty set by dynamically perturbing the low-fidelity model. This process assists decision-makers in assessing the vulnerability of a given scheduling policy to model errors stemming from the low-fidelity model. Moreover, our proposed robust control framework is complemented by practical data-driven schemes for uncertainty set selection. Extensive numerical experiments, including a case study based on a U.S. call center data set, substantiate the effectiveness of our framework by revealing scheduling policies that can significantly reduce the system’s costs in comparison with established benchmarks in the literature.