Comparative Analysis of Distance Metrics for Distributionally Robust Optimization in Queuing Systems: Wasserstein vs. Kingman

This study examines the effectiveness of different metrics in constructing ambiguity sets for Distributionally Robust Optimization (DRO). Two main approaches for building ambiguity sets are the moment- and the discrepancy-based approaches. The latter is more widely adopted because it incorporates a broader range of distributional information beyond moments. Among discrepancy-based metrics, the Wasserstein distance is often preferred for its advantageous properties over ¢-divergence. In this study, we propose a moment-based Kingman distance, an approximation of mean waiting time in G/G/1 queues, to determine the ambiguity set. We demonstrate that the Kingman distance provides a straightforward and efficient method for identifying worst-case scenarios for simple queue settings. In contrast, the Wasserstein distance requires exhaustive exploration of the entire ambiguity set to pinpoint the worst-case distributions. These findings suggest that the Kingman distance could offer a practical and effective alternative for DRO applications in some cases.