Abstract. Queueing models explain waiting times, predict sojourn times and help to identify and avoid bottlenecks. Domain experts usually create these models by intensive handcrafting, often resulting in idealized models not fitting the actual process behavior well. Discovering queueing models from data can alleviate this effort, but existing methods do not suffice as they are unable to model complex queueing behaviors.

We propose a novel approach to discover queueing models for interpretable waiting time prediction using a rich modeling language to fit complex processes. We formalize the problem in terms of the Minimum Description Length (MDL) principle, by which the best model gives the best lossless compression. The resulting optimization problem is computationally hard, and hence we propose the greedy CueMin algorithm to efficiently find good queueing models from data. Through an extensive set of experiments including a case study on call center data, we show it discovers inherently interpretable models, which explain and predict behavior of waiting lines better than the state of the art.