Probabilistic time-series crowd forecasting at Hague Beach, the Netherlands

Abstract

Accurate forecasting of visitor crowd count enables crowd safety managers to anticipate potential risks, deploy personnel strategically, and implement timely interventions. Using The Hague Beach in the Netherlands as a case study, this research develops a probabilistic framework that produces 14-day, hourly crowd forecasts. The study benchmarks three uncertainty-quantification methods: Quantile Regression (QR), Split Conformal Prediction (CP), and Conformalized Quantile Regression (CQR), applied to three base forecasting models: a seasonal weekly naive model, LightGBM, and the Temporal Fusion Transformer (TFT). Results show that conformalization markedly improves calibration over standard QR. CQR achieves near-nominal coverage while producing narrower, more adaptive prediction intervals than Split CP. The combination of TFT with CQR yields the best overall distributional accuracy, offering a practical and robust tool for proactive crowd management in a dynamic beach environment.