When can I park?-A Physics-Informed Deep Learning Method for Waiting Time Estimation in Saturated Parking Garages

Abstract

This study addresses the problem of estimating waiting time for vehicles queuing outside saturated parking garages—a metric more directly useful to drivers than traditional parking occupancy predictions. We propose a cascaded queuing framework to model the interaction between the external queue and the parking system under saturation. A saturation balance equation is derived to estimate saturation duration and individual waiting times using only vacancy data and real-time queue length. To enhance flexibility and robustness, a Physics-Informed Deep Learning (PIDL) approach is introduced to learn key system parameters while preserving physical consistency. The method is validated through both simulation and real-world data collected at the Kennedy Town Car Park in Hong Kong. Results show that the proposed approach achieves accurate waiting time prediction and outperforms baseline methods, while maintaining strong interpretability.