Problem definition: Curb space has long been a scarce public resource in automobilized cities, serving competing uses for passenger parking and commercial activities. The rapid growth of e-commerce and home deliveries, combined with increasing urban density, has further intensified pressure on this already constrained resource, making effective curbspace management a critical policy challenge. Yet, in practice, curb access remains largely unmanaged, relying on first-come–first-served rules or, more recently, static loading-zone allocations that fail to exploit real-time sensing and control capabilities to improve utilization. In this study, we address this gap by examining the dynamic parking space allocation problem (DyPARK) from the perspective of public authorities that regulate curb access, with the explicit objective of enhancing urban sustainability and social welfare. Methodology/results: We formulate DyPARK as an admission-control problem for a stochastic service system with heterogeneous users. Our methodology accommodates general phase-type representations of parking durations, allowing empirically supported, non-exponential service-time behaviour to be incorporated. To address uncertainty in demand and parking characteristics, we develop a robust optimization framework that relies on a novel machine-learning-based performance approximation, enabling tractable evaluation of robust policies when classical dynamic programming approaches are infeasible. The framework is calibrated using detailed curbside parking data from Istanbul and validated with large-scale data from Melbourne. Numerical experiments show that dynamic curb management substantially reduces congestion- and emission-related externalities—by more than 40% relative to unmanaged access and by up to 21% compared to static allocation schemes—particularly under demand uncertainty. Managerial implications: The results provide critical insights for public agencies on how flexible, data-driven curbside governance can improve the societal value generated by scarce public space. We identify when investments in sensing, monitoring, and enforcement technologies are justified by reductions in traffic delays and emissions, and when simpler policies suffice.