Repairing the Urban Metabolism: A Dynamic Life-Cycle and HJB Optimization Model for Resolving Spatio-Temporal Conflicts in Shared Parking Systems

Urban shared parking systems represent a complex socio-technical challenge. Despite vast potential, utilization remains persistently low (<15%), revealing a critical policy failure. To address this, this study develops a dynamic system framework based on Life-Cycle Cost (LCC) and Hamilton-Jacobi-Bellman (HJB) optimization to analyze and calibrate the key policy levers influencing owner participation timing (T*). The model, resolved using finite difference methods, captures the system’s non-linear threshold effects by simulating critical system parameters, including system instability (price volatility, σp), internal friction (management fee, wggt), and demand signals (transaction ratio, Q). Simulations reveal extreme non-linear system responses: a 100% increase in system instability (σp) delays participation by 325.5%. More critically, a 100% surge in internal friction (management fees) delays T* by 492% and triggers a 95% revenue collapse—demonstrating the risk of systemic collapse. Conversely, a 20% rise in the demand signal (Q) advances T* by 100% (immediate participation), indicating the system can be rapidly shifted to a new equilibrium by activating positive feedback loops. These findings support a sequenced calibration strategy: regulators must first manage instability via price stabilization, then counteract high friction with subsidies (e.g., 60%), and amplify demand loops. The LCC framework provides a novel dynamic decision support system for calibrating complex urban transportation systems, offering policymakers a tool for scenario testing to accelerate policy adoption and alleviate urban congestion.