{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T17:40:31Z","timestamp":1768585231148,"version":"3.49.0"},"reference-count":39,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Science and Technology Major Project","award":["AA22068057"],"award-info":[{"award-number":["AA22068057"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62262009"],"award-info":[{"award-number":["62262009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62495083"],"award-info":[{"award-number":["62495083"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Urban shared parking systems represent a complex socio-technical challenge. Despite vast potential, utilization remains persistently low (&lt;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\u2019s non-linear threshold effects by simulating critical system parameters, including system instability (price volatility, \u03c3p), internal friction (management fee, wggt), and demand signals (transaction ratio, Q). Simulations reveal extreme non-linear system responses: a 100% increase in system instability (\u03c3p) 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\u2014demonstrating 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.<\/jats:p>","DOI":"10.3390\/systems14010091","type":"journal-article","created":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T08:26:36Z","timestamp":1768465596000},"page":"91","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Repairing the Urban Metabolism: A Dynamic Life-Cycle and HJB Optimization Model for Resolving Spatio-Temporal Conflicts in Shared Parking Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0256-1382","authenticated-orcid":false,"given":"Jiangfeng","family":"Li","sequence":"first","affiliation":[{"name":"School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianlong","family":"Xiang","sequence":"additional","affiliation":[{"name":"School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8606-3648","authenticated-orcid":false,"given":"Fujian","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longxin","family":"Zeng","sequence":"additional","affiliation":[{"name":"School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiquan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Architecture and Transportation Engineering, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5801-4937","authenticated-orcid":false,"given":"Yujie","family":"Li","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongyi","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.ecotra.2015.04.001","article-title":"Cruising-for-Parking in Congested Cities with an MFD Representation","volume":"4","author":"Geroliminis","year":"2015","journal-title":"Econ. Transp."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108194","DOI":"10.1016\/j.resconrec.2025.108194","article-title":"Metabolism of Interconnected Cities: A Review of the Literature and Analytical Framework","volume":"217","author":"Verma","year":"2025","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.envpol.2013.03.052","article-title":"Urban Metabolism: A Review of Research Methodologies","volume":"178","author":"Zhang","year":"2013","journal-title":"Environ. Pollut."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"100628","DOI":"10.1016\/j.envdev.2021.100628","article-title":"The Stock-Flow-Service Nexus of Personal Mobility in an Urban Context: Vienna, Austria","volume":"41","author":"Wiedenhofer","year":"2022","journal-title":"Environ. Dev."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1038\/nphys2160","article-title":"Modelling Dynamical Processes in Complex Socio-Technical Systems","volume":"8","author":"Vespignani","year":"2012","journal-title":"Nat. Phys."},{"key":"ref_6","first-page":"9955686","article-title":"Study on the Intention of Private Parking Space Owners of Different Levels of Cities to Participate in Shared Parking in China","volume":"2021","author":"Wang","year":"2021","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"102834","DOI":"10.1016\/j.trb.2023.102834","article-title":"The Economics of Speed Choice and Control in the Presence of Driverless Vehicle Cruising and Parking-as-a-Substitute-for-Cruising","volume":"178","author":"Tscharaktschiew","year":"2023","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s11116-021-10241-0","article-title":"Impact of Self-Parking Autonomous Vehicles on Urban Traffic Congestion","volume":"50","author":"Shafiei","year":"2023","journal-title":"Transportation"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.tra.2021.08.014","article-title":"Measuring Willingness to Pay for Shared Parking","volume":"152","author":"Ardeshiri","year":"2021","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Thi Kim, O.T., Dang Tri, N., Nguyen, V.D., Tran, N.H., and Hong, C.S. (2015, January 19\u201321). A Shared Parking Model in Vehicular Network Using Fog and Cloud Environment. Proceedings of the 2015 17th Asia-Pacific Network Operations and Management Symposium (APNOMS), Busan, Republic of Korea.","DOI":"10.1109\/APNOMS.2015.7275447"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.trc.2016.08.010","article-title":"A Simple Reservation and Allocation Model of Shared Parking Lots","volume":"71","author":"Shao","year":"2016","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_12","first-page":"322","article-title":"Bi-Level Model for Shared Parking Decision-Making Based on Parking Lot Assignment Simulation","volume":"27","author":"Ran","year":"2011","journal-title":"J. Southeast Univ. (Engl. Ed.)"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1080\/19427867.2024.2303225","article-title":"Research on Shared Parking Allocation Considering the Heterogeneity of Parking Slot Providers\u2019 Temporary Parking Demand","volume":"16","author":"Li","year":"2024","journal-title":"Transp. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhou, X., Jiang, H., Bai, M., and Chen, R. (2025, January 19). Online Pricing for Balancing Parking Demand and Supply in a Shared Parking Case. Proceedings of the 2025 7th International Conference on Data-driven Optimization of Complex Systems (DOCS), Taiyuan, China.","DOI":"10.1109\/DOCS67533.2025.11200568"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"102062","DOI":"10.1016\/j.tre.2020.102062","article-title":"Optimal Allocation of Shared Parking Slots Considering Parking Unpunctuality under a Platform-Based Management Approach","volume":"142","author":"Jiang","year":"2020","journal-title":"Transp. Res. Part E Logist. Transp. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"04021026","DOI":"10.1061\/JTEPBS.0000522","article-title":"Spatiotemporal Deep-Learning Networks for Shared-Parking Demand Prediction","volume":"147","author":"Liu","year":"2021","journal-title":"J. Transp. Eng. Part A Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103484","DOI":"10.1016\/j.trc.2021.103484","article-title":"A Reservation and Allocation Model for Shared-Parking Addressing the Uncertainty in Drivers\u2019 Arrival\/Departure Time","volume":"135","author":"Wang","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105083","DOI":"10.1016\/j.cor.2020.105083","article-title":"Two-Stage Matching-and-Scheduling Algorithm for Real-Time Private Parking-Sharing Programs","volume":"125","author":"Yan","year":"2021","journal-title":"Comput. Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"04021028","DOI":"10.1061\/JTEPBS.0000534","article-title":"Matching Model between Private Idle Parking Slots and Demanders for Parking Slot Sharing","volume":"147","author":"Jiang","year":"2021","journal-title":"J. Transp. Eng. Part A Syst."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1016\/j.trb.2018.01.008","article-title":"Shared Parking Problem: A Novel Truthful Double Auction Mechanism Approach","volume":"109","author":"Xiao","year":"2018","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.trc.2018.05.023","article-title":"How to Restrain Participants Opt out in Shared Parking Market? A Fair Recurrent Double Auction Approach","volume":"93","author":"Xiao","year":"2018","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1088\/0031-9112\/28\/9\/027","article-title":"Synergetics","volume":"28","author":"Haken","year":"1977","journal-title":"Phys. Bull."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Haken, H. (2004). An Introduction: Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology. Synergetics: Introduction and Advanced Topics, Springer.","DOI":"10.1007\/978-3-662-10184-1_1"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Portugali, J., and Haken, H. (2021). Synergetic Cities. Handbook on Cities and Complexity, Edward Elgar Publishing.","DOI":"10.4337\/9781789900125.00014"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1080\/002075498193444","article-title":"Product Life Cycle Cost Analysis: State of the Art Review","volume":"36","author":"Asiedu","year":"1998","journal-title":"Int. J. Prod. Res."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Farr, J.V. (2011). Systems Life Cycle Costing: Economic Analysis, Estimation, and Management, CRC Press.","DOI":"10.1201\/b10963"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1080\/19427867.2022.2088568","article-title":"Private Owners\u2019 Propensity to Engage in Shared Parking Schemes under Uncertainty: Comparison of Alternate Hybrid Expected Utility-Regret-Rejoice Choice Models","volume":"15","author":"Yan","year":"2023","journal-title":"Transp. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s10957-023-02364-4","article-title":"Application of Hamilton\u2013Jacobi\u2013Bellman Equation\/Pontryagin\u2019s Principle for Constrained Optimal Control","volume":"200","author":"Weston","year":"2024","journal-title":"J. Optim. Theory Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"A2153","DOI":"10.1137\/22M1498401","article-title":"Data-Driven Tensor Train Gradient Cross Approximation for Hamilton\u2013Jacobi\u2013Bellman Equations","volume":"45","author":"Dolgov","year":"2023","journal-title":"SIAM J. Sci. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Litman, T. (2020). Parking Management Best Practices, Routledge.","DOI":"10.4324\/9781351179546"},{"key":"ref_31","unstructured":"Tyndall & Associates (2019). Landscape B03: Coordinated Parking\u2014Operational Cost Analysis. Landscape Master Plan B.Framework, U.S. Air Force."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Gonz\u00e1lez-Mu\u00f1oz, R.-I., Molina-Mu\u00f1oz, J., Mora-Valencia, A., and Perote, J. (2024). Real Options Volatility Surface for Valuing Renewable Energy Projects. Energies, 17.","DOI":"10.3390\/en17051225"},{"key":"ref_33","unstructured":"Litman, T. (2023). Autonomous Vehicle Implementation Predictions, VTPI."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2087","DOI":"10.1016\/j.rser.2011.01.016","article-title":"Application of an Advanced Real Options Approach for Renewable Energy Generation Projects Planning","volume":"15","author":"Mutale","year":"2011","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_35","first-page":"105","article-title":"Operational situation and outlook of China\u2019s urban economy (2023\u20132024)","volume":"39","author":"Gao","year":"2024","journal-title":"Bull. Chin. Acad. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1257\/aer.20231246","article-title":"Corporate Discount Rates","volume":"115","author":"Gormsen","year":"2025","journal-title":"Am. Econ. Rev."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"707","DOI":"10.2307\/1884175","article-title":"The Value of Waiting to Invest","volume":"101","author":"McDonald","year":"1986","journal-title":"Q. J. Econ."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.tra.2020.04.003","article-title":"Effect of On-Street Parking Pricing Policies on Parking Characteristics: A Case Study of Nanning","volume":"137","author":"Wang","year":"2020","journal-title":"Transp. Res. Part A Policy Pract."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.tra.2021.04.013","article-title":"Impact of Pricing Policy Change on On-Street Parking Demand and User Satisfaction: A Case Study in Nanning, China","volume":"148","author":"Mo","year":"2021","journal-title":"Transp. Res. Part A Policy Pract."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/1\/91\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T06:22:53Z","timestamp":1768544573000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/1\/91"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,14]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["systems14010091"],"URL":"https:\/\/doi.org\/10.3390\/systems14010091","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,14]]}}}