{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T06:03:58Z","timestamp":1772517838848,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T00:00:00Z","timestamp":1771977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52402401"],"award-info":[{"award-number":["52402401"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2024M750440"],"award-info":[{"award-number":["2024M750440"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Jiangsu Funding Program for Excellent Postdoctoral Talent","award":["2024ZB073"],"award-info":[{"award-number":["2024ZB073"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Coordinated control of ramp metering, variable speed limits, and intersection signals is critical for mitigating congestion and enhancing efficiency at urban expressway\u2013arterial interfaces. Existing strategies often operate in isolation, leading to fragmented responses and limited adaptability under heterogeneous traffic demands. This study develops a multi-agent reinforcement learning framework based on MADDPG to achieve cooperative decision-making across heterogeneous controllers. An asynchronous control cycle mechanism is designed to accommodate different temporal requirements of ramp meters, speed limits, and signal controllers, ensuring practical feasibility in real-time operations. A conflict-aware reward design further embeds density regulation, speed harmonization, and spillback prevention to stabilize flow dynamics. Simulation experiments on a calibrated urban network demonstrate that the proposed framework delays congestion onset, reduces shockwave propagation, and improves throughput compared with classical benchmarks. In particular, at the mainline merge, average travel time is reduced to 13.56 s (62.4% of VSL-only); at the ramp, occupancy is lowered to 6.4% (40.6% of ALINEA); and at the signalized approach, average delay decreases to 85.71 s (62.7% of actuated control). These results highlight the scalability and deployment potential of the proposed cooperative control approach for system-level traffic management in mixed traffic environments.<\/jats:p>","DOI":"10.3390\/systems14030231","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T13:37:37Z","timestamp":1772026657000},"page":"231","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Agent Deep Deterministic Policy Gradient-Based Coordinated Control for Urban Expressway Entrance\u2013Arterial Interfaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7826-5880","authenticated-orcid":false,"given":"Shunchao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9617-4405","authenticated-orcid":false,"given":"Zhigang","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wangzi","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7655","DOI":"10.1109\/TITS.2025.3559893","article-title":"Integrated freeway traffic control using Q-learning with adjacent arterial traffic considerations","volume":"26","author":"Yuan","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.trc.2013.09.011","article-title":"Computer-aided analysis and evaluation on ramp spacing along urban expressways","volume":"36","author":"Chen","year":"2013","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.aap.2017.06.003","article-title":"Analysis of real-time crash risk for expressway ramps using traffic, geometric, trip generation, and socio-demographic predictors","volume":"122","author":"Wang","year":"2019","journal-title":"Accid. Anal. Prev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"25664","DOI":"10.1109\/ACCESS.2025.3539370","article-title":"Enhancing expressway ramp merge safety and efficiency via spatiotemporal cooperative control","volume":"13","author":"Peng","year":"2025","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Xu, Z., Zheng, Y., and Li, Y. (2024). Coordinated control of urban expressways and connecting intersection based on genetic algorithm. Proceedings of the 2024 9th International Conference on Computer and Communication Systems (ICCCS), Xi\u2019an, China, 19\u201322 April 2024, IEEE.","DOI":"10.1109\/ICCCS61882.2024.10603142"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ma, J., Zeng, Y., and Chen, D. (2023). Ramp spacing evaluation of expressway based on entropy-weighted TOPSIS estimation method. Systems, 11.","DOI":"10.3390\/systems11030139"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0191-2615(80)90015-6","article-title":"A new approach to time-of-day control based on a dynamic freeway traffic model","volume":"14","author":"Papageorgiou","year":"1980","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_8","first-page":"58","article-title":"ALINEA: A local feedback control law for on-ramp metering","volume":"1320","author":"Papageorgiou","year":"1991","journal-title":"Transp. Res. Rec."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yue, W., Yang, H., Li, M., Wang, Y., Zhou, Y., and Zheng, P. (2025). Hierarchical control based on ramp metering and variable speed limit for port motorway. Systems, 13.","DOI":"10.3390\/systems13060446"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Cheng, R., Lou, H., and Wei, Q. (2025). Analysis of the impact for mixed traffic flow based on the time-varying model predictive control. Systems, 13.","DOI":"10.3390\/systems13060481"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0191-2615(90)90023-R","article-title":"Control of freeway traffic flow by variable speed signs","volume":"24","author":"Smulders","year":"1990","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_12","first-page":"128768","article-title":"Variable speed limit control strategy at freeway tunnel entrance based on cooperative lane changing","volume":"620","author":"Ma","year":"2023","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_13","first-page":"04024024","article-title":"Variable speed limits for mixed traffic flow with connected autonomous vehicles: A reinforcement learning approach","volume":"150","author":"Guo","year":"2024","journal-title":"J. Transp. Eng. Part A Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"129366","DOI":"10.1016\/j.physa.2023.129366","article-title":"Differential variable speed limit control strategy consider lane assignment at the freeway lane drop bottleneck","volume":"633","author":"Jin","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.sbspro.2014.07.221","article-title":"Variable speed limit design to relieve traffic congestion based on cooperative vehicle infrastructure system","volume":"138","author":"Sun","year":"2014","journal-title":"Procedia Soc. Behav. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.trc.2014.05.016","article-title":"An optimal variable speed limits system to ameliorate traffic safety risk","volume":"46","author":"Yu","year":"2014","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.trc.2015.07.014","article-title":"Variable speed limit: A microscopic analysis in a connected vehicle environment","volume":"58","author":"Khondaker","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"103121","DOI":"10.1016\/j.trc.2021.103121","article-title":"A linear Lagrangian model predictive controller of macro- and micro- variable speed limits to eliminate freeway jam waves","volume":"128","author":"Han","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"128542","DOI":"10.1016\/j.physa.2023.128542","article-title":"MPC-based dynamic speed control of CAVs in multiple sections upstream of the bottleneck area within a mixed vehicular environment","volume":"613","author":"Ding","year":"2023","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"130216","DOI":"10.1016\/j.physa.2024.130216","article-title":"Variable speed limit control strategy considering traffic flow lane assignment in mixed-vehicle driving environment","volume":"656","author":"Zhang","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_21","first-page":"610","article-title":"Feedback-based mainstream traffic flow control for multiple bottlenecks on motorways","volume":"16","author":"Iordanidou","year":"2015","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Qiu, S., Li, Z., Pang, Z., Li, Z., and Tao, Y. (2023). Multi-agent optimal control for central chiller plants using reinforcement learning and game theory. Systems, 11.","DOI":"10.3390\/systems11030136"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Karalakou, A., Troullinos, D., Chalkiadakis, G., and Papageorgiou, M. (2023). Deep reinforcement learning reward function design for autonomous driving in lane-free traffic. Systems, 11.","DOI":"10.3390\/systems11030134"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"126277","DOI":"10.1016\/j.eswa.2024.126277","article-title":"Variable speed limit control strategy for freeway tunnels based on a multi-objective deep reinforcement learning framework with safety perception","volume":"267","author":"Jin","year":"2025","journal-title":"Expert Syst. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"103264","DOI":"10.1016\/j.trc.2021.103264","article-title":"Adaptive signal control for bus service reliability with connected vehicle technology via reinforcement learning","volume":"129","author":"Chow","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"102645","DOI":"10.1016\/j.trc.2020.102645","article-title":"Coordinated control of urban expressway integrating adjacent signalized intersections based on pinning synchronization of complex networks","volume":"116","author":"Pang","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Deng, M., Chen, F., Gong, Y., Li, X., and Li, S. (2023). Optimization of signal timing for urban expressway exit ramp connecting intersection. Sensors, 23.","DOI":"10.3390\/s23156884"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2435643","DOI":"10.1155\/2022\/2435643","article-title":"Adaptive coordinated variable speed limit between highway mainline and on-ramp with deep reinforcement learning","volume":"2022","author":"Cheng","year":"2022","journal-title":"J. Adv. Transp."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"04024054","DOI":"10.1061\/JTEPBS.TEENG-8369","article-title":"Integrated feedback perimeter control-based ramp metering and variable speed limits for multibottleneck freeways","volume":"150","author":"He","year":"2024","journal-title":"J. Transp. Eng. Part A Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.trc.2004.08.001","article-title":"Model predictive control for optimal coordination of ramp metering and variable speed limits","volume":"13","author":"Hegyi","year":"2005","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1080\/19427867.2023.2231638","article-title":"A dynamic self-improving ramp metering algorithm based on multi-agent deep reinforcement learning","volume":"16","author":"Deng","year":"2024","journal-title":"Transp. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107570","DOI":"10.1016\/j.aap.2024.107570","article-title":"A variable speed limit control approach for freeway tunnels based on the model-based reinforcement learning framework with safety perception","volume":"201","author":"Jin","year":"2024","journal-title":"Accid. Anal. Prev."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"103900","DOI":"10.1016\/j.trc.2022.103900","article-title":"A new reinforcement learning-based variable speed limit control approach to improve traffic efficiency against freeway jam waves","volume":"144","author":"Han","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"104221","DOI":"10.1016\/j.trc.2023.104221","article-title":"TD3LVSL: A lane-level variable speed limit approach based on twin delayed deep deterministic policy gradient in a connected automated vehicle environment","volume":"153","author":"Lu","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"104267","DOI":"10.1016\/j.trc.2023.104267","article-title":"Ramp metering to maximize freeway throughput under vehicle safety constraints","volume":"154","author":"Pooladsanj","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"104582","DOI":"10.1016\/j.trc.2024.104582","article-title":"A large-scale traffic signal control algorithm based on multi-layer graph deep reinforcement learning","volume":"162","author":"Wang","year":"2024","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"104663","DOI":"10.1016\/j.trc.2024.104663","article-title":"Multi-agent deep reinforcement learning collaborative traffic signal control method considering intersection heterogeneity","volume":"164","author":"Bie","year":"2024","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"104528","DOI":"10.1016\/j.trc.2024.104528","article-title":"Cooperative traffic signal control through a counterfactual multi-agent deep actor critic approach","volume":"160","author":"Song","year":"2024","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3643","DOI":"10.1109\/TITS.2024.3521460","article-title":"Multi-Agent Game Theory-Based Coordinated Ramp Metering Method for Urban Expressways With Multi-Bottleneck","volume":"26","author":"Lin","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/3\/231\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T05:37:16Z","timestamp":1772516236000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/3\/231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,25]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["systems14030231"],"URL":"https:\/\/doi.org\/10.3390\/systems14030231","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,25]]}}}