{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T16:35:40Z","timestamp":1778258140458,"version":"3.51.4"},"reference-count":43,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T00:00:00Z","timestamp":1750118400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Program of Humanities and Social Science of Education Ministry of China","award":["24YJA630013"],"award-info":[{"award-number":["24YJA630013"]}]},{"name":"the Program of Humanities and Social Science of Education Ministry of China","award":["2024J125"],"award-info":[{"award-number":["2024J125"]}]},{"name":"the Ningbo Natural Science Foundation of China","award":["24YJA630013"],"award-info":[{"award-number":["24YJA630013"]}]},{"name":"the Ningbo Natural Science Foundation of China","award":["2024J125"],"award-info":[{"award-number":["2024J125"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>The connected and automated vehicles (CAV) smoothing mixed traffic flow has gained attention, and a thorough assessment of these control algorithms is necessary. Our previous research proposed the time-varying model predictive control (TV-MPC) strategy, which considers the time-varying driving style of human driven vehicles (HDV), performing better than current baseline models. Due TV-MPC can be applied to any traffic congestion scenario and the dynamic modeling that considers driving style, can be easily transferred to other control algorithms. Thus, TV-MPC enable to represent typical control algorithms in mixed traffic flow. This study investigates the performance of TV-MPC under diverse disturbance characteristics and mixed platoons. Firstly, quantifying mixed traffic flow with different CAV penetration rates and platooning intensities by a Markov chain model. Secondly, by constructing evaluation indicators for micro-level operation of mixed traffic flow, this paper analyzed the impact of TV-MPC on the operation of mixed traffic flow through simulation. The results demonstrate that (1) CAV achieve optimal control at specific positions within mixed traffic flow; (2) higher CAV penetration enhances TV-MPC performance; (3) dispersed CAV distributions improve control effectiveness; and (4) TV-MPC excels in scenarios with significant disturbances.<\/jats:p>","DOI":"10.3390\/systems13060481","type":"journal-article","created":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T05:52:47Z","timestamp":1750139567000},"page":"481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Analysis of the Impact for Mixed Traffic Flow Based on the Time-Varying Model Predictive Control"],"prefix":"10.3390","volume":"13","author":[{"given":"Rongjun","family":"Cheng","sequence":"first","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoli","family":"Lou","sequence":"additional","affiliation":[{"name":"Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9852-5902","authenticated-orcid":false,"given":"Qi","family":"Wei","sequence":"additional","affiliation":[{"name":"College of International Economics and Trade, Ningbo University of Finance and Economics, Ningbo 315175, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.trb.2016.05.007","article-title":"Parsimonious shooting heuristic for trajectory design of connected automated traffic part I: Theoretical analysis with generalized time geography","volume":"95","author":"Zhou","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1631\/jzus.A2300026","article-title":"Bifurcation control of solid angle car-following model through a time-delay feedback method","volume":"24","author":"Ji","year":"2023","journal-title":"J. Zhejiang Univ.-Sci. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"103989","DOI":"10.1016\/j.trc.2022.103989","article-title":"Analysis of the impact of maximum platoon size of CAVs on mixed traffic flow: An analytical and simulation method","volume":"147","author":"Yao","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7624","DOI":"10.1109\/TITS.2025.3559916","article-title":"Intelligent Eco-Driving Control for Urban CAVs Using a Model-Based Controller Assisted Deep Reinforcement Learning","volume":"26","author":"Li","year":"2025","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/MWC.005.2300030","article-title":"Convergence of communications, control, and machine learning for secure and autonomous vehicle navigation","volume":"31","author":"Zeng","year":"2024","journal-title":"IEEE Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"102954","DOI":"10.1016\/j.trc.2020.102954","article-title":"Simulating the effectiveness of wave dissipation by FollowerStopper autonomous vehicles","volume":"123","author":"Cummins","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5309","DOI":"10.1109\/TNNLS.2021.3071959","article-title":"A reinforcement learning-based vehicle platoon control strategy for reducing energy consumption in traffic oscillations","volume":"32","author":"Li","year":"2021","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_8","first-page":"2327","article-title":"Implementation and experimental validation of data-driven predictive control for dissipating stop-and-go waves in mixed traffic","volume":"11","author":"Wang","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6463","DOI":"10.1109\/TITS.2022.3215172","article-title":"A longitudinal velocity CF-MPC model for connected and automated vehicle platooning","volume":"24","author":"Wen","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Luo, W., Li, X., Hu, J., and Hu, W. (2023). Modeling and optimization of connected and automated vehicle platooning cooperative control with measurement errors. Sensors, 23.","DOI":"10.3390\/s23219006"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.apm.2023.04.010","article-title":"Longitudinal car-following control strategy integrating predictive collision risk","volume":"121","author":"Li","year":"2023","journal-title":"Appl. Math. Model."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"17948","DOI":"10.1109\/JIOT.2025.3540215","article-title":"Uncertainty-Aware Dynamics Modeling and Data-Driven Robust Predictive Control for Mixed Vehicle Platoon","volume":"12","author":"Lyu","year":"2025","journal-title":"IEEE Internet Things J."},{"key":"ref_13","first-page":"189","article-title":"A real-time adaptive signal control method for multi-intersections in mixed connected vehicle environments","volume":"1","author":"Li","year":"2025","journal-title":"J. Zhejiang Univ.-Sci. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103219","DOI":"10.1016\/j.trb.2025.103219","article-title":"A novel hierarchical perimeter control method for road networks considering boundary congestion in a mixed CAV and HV traffic environment","volume":"195","author":"Ding","year":"2025","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"59225","DOI":"10.1109\/ACCESS.2020.2982702","article-title":"DDPG-based decision-making strategy of adaptive cruising for heavy vehicles considering stability","volume":"8","author":"Sun","year":"2020","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"114030","DOI":"10.1016\/j.apenergy.2019.114030","article-title":"Jointly dampening traffic oscillations and improving energy consumption with electric, connected and automated vehicles: A reinforcement learning based approach","volume":"257","author":"Qu","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1109\/TAC.2021.3049335","article-title":"Probabilistic model predictive safety certification for learning-based control","volume":"67","author":"Wabersich","year":"2021","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"104600","DOI":"10.1016\/j.trc.2024.104600","article-title":"Learning-based modeling of human-autonomous vehicle interaction for improved safety in mixed-vehicle platooning control","volume":"162","author":"Wang","year":"2024","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"104019","DOI":"10.1016\/j.trc.2023.104019","article-title":"A deep reinforcement learning based distributed control strategy for connected automated vehicles in mixed traffic platoon","volume":"148","author":"Shi","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2404","DOI":"10.1109\/TITS.2014.2316016","article-title":"Sampled-data cooperative adaptive cruise control of vehicles with sensor failures","volume":"15","author":"Guo","year":"2014","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Akram, M.A., Liu, P., Wang, Y., and Qian, J. (2018). Gnss positioning accuracy enhancement based on robust statistical mm estimation theory for ground vehicles in challenging environments. Appl. Sci., 8.","DOI":"10.3390\/app8060876"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1850135","DOI":"10.1142\/S0217979218501357","article-title":"A spring-mass-damper system dynamics-based driver-vehicle integrated model for representing heterogeneous traffic","volume":"32","author":"Munigety","year":"2018","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1950025","DOI":"10.1142\/S0217979219500255","article-title":"Conformity and stability analysis of a modified spring\u2013mass\u2013damper system dynamics-based car-following model","volume":"33","author":"Munigety","year":"2019","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wildhagen, S., Pezzutto, M., Schenato, L., and Allg\u00f6wer, F. (2022, January 6\u20139). Self-triggered MPC robust to bounded packet loss via a min-max approach. Proceedings of the 2022 IEEE 61st Conference on Decision and Control (CDC), Cancun, Mexico.","DOI":"10.1109\/CDC51059.2022.9992581"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2625","DOI":"10.1109\/TAC.2022.3163110","article-title":"Robust stability analysis of a simple data-driven model predictive control approach","volume":"68","author":"Bongard","year":"2022","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"104038","DOI":"10.1016\/j.trc.2023.104038","article-title":"Model predictive control policy design, solutions, and stability analysis for longitudinal vehicle control considering shockwave damping","volume":"148","author":"Wang","year":"2023","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1109\/TAC.2022.3171410","article-title":"Model predictive control for linear uncertain systems using integral quadratic constraints","volume":"68","author":"Schwenkel","year":"2022","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"14344","DOI":"10.1016\/j.ifacol.2020.12.1381","article-title":"Safety-extended explicit MPC for autonomous truck platooning on varying road conditions","volume":"53","author":"Schirrer","year":"2020","journal-title":"IFAC-PapersOnLine"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"17354","DOI":"10.1109\/TITS.2022.3153307","article-title":"Distributed model predictive control for vehicle platoon with mixed disturbances and model uncertainties","volume":"23","author":"Hu","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_30","first-page":"100467","article-title":"Connected and automated vehicle platoon maintenance under communication failures","volume":"35","author":"Liu","year":"2022","journal-title":"Veh. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2760","DOI":"10.1109\/TCST.2023.3288636","article-title":"DeeP-LCC: Data-enabled predictive leading cruise control in mixed traffic flow","volume":"31","author":"Wang","year":"2023","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.trc.2016.07.007","article-title":"Influence of connected and autonomous vehicles on traffic flow stability and throughput","volume":"71","author":"Talebpour","year":"2016","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"14563","DOI":"10.1109\/TVT.2024.3412992","article-title":"STdi4DMPC: Distributed Model Predictive Control for Connected and Automated Truck Platoon with Mixed Traffic Flow Based on Spatiotemporal Trajectory Prediction","volume":"73","author":"Li","year":"2024","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103381","DOI":"10.1016\/j.trd.2022.103381","article-title":"Connected automated vehicle impacts in Southern California part-II: VMT, emissions, and equity","volume":"109","author":"Jiang","year":"2022","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Liu, M., Li, Y., Liu, X., Chen, Y., and Hao, R. (2025). An Integrated Optimization Framework for Connected and Automated Vehicles and Traffic Signals in Urban Networks. Systems, 13.","DOI":"10.3390\/systems13040224"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"103911","DOI":"10.1016\/j.trd.2023.103911","article-title":"Carbon emission impacts of longitudinal disturbance on low-penetration connected automated vehicle environments","volume":"123","author":"Zong","year":"2023","journal-title":"Transp. Res. Part D Transp. Environ."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"15951","DOI":"10.1109\/TITS.2022.3146612","article-title":"Cooperative formation of autonomous vehicles in mixed traffic flow: Beyond platooning","volume":"23","author":"Li","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Chang, Q., and Chen, H. (2024). Enhancing Freeway Traffic Capacity: The Impact of Autonomous Vehicle Platooning Intensity. Appl. Sci., 14.","DOI":"10.3390\/app14041362"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.trb.2017.09.022","article-title":"A mixed traffic capacity analysis and lane management model for connected automated vehicles: A Markov chain method","volume":"106","author":"Ghiasi","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.trb.2017.01.017","article-title":"Towards vehicle automation: Roadway capacity formulation for traffic mixed with regular and automated vehicles","volume":"100","author":"Chen","year":"2017","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"128557","DOI":"10.1016\/j.physa.2023.128557","article-title":"A mixed capacity analysis and lane management model considering platoon size and intensity of CAVs","volume":"615","author":"Jiang","year":"2023","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"129606","DOI":"10.1016\/j.physa.2024.129606","article-title":"A time-varying driving style oriented model predictive control for smoothing mixed traffic flow","volume":"637","author":"Lou","year":"2024","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_43","first-page":"485","article-title":"Guide to fuel consumption analyses for urban traffic management","volume":"21","author":"Bowyer","year":"1984","journal-title":"Syd. Aust. Aust. Road Res. Board"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/13\/6\/481\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:53:21Z","timestamp":1760032401000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/13\/6\/481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,17]]},"references-count":43,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["systems13060481"],"URL":"https:\/\/doi.org\/10.3390\/systems13060481","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,17]]}}}