{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:36:23Z","timestamp":1772757383744,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program in China","award":["2018YFB1600600"],"award-info":[{"award-number":["2018YFB1600600"]}]},{"name":"MOE (Ministry of Education in China) Project of Humanities and Social Sciences","award":["20YJAZH083"],"award-info":[{"award-number":["20YJAZH083"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51878161"],"award-info":[{"award-number":["51878161"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Connected vehicle (CV) technologies are changing the form of traditional traffic models. In the CV driving environment, abundant and accurate information is available to vehicles, promoting the development of control strategies and models. Under these circumstances, this paper proposes a bidirectional vehicles information structure (BDVIS) by making use of the acceleration information of one preceding vehicle and one following vehicle to improve the car-following models. Then, we deduced the derived multiple vehicles information structure (DMVIS), including historical movement information of multiple vehicles, without the acceleration information. Next, the paper embeds the four kinds of basic car-following models into the framework to investigate the stability condition of two structures under the small perturbation of traffic flow and explored traffic response properties with different proportions of forward-looking or backward-looking terms. Under the open boundary condition, simulations on a single lane are conducted to validate the theoretical analysis. The results indicated that BDVIS and the DMVIS perform better than the original car-following model in improving the traffic flow stability, but that they have their own advantages for differently positioned vehicles in the platoon. Moreover, increasing the proportions of the preceding and following vehicles presents a benefit to stability, but if traffic is stable, an increase in any of the parameters would extend the influence time, which reveals that neither \u03b21 or \u03b22 is the biggest the best for the traffic.<\/jats:p>","DOI":"10.3390\/s21248322","type":"journal-article","created":{"date-parts":[[2021,12,14]],"date-time":"2021-12-14T01:22:05Z","timestamp":1639444925000},"page":"8322","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Controlling the Connected Vehicle with Bi-Directional Information: Improved Car-Following Models and Stability Analysis"],"prefix":"10.3390","volume":"21","author":[{"given":"Ziwei","family":"Yi","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"},{"name":"Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenqi","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"},{"name":"Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Qu","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"},{"name":"Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"},{"name":"Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peipei","family":"Mao","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"},{"name":"Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Ran","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 211189, China"},{"name":"Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University, Nanjing 211189, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.trb.2015.02.011","article-title":"An anisotropic continuum model considering bi-directional information impact","volume":"75","author":"Zheng","year":"2015","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.trc.2019.05.005","article-title":"A mixed traffic speed harmonization model with connected autonomous vehicles","volume":"104","author":"Ghiasi","year":"2019","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_3","first-page":"242","article-title":"Cooperative adaptive cruise control for connected autonomous vehicles by factoring communication-related constraints","volume":"38","author":"Wang","year":"2019","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2050071","DOI":"10.1142\/S0217984920500712","article-title":"Lattice hydrodynamic modeling with continuous self-delayed traffic flux integral and vehicle overtaking effect","volume":"34","author":"Zhai","year":"2020","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1950223","DOI":"10.1142\/S0217984919502233","article-title":"Nonlinear analysis of a new two-lane lattice hydrodynamic model accounting for \u201cbackward looking\u201d effect and relative flow information","volume":"33","author":"Qi","year":"2019","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"122362","DOI":"10.1016\/j.physa.2019.122362","article-title":"Nonlinear analysis for a modified continuum model considering electronic throttle (ET) and backward looking effect","volume":"535","author":"Jiao","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"122988","DOI":"10.1016\/j.physa.2019.122988","article-title":"An extended macro model accounting for the driver\u2019s timid and aggressive attributions and bounded rationality","volume":"540","author":"Wang","year":"2020","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_8","first-page":"100","article-title":"Multi anticipative bidirectional macroscopic traffic model considering cooperative driving strategy","volume":"5","author":"Ngoduy","year":"2017","journal-title":"Transp. B"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1007\/s11071-017-3908-0","article-title":"An improved lattice hydrodynamic model considering the \u201cbackward looking\u201d effect and the traffic interruption probability","volume":"91","author":"Jiang","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1007\/s11071-014-1265-9","article-title":"A new car-following model with consideration of inter-vehicle communication","volume":"76","author":"Tang","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.cnsns.2015.11.011","article-title":"An improved car-following model considering relative velocity fluctuation","volume":"36","author":"Yu","year":"2016","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1016\/j.physa.2017.11.133","article-title":"A new car-following model for autonomous vehicles flow with mean expected velocity field","volume":"492","year":"2018","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1016\/j.physa.2016.12.071","article-title":"An improved car-following model with multiple preceding cars\u2019 velocity fluctuation feedback","volume":"471","author":"Guo","year":"2017","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/tse\/tdaa024","article-title":"Traffic flow cellular automaton model with bi-directional information in an open boundary condition","volume":"3","author":"Zheng","year":"2021","journal-title":"Transp. Saf. Environ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1287\/opre.7.1.86","article-title":"Traffic dynamics: Analysis of stability in car following","volume":"7","author":"Herman","year":"1959","journal-title":"Oper. Res."},{"key":"ref_16","first-page":"016112","article-title":"Effect of looking at the car that follows in an optimal velocity model of traffic flow","volume":"65","author":"Nakayama","year":"2002","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_17","first-page":"6","article-title":"Dynamical model of a cooperative driving system for freeway traffic","volume":"68","author":"Hasebe","year":"2003","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1140\/epjb\/e2007-00014-x","article-title":"Effect of looking backward on traffic flow in a cooperative driving car following model","volume":"54","author":"Ge","year":"2006","journal-title":"Eur. Phys. J. B"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"011016","DOI":"10.1115\/1.4007310","article-title":"A new extended multiple car-following model considering the backward-looking effect on traffic flow","volume":"8","author":"Yang","year":"2013","journal-title":"J. Comput. Nonlinear Dyn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.physa.2010.10.016","article-title":"Effect of looking backward on traffic flow in an extended multiple car-following model","volume":"390","author":"Sun","year":"2011","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"126372","DOI":"10.1016\/j.physa.2021.126372","article-title":"Multi-anticipative bi-directional visual field traffic flow models in the connected vehicle environment","volume":"584","author":"Hu","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"125538","DOI":"10.1016\/j.physa.2020.125538","article-title":"Dynamics of traffic flow affected by the future motion of multiple preceding vehicles under vehicle-connected environment: Modeling and stabilization","volume":"565","author":"Zhang","year":"2021","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jiao, S., Zhang, S., Zhou, B., Zhang, Z., and Xue, L. (2020). An extended car-following model considering the drivers\u2019 characteristics under a V2V communication environment. Sustainability, 12.","DOI":"10.3390\/su12041552"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2092","DOI":"10.1016\/j.cjph.2017.08.027","article-title":"An extended car-following model based on visual angle and backward looking effect","volume":"55","author":"Hou","year":"2017","journal-title":"Chin. J. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.physa.2019.03.099","article-title":"An extended car-following model considering driver\u2019s sensory memory and the backward looking effect","volume":"525","author":"Chen","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"105221","DOI":"10.1016\/j.cnsns.2020.105221","article-title":"An improved car-following model accounting for the time-delayed velocity difference and backward looking effect","volume":"85","author":"Ma","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"034501","DOI":"10.1088\/1674-1056\/abc3b3","article-title":"Modeling and analysis of car-following behavior considering backward-looking effect","volume":"30","author":"Ma","year":"2021","journal-title":"Chin. Phys. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1140\/epjb\/e2012-30688-6","article-title":"Safe distance car-following model including backward-looking and its stability analysis","volume":"86","author":"Yang","year":"2013","journal-title":"Eur. Phys. J. B"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.laa.2015.04.010","article-title":"Distributional chaos for the Forward and Backward Control traffic model","volume":"479","author":"Barrachina","year":"2015","journal-title":"Linear Algebra Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.trb.2020.11.009","article-title":"On string stability of a mixed and heterogeneous traffic flow: A unifying modelling framework","volume":"144","author":"Montanino","year":"2021","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.trb.2021.01.009","article-title":"From homogeneous to heterogeneous traffic flows: Lp String stability under uncertain model parameters","volume":"146","author":"Montanino","year":"2021","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1109\/TITS.2015.2505674","article-title":"Cooperative Car-Following Control: Distributed Algorithm and Impact on Moving Jam Features","volume":"17","author":"Wang","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3499","DOI":"10.1007\/s11771-020-4560-2","article-title":"An Intelligent Back-Looking Distance Driver Model and Stability Analysis for Connected and Automated Vehicles","volume":"27","author":"Yi","year":"2020","journal-title":"J. Cent. South Univ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1750090","DOI":"10.1142\/S0217984917500907","article-title":"An extended microscopic traffic flow model based on the spring-mass system theory","volume":"31","author":"Li","year":"2017","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Jin, P., Yang, D., Ran, B., Cebelak, M., and Walton, C. (2013). Bidirectional control characteristics of general motors and optimal velocity car-following models. Transp. Res. Rec., 110\u2013119.","DOI":"10.3141\/2381-13"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Du, W., Li, Y., and Zhang, J. (2021). Stability Analysis and Control of an Extended Car-Following Model under Honk Environment. Int. J. Intell. Transp. Syst. Res., 1\u201310.","DOI":"10.1007\/s13177-021-00267-0"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.physa.2014.10.063","article-title":"Stability analysis of an extended intelligent driver model and its simulations under open boundary condition","volume":"419","author":"Li","year":"2015","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.trb.2018.01.013","article-title":"Stability analysis methods and their applicability to car-following models in conventional and connected environments","volume":"109","author":"Sun","year":"2018","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1805","DOI":"10.1103\/PhysRevE.62.1805","article-title":"Congested traffic states in empirical observations and microscopic simulations","volume":"62","author":"Treiber","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Kesting, A., Treiber, M., Sch\u00f6nhof, M., Kranke, F., and Helbing, D. (2007). Jam-Avoiding Adaptive Cruise Control (ACC) and its Impact on Traffic Dynamics. Traffic Granul. Flow\u201905, Springer.","DOI":"10.1007\/978-3-540-47641-2_62"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1016\/j.trc.2007.12.004","article-title":"Adaptive cruise control design for active congestion avoidance","volume":"16","author":"Kesting","year":"2008","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_42","first-page":"4","article-title":"Full velocity difference model for a car-following theory","volume":"64","author":"Jiang","year":"2001","journal-title":"Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1016\/j.cnsns.2012.09.014","article-title":"Full velocity difference and acceleration model for a car-following theory","volume":"18","author":"Yu","year":"2013","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/j.trc.2014.09.001","article-title":"Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data","volume":"48","author":"Shladover","year":"2014","journal-title":"Transp. Res. Part C Emerg. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/24\/8322\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:46:30Z","timestamp":1760168790000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/24\/8322"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,13]]},"references-count":44,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["s21248322"],"URL":"https:\/\/doi.org\/10.3390\/s21248322","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,13]]}}}