AI Chat Paper
Discover the SciOpen Platform and Achieve Your Research Goals with Ease.
• Provides a holistic review of continuum models for traditional traffic.
• Reviews existing models for connected and automated vehicles considering empirical findings.
• Investigates potentials, limitations, and critical issues of various modeling frameworks.
• Revisits the applicability and significance of issues with the continuum framework.
• Discusses research needs for model development in the era of connected and automated driving.
Connected and automated vehicles (CAVs) are expected to reshape traffic flow dynamics and present new challenges and opportunities for traffic flow modeling. While numerous studies have proposed optimal modeling and control strategies for CAVs with various objectives (e.g., traffic efficiency and safety), there are uncertainties about the flow dynamics of CAVs in real-world traffic. The uncertainties are especially amplified for mixed traffic flows, consisting of CAVs and human-driven vehicles, where the implications can be significant from the continuum-modeling perspective, which aims to capture macroscopic traffic flow dynamics based on hyperbolic systems of partial differential equations. This paper aims to highlight and discuss some essential problems in continuum modeling of real-world freeway traffic flows in the era of CAVs. We first provide a select review of some existing continuum models for conventional human-driven traffic as well as the recent attempts for incorporating CAVs into the continuum-modeling framework. Wherever applicable, we provide new insights about the properties of existing models and revisit their implications for traffic flows of CAVs using recent empirical observations with CAVs and the previous discussions and debates in the literature. The paper then discusses some major problems inherent to continuum modeling of real-world (mixed) CAV traffic flows modeling by distinguishing between two major research directions: (a) modeling for explaining purposes, where making reproducible inferences about the physical aspects of macroscopic properties is of the primary interest, and (b) modeling for practical purposes, in which the focus is on the reliable predictions for operation and control. The paper proposes some potential solutions in each research direction and recommends some future research topics.
Abgrall, R., Karni, S., 2010. A comment on the computation of non-conservative products. J. Comput. Phys. 229, 2759-2763.
Ali, Y., Zheng, Z., Haque, M.M., Wang, M., 2019. A game theory-based approach for modelling mandatory lane-changing behaviour in a connected environment. Transport. Res. C Emerg. Technol. 106, 220-242.
Ali, Y., Zheng, Z., Haque, M.M., Yildirimoglu, M., Washington, S., 2020. Understanding the discretionary lane-changing behaviour in the connected environment. Accid. Anal. Prev. 137, 105463.
Ali, Y., Haque, M.M., Zheng, Z., Bliemer, M.C.J., 2021. Stop or go decisions at the onset of yellow light in a connected environment: a hybrid approach of decision tree and panel mixed logit model. Anal Meth Accid Res 31, 100165.
Ansorge, R., 1990. What does the entropy condition mean in traffic flow theory? Transp. Res. Part B Methodol. 24, 133-143.
Aw, A., Rascle, M., 2000. Resurrection of “second order” models of traffic flow. SIAM J. Appl. Math. 60, 916-938.
Aw, A., Klar, A., Rascle, M., Materne, T., 2002. Derivation of continuum traffic flow models from microscopic follow-the-leader models. SIAM J. Appl. Math. 63, 259-278.
Banks, J., 1991. The two-capacity phenomenon: some theoretical issues. Transport. Res. Rec. 1320, 234-241.
Bellomo, N., Dogbe, C., 2011. On the modeling of traffic and crowds: a survey of models, speculations, and perspectives. SIAM Rev. 53, 409-463.
Berg, P., Mason, A., Woods, A., 2000. Continuum approach to car-following models. Phys. Rev. E 61, 1056-1066.
Blandin, S., Work, D., Goatin, P., Piccoli, B., Bayen, A., 2011. A general phase transition model for vehicular traffic. SIAM J. Appl. Math. 71, 107-127.
Blandin, S., Argote, J., Bayen, A.M., Work, D.B., 2013. Phase transition model of non-stationary traffic flow: definition, properties and solution method. Transp. Res. Part B Methodol. 52, 31-55.
Bonzani, I., Mussone, L., 2002. Stochastic modelling of traffic flow. Math. Comput. Model. 36, 109-119.
Buli, J., Xing, Y., 2020. A discontinuous Galerkin method for the Aw-Rascle traffic flow model on networks. J. Comput. Phys. 406, 109183.
Calvert, S.C., Schakel, W.J., van Lint, J.W.C., 2017. Will automated vehicles negatively impact traffic flow? J. Adv. Transport., 1-17.
Can, A., Leclercq, L., Lelong, J., Botteldooren, D., 2010. Traffic noise spectrum analysis: dynamic modeling vs. experimental observations. Appl. Acoust. 71, 764-770.
Cao, Y., Kurganov, A., Liu, Y., Xin, R., 2022. Flux globalization based well-balanced path-conservative central-upwind schemes for shallow water models. J. Sci. Comput. 3, 95.
Cao, Y., Kurganov, A., Liu, Y., Zeitlin, V., 2023. Flux globalization based well-balanced path-conservative central-upwind scheme for two-layer thermal rotating shallow water equations. J. Comput. Phys. 474, 111790.
Cassidy, M.J., 1998. Bivariate relations in nearly stationary highway traffic. Transp. Res. Part B Methodol. 32, 49-59.
Castro Díaz, M.J., Kurganov, A., Morales de Luna, T., 2019. Path-conservative central-upwind schemes for nonconservative hyperbolic systems. ESAIM Math. Model. Numer. Anal. 53, 959-985.
Chalons, C., Goatin, P., 2008. Godunov scheme and sampling technique for computing phase transitions in traffic flow modeling. Interfaces Free Boundaries, 197-221.
Chanut, S., Buisson, C., 2003. Macroscopic model and its numerical solution for two-flow mixed traffic with different speeds and lengths. Transport. Res. Rec. 1852, 209-219.
Chen, J.Z., Shi, Z.K., Hu, Y.M., 2009. A relaxation scheme for a multi-class Lighthill-Whitham-Richards traffic flow model. J. Zhejiang Univ. - Sci. A 10, 1835-1844.
Chen, D., Laval, J.A., Ahn, S., Zheng, Z., 2012. Microscopic traffic hysteresis in traffic oscillations: a behavioral perspective. Transp. Res. Part B Methodol. 46, 1440-1453.
Chiarello, F.A., Goatin, P., 2018a. Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel. ESAIM Math. Model. Numer. Anal. 52, 163-180.
Chiarello, F.A., Goatin, P., 2018b. Non-local multi-class traffic flow models. Netw Heterog Medium 14, 371-387.
Chu, S., Kurganov, A., Mohammadian, S., Zheng, Z., 2022. Fifth-order a-weno path-conservative central-upwind scheme for behavioural non-equilibrium traffic models. Commun. Comput. Phys. 33, 692-732.
Ciuffo, B., Mattas, K., Makridis, M., Albano, G., Anesiadou, A., He, Y., et al., 2021. Requiem on the positive effects of commercial adaptive cruise control on motorway traffic and recommendations for future automated driving systems. Transport. Res. C Emerg. Technol. 130, 103305.
Colombo, R.M., 2002. A 2 × 2 hyperbolic traffic flow model. Math. Comput. Model. 35, 683-688.
Daganzo, C.F., 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transp. Res. Part B Methodol. 28, 269-287.
Daganzo, C.F., 1995. Requiem for second-order fluid approximations of traffic flow. Transp. Res. Part B Methodol. 29, 277-286.
Daganzo, C.F., 2002. A behavioral theory of multi-lane traffic flow. Part I: long homogeneous freeway sections. Transp. Res. Part B Methodol. 36, 131-158.
Daganzo, C.F., 2005. A variational formulation of kinematic waves: solution methods. Transp. Res. Part B Methodol. 39, 934-950.
Daganzo, C.F., 2006a. In traffic flow, cellular automata=kinematic waves. Transp. Res. Part B Methodol. 40, 396-403.
Daganzo, C.F., 2006b. On the variational theory of traffic flow: well-posedness, duality and applications. Netw Heterog Medium 1, 601-619.
Daganzo, C.F., Lin, W.H., Del Castillo, J.M., 1997. A simple physical principle for the simulation of freeways with special lanes and priority vehicles. Transp. Res. Part B Methodol. 31, 103-125.
Daganzo, C.F., Cassidy, M.J., Bertini, R.L., 1999. Possible explanations of phase transitions in highway traffic. Transport. Res. Part A Policy Pract 33, 365-379.
Dai, Y., Wang, C., Xie, Y., 2023. Explicitly incorporating surrogate safety measures into connected and automated vehicle longitudinal control objectives for enhancing platoon safety. Accid. Anal. Prev. 183, 106975.
Darbha, S., Rajagopal, K.R., 1999. Intelligent cruise control systems and traffic flow stability. Transport. Res. C Emerg. Technol. 7, 329-352.
Davis, L.C., 2004. Effect of adaptive cruise control systems on traffic flow. Phys. Rev. E - Stat. Nonlinear Soft Matter Phys. 69, 066110.
Del Castillo, J.M., 2001. Propagation of perturbations in dense traffic flow: a model and its implications. Transp. Res. Part B Methodol. 35, 367-389.
Del Castillo, J.M., 2012. Three new models for the flow–density relationship: derivation and testing for freeway and urban data. Transportmetrica 8, 443-465.
Del Castillo, J.M., Benítez, F.G., 1995a. On the functional form of the speed-density relationship—I: general theory. Transp. Res. Part B Methodol. 29, 373-389.
Del Castillo, J.M., Benítez, F.G., 1995b. On the functional form of the speed-density relationship—II: empirical investigation. Transp. Res. Part B Methodol. 29, 391-406.
Del Castillo, J.M., Pintado, P., Benitez, F.G., 1994. The reaction time of drivers and the stability of traffic flow. Transp. Res. Part B Methodol. 28, 35-60.
Delis, A.I., Nikolos, I.K., Papageorgiou, M., 2014. High-resolution numerical relaxation approximations to second-order macroscopic traffic flow models. Transport. Res. C Emerg. Technol. 44, 318-349.
Delis, A.I., Nikolos, I.K., Papageorgiou, M., 2015. Macroscopic traffic flow modeling with adaptive cruise control: development and numerical solution. Comput. Math. Appl. 70, 1921-1947.
Delis, A.I., Nikolos, I.K., Papageorgiou, M., 2018. A macroscopic multi-lane traffic flow model for ACC/CACC traffic dynamics. Transport. Res. Rec. 2672, 178-192.
Fan, S., Seibold, B., 2013. Data-fitted first-order traffic models and their second-order generalizations. Transport. Res. Rec. 2391, 32-43.
Fuller, R., McHugh, C., Pender, S., 2008. Task difficulty andrisk inthedetermination ofdriver behaviour. Eur. Rev. Appl. Psychol. 58, 13-21.
Gan, Q.J., Jin, W.L., 2013. Validation of a macroscopic lane-changing model. Transport. Res. Rec. 2391, 113-123.
Garavello, M., Goatin, P., 2011. The Aw–Rascle traffic model with locally constrained flow. J. Math. Anal. Appl. 378, 634-648.
Garavello, M., Piccoli, B., 2006b. Traffic flow on a road network using the aw–rascle model. Commun. Part. Differ. Equ. 31, 243-275.
Gazis, D.C., Herman, R., Rothery, R.W., 1961. Nonlinear follow-the-leader models of traffic flow. Oper. Res. 9, 545-567.
Goatin, P., 2006. The Aw-Rascle vehicular traffic flow model with phase transitions. Math. Comput. Model. 44, 287-303.
Goatin, P., Scialanga, S., 2016. Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity. Netw Heterog Medium 11, 107-121.
Greenberg, J.M., 2002. Extensions and amplifications of a traffic model of aw and rascle. SIAM J. Appl. Math. 62, 729-745.
Guanetti, J., Kim, Y., Borrelli, F., 2018. Control of connected and automated vehicles: state of the art and future challenges. Annu. Rev. Control 45, 18-40.
Gunter, G., Gloudemans, D., Stern, R.E., McQuade, S., Bhadani, R., Bunting, M., et al., 2021. Are commercially implemented adaptive cruise control systems string stable? IEEE Trans. Intell. Transport. Syst. 22, 6992-7003.
Gupta, A.K., Katiyar, V.K., 2006. A new anisotropic continuum model for traffic flow. Phys. Stat. Mech. Appl. 368, 551-559.
Gupta, A.K., Katiyar, V.K., 2007. A new multi-class continuum model for traffic flow. Transportmetrica 3, 73-85.
Hall, F., Agyemang-Duah, K., 1991. Freeway capacity drop and the definition of capacity. Transport. Res. Rec. 1320.
Han, Y., Wang, M., He, Z., Li, Z., Wang, H., Liu, P., 2021a. A linear Lagrangian model predictive controller of macro- and micro- variable speed limits to eliminate freeway jam waves. Transport. Res. C Emerg. Technol. 128, 103121.
Han, Y., Yu, H., Li, Z., Xu, C., Ji, Y., Liu, P., 2021b. An optimal control-based vehicle speed guidance strategy to improve traffic safety and efficiency against freeway jam waves. Accid. Anal. Prev. 163, 106429.
Helbing, D., 1996a. Derivation and empirical validation of a refined traffic flow model. Phys. Stat. Mech. Appl. 233, 253-282.
Helbing, D., 1996b. Gas-kinetic derivation of Navier-Stokes-like traffic equations. Phys. Rev. E 53, 2366-2381.
Helbing, D., 2001. Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067-1141.
Helbing, D., 2009. Reply to comment on “On the controversy around Daganzo's requiem for and Aw-Rascle’s resurrection of second-order traffic flow models” by HM Zhang. Eur. Phys. J. B 69, 569-570.
Helbing, D., Johansson, A.F., 2009. On the controversy around daganzo's requiem for and aw–rascle’s resurrection of second-order traffic flow models. Eur. Phys. J. B 69, 549-562.
Helbing, D., Tilch, B., 1998. Generalized force model of traffic dynamics. Phys. Rev. E 58, 133-138.
Helbing, D., Treiber, M., 1999. Numerical simulation of macroscopic traffic equations. Comput. Sci. Eng. 1, 89-98.
Helbing, D., Hennecke, A., Treiber, M., 1999. Phase diagram of traffic states in the presence of inhomogeneities. Phys. Rev. Lett. 82, 4360-4363.
Helbing, D., Hennecke, A., Shvetsov, V., Treiber, M., 2001. MASTER: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transp. Res. Part B Methodol. 35, 183-211.
Helly, W., 1959. Simulation of bottlenecks in single-lane traffic flow. Transport. Res. Rec., 207-238.
Hicks, D.J., 2018. The safety of autonomous vehicles: lessons from philosophy of science. IEEE Technol. Soc. Mag. 37, 62-69.
Hoogendoorn, S.P., Bovy, P.H.L., 1998. Modeling multiple user-class traffic. Transport. Res. Rec. 1644, 57-69.
Hoogendoorn, S.P., Bovy, P.H.L., 2000. Continuum modeling of multiclass traffic flow. Transp. Res. Part B Methodol. 34, 123-146.
Hoogendoorn, S.P., Bovy, P.L., 2001. State-of-the-art of vehicular traffic flow modelling. Proc. Inst. Mech. Eng. Part I J Syst Contr Eng 215, 283-303.
Hu, X., Zheng, Z., Chen, D., Zhang, X., Sun, J., 2022. Processing, assessing, and enhancing the Waymo autonomous vehicle open dataset for driving behavior research. Transport. Res. C Emerg. Technol. 134, 103490.
Hu, X., Zheng, Z., Chen, D., Sun, J., 2023. Autonomous vehicle's impact on traffic: empirical evidence from waymo open dataset and implications from modelling. IEEE Trans. Intell. Transport. Syst. 24, 6711-6724.
Huang, K., Du, Q., 2022. Stability of a nonlocal traffic flow model for connected vehicles. SIAM J. Appl. Math. 82, 221-243.
Jabari, S.E., Liu, H.X., 2012. A stochastic model of traffic flow: theoretical foundations. Transp. Res. Part B Methodol. 46, 156-174.
Jiang, R., Wu, Q., Zhu, Z., 2001. Full velocity difference model for a car-following theory. Phys. Rev. E - Stat. Nonlinear Soft Matter Phys. 64, 017101.
Jiang, R., Wu, Q.S., Zhu, Z.J., 2002. A new continuum model for traffic flow and numerical tests. Transp. Res. Part B Methodol. 36, 405-419.
Jin, W.L., 2010. A kinematic wave theory of lane-changing traffic flow. Transp. Res. Part B Methodol. 44, 1001-1021.
Jin, W.L., 2012. A kinematic wave theory of multi-commodity network traffic flow. Transp. Res. Part B Methodol. 46, 1000-1022.
Jin, W.L., 2013. A multi-commodity Lighthill-Whitham-Richards model of lane-changing traffic flow. Transp. Res. Part B Methodol. 57, 361-377.
Jin, W.L., 2016. On the equivalence between continuum and car-following models of traffic flow. Transp. Res. Part B Methodol. 93, 543-559.
Jin, W.L., 2017a. Kinematic wave models of lane-drop bottlenecks. Transp. Res. Part B Methodol. 105, 507-522.
Jin, W.L., 2017b. A first-order behavioral model of capacity drop. Transp. Res. Part B Methodol. 105, 438-457.
Jin, W.L., Laval, J., 2018. Bounded acceleration traffic flow models: a unified approach. Transp. Res. Part B Methodol. 111, 1-18.
Jin, W., Yang, H., 2013. The lighthill-whitham-richards model for a platoon of vehicles. Transport. Res. Rec. 13, 1097.
Jin, W., Zhang, H.M., 2001. Solving the Payne-Whitham trac flow model as a hyperbolic system of conservation laws with relaxation. Transport. Sci. 1, 24.
Jin, Y., Yao, Z., Han, J., Hu, L., Jiang, Y., 2022. Variable cell transmission model for mixed traffic flow with connected automated vehicles and human-driven vehicles. J. Adv. Transport., 1-15.
Karafyllis, I., Theodosis, D., Papageorgiou, M., 2022. Analysis and control of a non-local PDE traffic flow model. Int. J. Control 95, 660-678.
Keimer, A., Pflug, L., 2017. Existence, uniqueness and regularity results on nonlocal balance laws. J. Differ. Equ. 263, 4023-4069.
Kerner, B.S., 2016. Failure of classical traffic flow theories: stochastic highway capacity and automatic driving. Phys. Stat. Mech. Appl. 450, 700-747.
Kerner, B.S., Konhäuser, P., 1993. Cluster effect in initially homogeneous traffic flow. Phys. Rev. E 48, R2335-R2338.
Kesting, A., Treiber, M., 2008. How reaction time, update time, and adaptation time influence the stability of traffic flow. Comput. Aided Civ. Infrastruct. Eng. 23, 125-137.
Khoshyaran, M.M., Lebacque, J.P., 2015. Capacity drop and traffic hysteresis as a consequence of bounded acceleration. IFAC-PapersOnLine 48, 766-771.
Kim, T., Zhang, H.M., 2008. A stochastic wave propagation model. Transp. Res. Part B Methodol. 42, 619-634.
Ko, S.M., Ji, Y.G., 2018. How we can measure the non-driving-task engagement in automated driving: comparing flow experience and workload. Appl. Ergon. 67, 237-245.
Kontorinaki, M., Spiliopoulou, A., Roncoli, C., Papageorgiou, M., 2017. First-order traffic flow models incorporating capacity drop: overview and real-data validation. Transp. Res. Part B Methodol. 106, 52-75.
Kotsialos, A., Papageorgiou, M., Diakaki, C., Pavlis, Y., Middelham, F., 2002. Traffic flow modeling of large-scale motorway networks using the macroscopic modeling tool METANET. IEEE Trans. Intell. Transport. Syst. 3, 282-292.
Kurganov, A., Polizzi, A., 2009. Non-oscillatory central schemes for traffic flow models with Arrhenius look-ahead dynamics. Netw Heterog Medium 4, 431-451.
Laurent-Brouty, N., Costeseque, G., Goatin, P., 2021. A macroscopic traffic flow model accounting for bounded acceleration. SIAM J. Appl. Math. 81, 173-189.
Laval, J.A., 2011. Hysteresis in traffic flow revisited: an improved measurement method. Transp. Res. Part B Methodol. 45, 385-391.
Laval, J.A., Daganzo, C.F., 2006. Lane-changing in traffic streams. Transp. Res. Part B Methodol. 40, 251-264.
Laval, J.A., Leclercq, L., 2010. A mechanism to describe the formation and propagation of stop-and-go waves in congested freeway traffic. Philos Trans A Math Phys Eng Sci 368, 4519-4541.
Lebacque, J.P., 1997. A finite acceleration scheme for first order macroscopic traffic flow models. IFAC Proc 30, 787-792.
Lebacque, J.P., Khoshyaran, M.M., 2013. A variational formulation for higher order macroscopic traffic flow models of the GSOM family. Transp. Res. Part B Methodol. 57, 245-265.
Lebacque, J.P., Mammar, S., Haj-Salem, H., 2007a. The Aw-Rascle and Zhang's model: vacuum problems, existence and regularity of the solutions of the Riemann problem. Transp. Res. Part B Methodol. 41, 710-721.
Leclercq, L., 2007. Bounded acceleration close to fixed and moving bottlenecks. Transp. Res. Part B Methodol. 41, 309-319.
Leclercq, L., Laval, J.A., Chiabaut, N., 2011. Capacity drops at merges: an endogenous model. Transp. Res. Part B Methodol. 45, 1302-1313.
Leo, C.J., Pretty, R.L., 1992. Numerical simulation of macroscopic continuum traffic models. Transp. Res. Part B Methodol. 26, 207-220.
LeVeque, R.J., 2002. Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge.
Li, X., 2022. Trade-off between safety, mobility and stability in automated vehicle following control: an analytical method. Transp. Res. Part B Methodol. 166, 1-18.
Li, L., Chen, X., 2017. Vehicle headway modeling and its inferences in macroscopic/microscopic traffic flow theory: a survey. Transport. Res. C Emerg. Technol. 76, 170-188.
Li, D., Li, T., 2011. Shock formation in a traffic flow model with Arrhenius look-ahead dynamics. Netw Heterog Medium 6, 681-694.
Li, P.Y., Shrivastava, A., 2002. Traffic flow stability induced by constant time headway policy for adaptive cruise control vehicles. Transport. Res. C Emerg. Technol. 10, 275-301.
Li, J., Zhang, H.M., 2011. Fundamental diagram of traffic flow. Transport. Res. Rec. 2260, 50-59.
Li, J., Zhang, H.M., 2013. The variational formulation of a non-equilibrium traffic flow model: theory and implications. Transp. Res. Part B Methodol. 57, 314-325.
Li, Y., Li, Z., Wang, H., Wang, W., Xing, L., 2017. Evaluating the safety impact of adaptive cruise control in traffic oscillations on freeways. Accid. Anal. Prev. 104, 137-145.
Li, T., Chen, D., Zhou, H., Laval, J., Xie, Y., 2021. Car-following behavior characteristics of adaptive cruise control vehicles based on empirical experiments. Transp. Res. Part B Methodol. 147, 67-91.
Li, J., Chen, D., Zhang, M., 2022a. Equilibrium modeling of mixed autonomy traffic flow based on game theory. Transp. Res. Part B Methodol. 166, 110-127.
Li, T., Chen, D., Zhou, H., Xie, Y., Laval, J., 2022b. Fundamental diagrams of commercial adaptive cruise control: worldwide experimental evidence. Transport. Res. C Emerg. Technol. 134, 103458.
Lighthill, W., 1955. On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. Lond. A 229, 317-345.
Liu, X., Mohammadian, A., Kurganov, A., Infante Sedano, J.A., 2015. Well-balanced central-up wind scheme for a fully coupled shallow water system modeling flows over erodible bed. J. Comput. Phys. 300, 202-218.
Logghe, S., Immers, L.H., 2008. Multi-class kinematic wave theory of traffic flow. Transp. Res. Part B Methodol. 42, 523-541.
Lu, X.Y., Varaiya, P., Horowitz, R., 2009. Fundamental diagram modelling and analysis based NGSIM data. IFAC Proc 42, 367-374.
Mahmassani, H.S., 2016. 50th anniversary invited article—autonomous vehicles and connected vehicle systems: flow and operations considerations. Transport. Sci. 50, 1140-1162.
Mammar, S., Lebacque, J.P., Salem, H.H., 2009. Riemann problem resolution and Godunov scheme for the aw-rascle-Zhang model. Transport. Sci. 43, 531-545.
Mannering, F., Bhat, C.R., Shankar, V., Abdel-Aty, M., 2020. Big data, traditional data and the tradeoffs between prediction and causality in highway-safety analysis. Anal Meth Accid Res 25, 100113.
Marques Jr., W., Méndez, A.R., 2013. On the kinetic theory of vehicular traffic flow: chapman–Enskog expansion versus Grad's moment method. Phys. Stat. Mech. Appl. 392, 3430-3440.
Maso, G.D., Lefloch, P.G., Murat, F., 1995. Definition and weak stability of nonconservative products. J. Math. Pure Appl. 74, 483-548.
Messmer, A., Papageorgiou, M., 1990. Metanet: a macroscopic simulation program for motorway networks. Traffic Eng. Control 31, 466-470.
Milanés, V., Shladover, S.E., 2014. Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data. Transport. Res. C Emerg. Technol. 48, 285-300.
Milanés, V., Shladover, S.E., 2016. Handling cut-In vehicles in strings of cooperative adaptive cruise control vehicles. J Intell Transp Syst 20, 178-191.
Mohammadian, S., Van Wageningen-Kessels, F., 2018. Improved numerical method for aw-rascle type continuum traffic flow models. Transport. Res. Rec. 2672, 262-276.
Mohammadian, S., Haque, M.M., Zheng, Z., Bhaskar, A., 2021a. Integrating safety into the fundamental relations of freeway traffic flows: a conflict-based safety assessment framework. Anal Meth Accid Res 32, 100187.
Mohammadian, S., Moghaddam, A.M., Sahaf, A., 2021b. On the performance of HLL, HLLC, and Rusanov solvers for hyperbolic traffic models. Comput. Fluids 231, 105161.
Mohammadian, S., Zheng, Z., Haque, M.M., Bhaskar, A., 2021c. Performance of continuum models for realworld traffic flows: comprehensive benchmarking. Transp. Res. Part B Methodol. 147, 132-167.
Mohammadian, S., Zheng, Z., Haque, M., Bhaskar, A., 2023. NET-RAT: non-equilibrium traffic model based on risk allostasis theory. Transport. Res. Part A Policy Pract 174, 103731.
Morando, M.M., Tian, Q., Truong, L.T., Vu, H.L., 2018. Studying the safety impact of autonomous vehicles using simulation-based surrogate safety measures. J. Adv. Transport. 2018, 6135183.
Naujoks, F., Höfling, S., Purucker, C., Zeeb, K., 2018. From partial and high automation to manual driving: relationship between non-driving related tasks, drowsiness and take-over performance. Accid. Anal. Prev. 121, 28-42.
Nelson, P., Sopasakis, A., 1998. The prigogine-herman kinetic model predicts widely scattered traffic flow data at high concentrations. Transp. Res. Part B Methodol. 32, 589-604.
Newell, G.F., 1962. Theories of instability in dense highway traffic. J. Oper. Res. Soc. Jpn. 5, 9-54.
Newell, G.F., 1998. A moving bottleneck. Transp. Res. Part B Methodol. 32, 531-537.
Newell, G.F., 2002. A simplified car-following theory: a lower order model. Transp. Res. Part B Methodol. 36, 195-205.
Ngoduy, D., 2012a. Application of gas-kinetic theory to modelling mixed traffic of manual and ACC vehicles. Transportmetrica 8, 43-60.
Ngoduy, D., 2012b. Effect of driver behaviours on the formation and dissipation of traffic flow instabilities. Nonlinear Dynam. 69, 969-975.
Ngoduy, D., 2013a. Instability of cooperative adaptive cruise control traffic flow: a macroscopic approach. Commun. Nonlinear Sci. Numer. Simul. 18, 2838-2851.
Ngoduy, D., 2013b. Platoon-based macroscopic model for intelligent traffic flow. Transp B Transp Dyn 1, 153-169.
Ngoduy, D., 2014. Generalized macroscopic traffic model with time delay. Nonlinear Dynam. 77, 289-296.
Ngoduy, D., Hoogendoorn, S.P., 2003. Positively conservative scheme for macroscopic traffic flow models. IFAC Proc 36, 257-262.
Ngoduy, D., Jia, D., 2017. Multi anticipative bidirectional macroscopic traffic model considering cooperative driving strategy. Transp B Transp Dyn 5, 96-110.
Ngoduy, D., Liu, R., 2007. Multiclass first-order simulation model to explain non-linear traffic phenomena. Phys. Stat. Mech. Appl. 385, 667-682.
Ngoduy, D., Maher, M.J., 2012. Calibration of second order traffic models using continuous cross entropy method. Transport. Res. C Emerg. Technol. 24, 102-121.
Ngoduy, D., Wilson, R.E., 2014. Multianticipative nonlocal macroscopic traffic model. Computer Aided Civil Eng 29, 248-263.
Ngoduy, D., Hoogendoorn, S.P., Van Zuylen, H.J., 2004. Comparison of numerical schemes for macroscopic traffic flow models. Transport. Res. Rec. 1876, 52-61.
Ngoduy, D., Hoogendoorn, S.P., Liu, R., 2009. Continuum modeling of cooperative traffic flow dynamics. Phys. Stat. Mech. Appl. 388, 2705-2716.
Papageorgiou, M., 1998. Some remarks on macroscopic traffic flow modelling. Transport. Res. Part A Policy Pract 32, 323-329.
Papageorgiou, M., Blosseville, J.M., Haj-Salem, H., 1990. Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part II: coordinated on-ramp metering. Transport. Res. Part A Gen 24, 361-370.
Papamichail, I., Bekiaris-Liberis, N., Delis, A.I., Manolis, D., Mountakis, K.S., Nikolos, I.K., et al., 2019. Motorway traffic flow modelling, estimation and control with vehicle automation and communication systems. Annu. Rev. Control 48, 325-346.
Park, P.Y., Abdel-Aty, M., 2011. A stochastic catastrophe model using two-fluid model parameters to investigate traffic safety on urban arterials. Accid. Anal. Prev. 43, 1267-1278.
Paveri-Fontana, S.L., 1975. On Boltzmann-like treatments for traffic flow: a critical review of the basic model and an alternative proposal for dilute traffic analysis. Transport. Res. 9, 225-235.
Payne, H.J., 1971. Models of freeway traffic and control. Mathematical Models of Public Systems, 51-61.
Payne, H.J., 1979. Freflo: a macroscopic simulation model of freeway traffic. Transport. Res. Rec., 68-77.
Phillips, W.F., 1979. A kinetic model for traffic flow with continuum implications. Transport. Plann. Technol. 5, 131-138.
Piccoli, B., Han, K., Friesz, T.L., Yao, T., Tang, J., 2015. Second-order models and traffic data from mobile sensors. Transport. Res. C Emerg. Technol. 52, 32-56.
Punzo, V., Zheng, Z., Montanino, M., 2021. About calibration of car-following dynamics of automated and human-driven vehicles: methodology, guidelines and codes. Transport. Res. C Emerg. Technol. 128, 103165.
Qiao, D.L., Zhang, P., Lin, Z.Y., Wong, S.C., Choi, K., 2017. A Runge-Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes. Appl. Math. Comput. 292, 309-319.
Qin, Y., Wang, H., Ni, D., 2021. Lighthill-whitham-richards model for traffic flow mixed with cooperative adaptive cruise control vehicles. Transport. Sci. 55, 815-967.
Richards, P.I., 1956. Shock waves on the highway. Oper. Res. 4, 42-51.
Saifuzzaman, M., Zheng, Z., 2014. Incorporating human-factors in car-following models: a review of recent developments and research needs. Transport. Res. C Emerg. Technol. 48, 379-403.
Saifuzzaman, M., Zheng, Z., Haque, M.M., Washington, S., 2015. Revisiting the Task-Capability Interface model for incorporating human factors into car-following models. Transp. Res. Part B Methodol. 82, 1-19.
Saifuzzaman, M., Zheng, Z., Haque, M.M., Washington, S., 2017. Understanding the mechanism of traffic hysteresis and traffic oscillations through the change in task difficulty level. Transp. Res. Part B Methodol. 105, 523-538.
Schoenmakers, M., Yang, D., Farah, H., 2021. Car-following behavioural adaptation when driving next to automated vehicles on a dedicated lane on motorways: a driving simulator study in The Netherlands. Transport. Res. F Traffic Psychol. Behav. 78, 119-129.
Schönhof, M., Helbing, D., 2009. Criticism of three-phase traffic theory. Transp. Res. Part B Methodol. 43, 784-797.
(Sean) Qian, Z., Li, J., Li, X., Zhang, M., Wang, H., 2017. Modeling heterogeneous traffic flow: a pragmatic approach. Transp. Res. Part B Methodol. 99, 183-204.
Seo, T., Bayen, A.M., Kusakabe, T., Asakura, Y., 2017. Traffic state estimation on highway: a comprehensive survey. Annu. Rev. Control 43, 128-151.
Seo, T., Kawasaki, Y., Kusakabe, T., Asakura, Y., 2019. Fundamental diagram estimation by using trajectories of probe vehicles. Transp. Res. Part B Methodol. 122, 40-56.
Serezhkin, A., Menshov, I., 2020. On solving the Riemann problem for non-conservative hyperbolic systems of partial differential equations. Comput. Fluids 210, 104675.
Sharma, A., Zheng, Z., Bhaskar, A., 2019a. Is more always better? The impact of vehicular trajectory completeness on car-following model calibration and validation. Transp. Res. Part B Methodol. 120, 49-75.
Sharma, A., Zheng, Z., Bhaskar, A., Haque, M.M., 2019b. Modelling car-following behaviour of connected vehicles with a focus on driver compliance. Transp. Res. Part B Methodol. 126, 256-279.
Sharma, A., Zheng, Z., Kim, J., Bhaskar, A., Haque, M.M., 2019c. Estimating and comparing response times in traditional and connected environments. Transport. Res. Rec. 2673, 674-684.
Sharma, A., Zheng, Z., Kim, J., Bhaskar, A., Haque, M.M., 2020. Is an informed driver a better decision maker? A grouped random parameters with heterogeneity-in-means approach to investigate the impact of the connected environment on driving behaviour in safety-critical situations. Anal Meth Accid Res 27, 100127.
Shi, X., Li, X., 2021. Constructing a fundamental diagram for traffic flow with automated vehicles: methodology and demonstration. Transp. Res. Part B Methodol. 150, 279-292.
Shladover, S.E., 2005. Automated vehicles for highway operations (automated highway systems). Proc. Inst. Mech. Eng. Part I J Syst Contr Eng 219, 53-75.
Shladover, S.E., 2018. Connected and automated vehicle systems: introduction and overview. J Intell Transp Syst 22, 190-200.
Shladover, S.E., Nowakowski, C., Lu, X.Y., Ferlis, R., 2015. Cooperative adaptive cruise control. Transport. Res. Rec. 2489, 145-152.
Sopasakis, A., Katsoulakis, M.A., 2006. Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with arrhenius look-ahead dynamics. SIAM J. Appl. Math. 66, 921-944.
Spiliopoulou, A., Kontorinaki, M., Papageorgiou, M., Kopelias, P., 2014. Macroscopic traffic flow model validation at congested freeway off-ramp areas. Transport. Res. C Emerg. Technol. 41, 18-29.
Spiliopoulou, A., Papamichail, I., Papageorgiou, M., Tyrinopoulos, I., Chrysoulakis, J., 2017. Macroscopic traffic flow model calibration using different optimization algorithms. Operational Research 17, 145-164.
Stern, R.E., Cui, S., Delle Monache, M.L., Bhadani, R., Bunting, M., Churchill, M., et al., 2018. Dissipation of stop-and-go waves via control of autonomous vehicles: field experiments. Transport. Res. C Emerg. Technol. 89, 205-221.
Sumalee, A., Zhong, R.X., Pan, T.L., Szeto, W.Y., 2011. Stochastic cell transmission model (SCTM): a stochastic dynamic traffic model for traffic state surveillance and assignment. Transp. Res. Part B Methodol. 45, 507-533.
Sun, Y., Tan, C., 2020. On a class of new nonlocal traffic flow models with look-ahead rules. Phys. Nonlinear Phenom. 413, 132663.
Sun, J., Zheng, Z., Sun, J., 2018. Stability analysis methods and their applicability to car-following models in conventional and connected environments. Transp. Res. Part B Methodol. 109, 212-237.
Sun, J., Zheng, Z., Sun, J., 2020a. The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller. Transp. Res. Part B Methodol. 142, 58-83.
Taiebat, M., Brown, A.L., Safford, H.R., Qu, S., Xu, M., 2018. A review on energy, environmental, and sustainability implications of connected and automated vehicles. Environ. Sci. Technol. 52, 11449-11465.
Talebpour, A., Mahmassani, H.S., Hamdar, S.H., 2018. Effect of information availability on stability of traffic flow: percolation theory approach. Transp. Res. Part B Methodol. 117, 624-638.
Tampère, C.M.J., van Arem, B., Hoogendoorn, S.P., 2003. Gas-kinetic traffic flow modeling including continuous driver behavior models. Transport. Res. Rec. 1852, 231-238.
Tampère, C.M.J., Hoogendoorn, S.P., van Arem, B., 2009. Continuous traffic flow modeling of driver support systems in multiclass traffic with intervehicle communication and drivers in the loop. IEEE Trans. Intell. Transport. Syst. 10, 649-657.
Thodi, B.T., Khan, Z.S., Jabari, S.E., Menéndez, M., 2022. Incorporating kinematic wave theory into a deep learning method for high-resolution traffic speed estimation. IEEE Trans. Intell. Transport. Syst. 23, 17849-17862.
Tilg, G., Yang, K., Menendez, M., 2018. Evaluating the effects of automated vehicle technology on the capacity of freeway weaving sections. Transport. Res. C Emerg. Technol. 96, 3-21.
Treiber, M., Helbing, D., 1999. Macroscopic simulation of widely scattered synchronized traffic states. J. Phys. Math. Gen. 32, L17-L23.
Treiber, M., Helbing, D., 2002. Reconstructing the spatio-temporal traffic dynamics from stationary detector data. Cooperative Transportation Dynamics 1, 1-21.
Treiber, M., Kesting, A., 2011. Evidence of convective instability in congested traffic flow: a systematic empirical and theoretical investigation. Transp. Res. Part B Methodol. 45, 1362-1377.
Treiber, M., Kesting, A., 2012. Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns. Transport. Res. C Emerg. Technol. 21, 31-41.
Treiber, M., Hennecke, A., Helbing, D., 1999. Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model. Phys. Rev. E 59, 239-253.
Treiber, M., Hennecke, A., Helbing, D., 2000. Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E 62, 1805-1824.
Treiber, M., Kesting, A., Helbing, D., 2006. Understanding widely scattered traffic flows, the capacity drop, and platoons as effects of variance-driven time gaps. Phys. Rev. E - Stat. Nonlinear Soft Matter Phys. 74, 016123.
Treiber, M., Kesting, A., Helbing, D., 2010. Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transp. Res. Part B Methodol. 44, 983-1000.
Treiterer, J., Myers, J.A., 1974. The hysteresis phenomenon in traffic flow. Transportation and Traffic Theory 6, 13-38.
Van Arem, B., van Driel, C.J.G., Visser, R., 2006. The impact of cooperative adaptive cruise control on traffic-flow characteristics. IEEE Trans. Intell. Transport. Syst. 7, 429-436.
Van Lint, J.W.C., Hoogendoorn, S.P., Schreuder, M., 2008. Fastlane: new multiclass first-order traffic flow mode. Transport. Res. Rec. 2088, 177-187.
Van Wageningen-Kessels, F., van Lint, H., Hoogendoorn, S.P., Vuik, K., 2014. New generic multiclass kinematic wave traffic flow model. Transport. Res. Rec. 2422, 50-60.
Van Wageningen-Kessels, F., van Lint, H., Vuik, K., Hoogendoorn, S., 2015. Genealogy of traffic flow models. EURO J Transp Logist 4, 445-473.
Varotto, S.F., Hoogendoorn, R.G., van Arem, B., Hoogendoorn, S.P., 2015. Empirical longitudinal driving behavior in authority transitions between adaptive cruise control and manual driving. Transport. Res. Rec. 2489, 105-114.
Varotto, S.F., Farah, H., Toledo, T., van Arem, B., Hoogendoorn, S.P., 2017. Resuming manual control or not? Modeling choices of control transitions in full-range adaptive cruise control. Transport. Res. Rec. 2622, 38-47.
Varotto, S.F., Farah, H., Toledo, T., van Arem, B., Hoogendoorn, S.P., 2018. Modelling decisions of control transitions and target speed regulations in full-range Adaptive Cruise Control based on Risk Allostasis Theory. Transp. Res. Part B Methodol. 117, 318-341.
Wang, L., Zhong, H., Ma, W., Abdel-Aty, M., Park, J., 2020. How many crashes can connected vehicle and automated vehicle technologies prevent: a meta-analysis. Accid. Anal. Prev. 136, 105299.
Wang, Y., Yu, X., Guo, J., Papamichail, I., Papageorgiou, M., Zhang, L., et al., 2022. Macroscopic traffic flow modelling of large-scale freeway networks with field data verification: state-of-the-art review, benchmarking framework, and case studies using METANET. Transport. Res. C Emerg. Technol. 145, 103904.
Wardrop, J.G., 1952. Road paper. some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. 1, 325-362.
Wong, G.C.K., Wong, S.C., 2002. A multi-class traffic flow model-an extension of LWR model with heterogeneous drivers. Transport. Res. Part A Policy Pract 36, 827-841.
Wu, Y., Lin, Y., Hu, R., Wang, Z., Zhao, B., Yao, Z., 2022. Modeling and simulation of traffic congestion for mixed traffic flow with connected automated vehicles: a cell transmission model approach. J. Adv. Transport., 1-20.
Würth, A., Binois, M., Goatin, P., Göttlich, S., 2022. Data-driven uncertainty quantification in macroscopic traffic flow models. Adv. Comput. Math. 48, 1-26.
Xiao, L., Wang, M., van Arem, B., 2017. Realistic car-following models for microscopic simulation of adaptive and cooperative adaptive cruise control vehicles. Transport. Res. Rec. 2623, 1-9.
Yao, Z., Hu, R., Jiang, Y., Xu, T., 2020. Stability and safety evaluation of mixed traffic flow with connected automated vehicles on expressways. J. Saf. Res. 75, 262-274.
Yi, J., Horowitz, R., 2006. Macroscopic traffic flow propagation stability for adaptive cruise controlled vehicles. Transport. Res. C Emerg. Technol. 14, 81-95.
Yu, H., Jiang, R., He, Z., Zheng, Z., Li, L., Liu, R., et al., 2021. Automated vehicle-involved traffic flow studies: a survey of assumptions, models, speculations, and perspectives. Transport. Res. C Emerg. Technol. 127, 103101.
Yuan, Y., Zhang, Z., Yang, X.T., Zhe, S., 2021. Macroscopic traffic flow modeling with physics regularized Gaussian process: a new insight into machine learning applications in transportation. Transp. Res. Part B Methodol. 146, 88-110.
Zhang, H.M., 1998. A theory of nonequilibrium traffic flow. Transp. Res. Part B Methodol. 32, 485-498.
Zhang, H.M., 1999. A mathematical theory of traffic hysteresis. Transp. Res. Part B Methodol. 33, 1-23.
Zhang, H.M., 2000. Structural properties of solutions arising from a nonequilibrium traffic flow theory. Transp. Res. Part B Methodol. 34, 583-603.
Zhang, H.M., 2001. New perspectives on continuum traffic flow models. Network. Spatial Econ. 1, 9-33.
Zhang, H.M., 2002. A non-equilibrium traffic model devoid of gas-like behavior. Transp. Res. Part B Methodol. 36, 275-290.
Zhang, H.M., 2003. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B Methodol. 37, 27-41.
Zhang, H.M., 2009. Comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models" by D. Helbing and A.F. Johansson. Eur. Phys. J. B 69, 563-568.
Zhang, H.M., Jin, W.L., 2002. Kinematic wave traffic flow model for mixed traffic. Transport. Res. Rec. 1802, 197-204.
Zhang, H.M., Kim, T., 2005. A car-following theory for multiphase vehicular traffic flow. Transp. Res. Part B Methodol. 39, 385-399.
Zhang, M., Shu, C.W., Wong, G.C.K., Wong, S.C., 2003. A weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model. J. Comput. Phys. 191, 639-659.
Zhang, P., Wong, S.C., Shu, C.W., 2006. A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway. J. Comput. Phys. 212, 739-756.
Zhang, P., Wong, S.C., Dai, S.Q., 2009. A conserved higher-order anisotropic traffic flow model: description of equilibrium and non-equilibrium flows. Transp. Res. Part B Methodol. 43, 562-574.
Zhang, B., de Winter, J., Varotto, S., Happee, R., Martens, M., 2019. Determinants of take-over time from automated driving: a meta-analysis of 129 studies. Transport. Res. F Traffic Psychol. Behav. 64, 285-307.
Zhao, S., Lardjane, N., Fedioun, I., 2014. Comparison of improved finite-difference WENO schemes for the implicit large eddy simulation of turbulent non-reacting and reacting high-speed shear flows. Comput. Fluids 95, 74-87.
Zhao, C., Li, L., Pei, X., Li, Z., Wang, F.Y., Wu, X., 2021. A comparative study of state-of-the-art driving strategies for autonomous vehicles. Accid. Anal. Prev. 150, 105937.
Zheng, Z., 2014. Recent developments and research needs in modeling lane changing. Transp. Res. Part B Methodol. 60, 16-32.
Zheng, Z., Ahn, S., Chen, D., Laval, J., 2011a. Applications of wavelet transform for analysis of freeway traffic: bottlenecks, transient traffic, and traffic oscillations. Transp. Res. Part B Methodol. 45, 372-384.
Zheng, Z., Ahn, S., Chen, D., Laval, J., 2011b. Freeway traffic oscillations: microscopic analysis of formations and propagations using wavelet transform. Procedia Soc Behav Sci 17, 702-716.
Zheng, Z., Ahn, S., Chen, D., Laval, J., 2013. The effects of lane-changing on the immediate follower: anticipation, relaxation, and change in driver characteristics. Transport. Res. C Emerg. Technol. 26, 367-379.
Zheng, L., Jin, P.J., Huang, H., 2015. An anisotropic continuum model considering bi-directional information impact. Transp. Res. Part B Methodol. 75, 36-57.
Zheng, F., Liu, C., Liu, X., Jabari, S.E., Lu, L., 2020. Analyzing the impact of automated vehicles on uncertainty and stability of the mixed traffic flow. Transport. Res. C Emerg. Technol. 112, 203-219.
Zhou, J., Zhu, F., 2020. Modeling the fundamental diagram of mixed human-driven and connected automated vehicles. Transport. Res. C Emerg. Technol. 115, 102614.
Zielke, B.A., Bertini, R.L., Treiber, M., 2008. Empirical measurement of freeway oscillation characteristics. Transport. Res. Rec., 57-67, 2088.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
