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Transportmetrica Volume 6, 2010 - Issue 2
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Original Articles

Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships

D. Ngoduy Institute for Transport Studies, The University of Leeds, LS2 9JT Leeds, UKCorrespondence[email protected]
Pages 121-141 | Received 11 Feb 2008, Accepted 28 Feb 2009, Published online: 08 Apr 2009

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Yu Jiang, W. Y. Szeto, Jiancheng Long & Ke Han. (2016) Multi-class dynamic traffic assignment with physical queues: intersection-movement-based formulation and paradox. Transportmetrica A: Transport Science 12:10, pages 878-908.
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Carlos D. Acosta, Raimund Bürger & Carlos E. Mejía. (2015) Efficient parameter estimation in a macroscopic traffic flow model by discrete mollification. Transportmetrica A: Transport Science 11:8, pages 702-715.
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D. Ngoduy. (2015) Effect of the car-following combinations on the instability of heterogeneous traffic flow. Transportmetrica B: Transport Dynamics 3:1, pages 44-58.
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Femke van Wageningen-Kessels, Bas van't Hof, Serge P. Hoogendoorn, Hans van Lint & Kees Vuik. (2013) Anisotropy in generic multi-class traffic flow models. Transportmetrica A: Transport Science 9:5, pages 451-472.
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Jose M. del Castillo. (2012) Three new models for the flow–density relationship: derivation and testing for freeway and urban data. Transportmetrica 8:6, pages 443-465.
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Jia Li, Qian-Yong Chen, Haizhong Wang & Daiheng Ni. (2012) Analysis of LWR model with fundamental diagram subject to uncertainties. Transportmetrica 8:6, pages 387-405.
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D. Ngoduy. (2011) Multiclass first-order traffic model using stochastic fundamental diagrams. Transportmetrica 7:2, pages 111-125.
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S M A Bin Al Islam & Ali Hajbabaie. (2022) An Enhanced Cell Transmission Model for Multi-Class Signal Control. IEEE Transactions on Intelligent Transportation Systems 23:8, pages 11215-11226.
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R. K. Pradhan, S. Shrestha & D. B. Gurung. (2022) Mathematical modeling of mixed-traffic in urban areas. Mathematical Modeling and Computing 9:2, pages 226-240.
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Daiheng Ni. (2021) Field Theory for Some Traffic Phenomena and Fundamental Diagram. Transportation Research Record: Journal of the Transportation Research Board 2675:9, pages 1195-1208.
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Yanyan Qin, Hao Wang & Daiheng Ni. (2021) Lighthill-Whitham-Richards Model for Traffic Flow Mixed with Cooperative Adaptive Cruise Control Vehicles. Transportation Science 55:4, pages 883-907.
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Michel MandjesJaap Storm. (2021) A Diffusion-Based Analysis of a Multiclass Road Traffic Network. Stochastic Systems 11:1, pages 60-81.
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A R Méndez, W MarquesJrJr & R M Velasco. (2019) Multi-class fundamental diagrams from the Prigogine–Herman–Boltzmann equation. Physica Scripta 94:11, pages 115008.
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Wen-Long Jin & Qinglong Yan. (2019) A formulation of unifiable multi-commodity kinematic wave model with relative speed ratios. Transportation Research Part B: Methodological 128, pages 236-253.
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Tie-Qiao Tang, Wei-Fang Shi, Hai-Jun Huang, Wen-Xiang Wu & Ziqi Song. (2019) A route-based traffic flow model accounting for interruption factors. Physica A: Statistical Mechanics and its Applications 514, pages 767-785.
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Jairus Odawa Malenje, Jing Zhao, Peng Li & Yin Han. (2018) An extended car-following model with the consideration of the illegal pedestrian crossing. Physica A: Statistical Mechanics and its Applications 508, pages 650-661.
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Jing Zhao & Peng Li. (2017) An extended car-following model with consideration of vehicle to vehicle communication of two conflicting streams. Physica A: Statistical Mechanics and its Applications 473, pages 178-187.
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Wen-Long Jin. (2017) Unifiable multi-commodity kinematic wave model. Transportation Research Procedia 23, pages 137-156.
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Dian-Liang Qiao, Peng Zhang, Zhi-Yang Lin, S.C. Wong & Keechoo Choi. (2017) A Runge–Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes. Applied Mathematics and Computation 292, pages 309-319.
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D. Ngoduy, N.H. Hoang, H.L. Vu & D. Watling. (2016) Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks. Transportation Research Part B: Methodological 92, pages 148-169.
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Alfredo Nantes, Dong Ngoduy, Ashish Bhaskar, Marc Miska & Edward Chung. (2016) Real-time traffic state estimation in urban corridors from heterogeneous data. Transportation Research Part C: Emerging Technologies 66, pages 99-118.
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Shuguang Li & Ke Wang. (2016) Estimated passenger car equivalent using backward wave speed. Proceedings of the Institution of Civil Engineers - Transport 169:1, pages 34-41.
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Femke van Wageningen-Kessels. (2016) Framework to Assess Multiclass Continuum Traffic Flow Models. Transportation Research Record: Journal of the Transportation Research Board 2553:1, pages 150-160.
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ShuGuang Li. (2016) A cell-based multiple vehicle type dynamic user equilibrium model with physical queues. Canadian Journal of Civil Engineering 43:1, pages 1-12.
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Femke van Wageningen-Kessels, Hans van Lint, Kees Vuik & Serge Hoogendoorn. (2015) Genealogy of traffic flow models. EURO Journal on Transportation and Logistics 4:4, pages 445-473.
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Chun-Xiu Wu. (2015) Traveling wave solution of higher-order traffic flow model with discontinuous fundamental diagram. International Journal of Modern Physics B 29:20, pages 1550137.
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Tie-Qiao Tang, Wei-Fang Shi, Hua-Yan Shang & Yun-Peng Wang. (2014) An extended car-following model with consideration of the reliability of inter-vehicle communication. Measurement 58, pages 286-293.
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Tie-Qiao Tang, Yun-Peng Wang, Xiao-Bao Yang & Hai-Jun Huang. (2014) A Multilane Traffic Flow Model Accounting for Lane Width, Lane-Changing and the Number of Lanes. Networks and Spatial Economics 14:3-4, pages 465-483.
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D. Ngoduy. (2014) Generalized macroscopic traffic model with time delay. Nonlinear Dynamics 77:1-2, pages 289-296.
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Tieqiao Tang, Weifang Shi, Huayan Shang & Yunpeng Wang. (2014) A new car-following model with consideration of inter-vehicle communication. Nonlinear Dynamics 76:4, pages 2017-2023.
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Tie-Qiao Tang, Lou Caccetta, Yong-Hong Wu, Hai-Jun Huang & Xiao-Bao Yang. (2014) A macro model for traffic flow on road networks with varying road conditions. Journal of Advanced Transportation 48:4, pages 304-317.
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T.Q. Tang, J.G. Li, H.J. Huang & X.B. Yang. (2014) A car-following model with real-time road conditions and numerical tests. Measurement 48, pages 63-76.
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Wen-Long Jin. (2013) A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow. Transportation Research Part B: Methodological 57, pages 361-377.
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D. Ngoduy. (2013) Analytical studies on the instabilities of heterogeneous intelligent traffic flow. Communications in Nonlinear Science and Numerical Simulation 18:10, pages 2699-2706.
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William H. K. LamMei Lam TamXinqing CaoXiangmin Li. (2013) Modeling the Effects of Rainfall Intensity on Traffic Speed, Flow, and Density Relationships for Urban Roads. Journal of Transportation Engineering 139:7, pages 758-770.
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Wen-Long Jin. (2013) A Multi-commodity Lighthill-Whitham-Richards Model of Lane-changing Traffic Flow. Procedia - Social and Behavioral Sciences 80, pages 658-677.
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Raimund Bürger, Christophe Chalons & Luis M. Villada. (2013) Antidiffusive and Random-Sampling Lagrangian-Remap Schemes for the Multiclass Lighthill--Whitham--Richards Traffic Model. SIAM Journal on Scientific Computing 35:6, pages B1341-B1368.
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Tie-Qiao Tang, Yun-Peng Wang, Gui-Zhen Yu & Hai-Jun Huang. (2012) A Stochastic LWR Model with Consideration of the Driver's Individual Property. Communications in Theoretical Physics 58:4, pages 583-589.
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Tieqiao Tang, Yunpeng Wang, Xiaobao Yang & Yonghong Wu. (2012) A new car-following model accounting for varying road condition. Nonlinear Dynamics 70:2, pages 1397-1405.
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D. Ngoduy. (2012) Effect of driver behaviours on the formation and dissipation of traffic flow instabilities. Nonlinear Dynamics 69:3, pages 969-975.
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Tieqiao Tang, Chuanyao Li, Haijun Huang & Huayan Shang. (2011) A new fundamental diagram theory with the individual difference of the driver’s perception ability. Nonlinear Dynamics 67:3, pages 2255-2265.
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Jian-zhong Chen, Zhong-ke Shi & Yan-mei Hu. (2012) Numerical solutions of a multi-class traffic flow model on an inhomogeneous highway using a high-resolution relaxed scheme. Journal of Zhejiang University SCIENCE C 13:1, pages 29-36.
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Xiqun Chen, Li Li, Qixin Shi & Jin-Xin Cao. (2010) Equilibrium analysis and comparison for general CTMs and LCTMs. Equilibrium analysis and comparison for general CTMs and LCTMs.
Peng Zhang, S. C. Wong & Shi-Qiang Dai. (2009) A note on the weighted essentially non-oscillatory numerical scheme for a multi-class Lighthill-Whitham-Richards traffic flow model. Communications in Numerical Methods in Engineering 25:11, pages 1120-1126.
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