Journal articles: 'Continuum traffic model'

1

Zhang, Yicai, Min Zhao, Dihua Sun, and Chen Dong. "An extended continuum mixed traffic model." Nonlinear Dynamics 103, no. 2 (2021): 1891–909. http://dx.doi.org/10.1007/s11071-021-06201-z.

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Wagner, C., C. Hoffmann, R. Sollacher, J. Wagenhuber, and B. Schürmann. "Second-order continuum traffic flow model." Physical Review E 54, no. 5 (1996): 5073–85. http://dx.doi.org/10.1103/physreve.54.5073.

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Ge, H. X., and X. L. Han. "Density viscous continuum traffic flow model." Physica A: Statistical Mechanics and its Applications 371, no. 2 (2006): 667–73. http://dx.doi.org/10.1016/j.physa.2006.03.034.

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Tang, C. F., R. Jiang, Q. S. Wu, B. Wiwatanapataphee, and Y. H. Wu. "Mixed Traffic Flow in Anisotropic Continuum Model." Transportation Research Record: Journal of the Transportation Research Board 1999, no. 1 (2007): 13–22. http://dx.doi.org/10.3141/1999-02.

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Marques Jr, W., and R. M. Velasco. "An improved second-order continuum traffic model." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 02 (2010): P02012. http://dx.doi.org/10.1088/1742-5468/2010/02/p02012.

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Gupta, A. K., and V. K. Katiyar. "A new anisotropic continuum model for traffic flow." Physica A: Statistical Mechanics and its Applications 368, no. 2 (2006): 551–59. http://dx.doi.org/10.1016/j.physa.2005.12.036.

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Mohan, Ranju, and Gitakrishnan Ramadurai. "Heterogeneous Traffic Flow Modelling Using Macroscopic Continuum Model." Procedia - Social and Behavioral Sciences 104 (December 2013): 402–11. http://dx.doi.org/10.1016/j.sbspro.2013.11.133.

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HUANG, DING-WEI. "TRIGGERED STOP-AND-GO TRAFFIC IN A CONTINUUM MODEL." International Journal of Modern Physics B 18, no. 12 (2004): 1679–85. http://dx.doi.org/10.1142/s0217979204024847.

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The triggered stop-and-go traffic states are investigated within the hydrodynamic approach. The detailed phase boundaries are obtained. Spatial–temporal profile of the congestion is analyzed. The smooth tail of the density profile provides a characteristic mechanism to trigger subsequent traffic jams.

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Strnad, Irena, and Rok Marsetič. "Differential Evolution Based Numerical Variable Speed Limit Control Method with a Non-Equilibrium Traffic Model." Mathematics 11, no. 2 (2023): 265. http://dx.doi.org/10.3390/math11020265.

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This paper introduces a numerical variable speed limit (VSL) control method on a motorway, modeled by the system of partial differential equations (PDEs) of a non- equilibrium continuum traffic model. The method consists of a macroscopic simulation (i.e., numerical solution of the system of PDEs of the continuum model), introduction of the solution-based cost function and numerical optimization with a differential evolution algorithm (DE). Due to the numerical solution scheme, the method enables application of a wide range of continuum traffic models without prior discretization of PDEs. In this way, the method overcomes the limitations of the basic continuum models and represents a step towards more accurate traffic modelling in control strategies. In this paper, we determine optimal variable speed limits with the DE algorithm on a motorway section modeled by the modified switching curve model, which is a non-equilibrium continuum model consistent with the three-phase traffic flow theory. The effectiveness of the determined variable speed limits is validated using microsimulations of the test section, which show promising reductions of queue lengths and number of stops.

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Liu, Guoqing, Anastasios S. Lyrintzis, and Panos G. Michalopoulos. "Improved High-Order Model for Freeway Traffic Flow." Transportation Research Record: Journal of the Transportation Research Board 1644, no. 1 (1998): 37–46. http://dx.doi.org/10.3141/1644-05.

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An improved high-order continuum model is developed based on hyperbolic conservation laws with relaxation, linearized stability analysis, and more realistic considerations of traffic flow. The improved high-order model allows smooth traveling wave solutions as well as contact shocks (different densities moving at the same speed), is able to describe the amplification of small disturbances on heavy traffic, and allows fluctuations of speed around the equilibrium values. Furthermore, unlike existing high-order models, it does not result in negative speeds at the tail of congested regions and disturbance propagation speeds greater than the traffic flow velocity because the improved model has a zero characteristic speed and a nonnegative characteristic speed that is equal to the traffic flow velocity. The relaxation time is a function of density and, in the equilibrium limit, the improved high-order model is consistent with the simple continuum model. The improved high-order model is compared with the simple continuum model. Exemplary test results suggest that the improved high-order model is intuitively correct. Comparison of numerical results with field data suggests that the improved high-order model yields lower error levels than the simple continuum model.

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11

Zheng, Shi-Teng, Rui Jiang, Bin Jia, Junfang Tian, and Ziyou Gao. "Impact of Stochasticity on Traffic Flow Dynamics in Macroscopic Continuum Models." Transportation Research Record: Journal of the Transportation Research Board 2674, no. 10 (2020): 690–704. http://dx.doi.org/10.1177/0361198120937704.

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Stochasticity is an indispensable factor for describing real traffic situations. Recent experimental study has shown that a model spanning a two-dimensional speed–spacing (or speed–density) relationship has the potential to reproduce the characteristics of traffic flow in both experiments and empirical observations. This paper studies the impact of stochasticity on traffic flow in macroscopic models utilizing the stochastic flow–density relationship. Numerical analysis is conducted under the periodic boundary to study the impact of stochasticity on stability. Traffic flow upstream of a bottleneck is also investigated to study the impact of stochasticity on the oscillation growth feature. It is shown that there is only a quantitative difference for model stability after introducing stochasticity. In contrast, a qualitative change of the traffic oscillation growth feature can be clearly observed. With the introduction of stochasticity, traffic oscillations begin to grow in a concave way along the road. Sensitivity analysis is also performed. It is found that, under the stochastic flow–density relationship: (i) with the decrease of relaxation time, the second-order model becomes stable; (ii) the smaller the propagation speed of small disturbance, the much stronger the traffic oscillation; (iii) the larger the fluctuation range, the sooner the traffic oscillation fully develops; and (iv) the changing probability has trivial impact on the simulation results. Finally, model calibration and validation are conducted. It is shown that the experimental spatiotemporal patterns can be captured by macroscopic models under the stochastic flow–density relationship, especially the second-order model.

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12

Ren, Weilin, Rongjun Cheng, and Hongxia Ge. "Bifurcation analysis of a heterogeneous continuum traffic flow model." Applied Mathematical Modelling 94 (June 2021): 369–87. http://dx.doi.org/10.1016/j.apm.2021.01.025.

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13

Gupta, A. K., and V. K. Katiyar. "A NEW MULTI-CLASS CONTINUUM MODEL FOR TRAFFIC FLOW." Transportmetrica 3, no. 1 (2007): 73–85. http://dx.doi.org/10.1080/18128600708685665.

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14

Yu, Lei. "A new continuum traffic flow model with two delays." Physica A: Statistical Mechanics and its Applications 545 (May 2020): 123757. http://dx.doi.org/10.1016/j.physa.2019.123757.

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15

Liu, Huaqing, Rongjun Cheng, Keqiang Zhu, and Hongxia Ge. "The study for continuum model considering traffic jerk effect." Nonlinear Dynamics 83, no. 1-2 (2015): 57–64. http://dx.doi.org/10.1007/s11071-015-2307-7.

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Jin, W. L., and H. M. Zhang. "Nonequilibrium Continuum Traffic Flow Model with Frozen Sound Wave Speed." Transportation Research Record: Journal of the Transportation Research Board 1852, no. 1 (2003): 183–92. http://dx.doi.org/10.3141/1852-23.

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Results are presented from a recent study on a variation of a new non-equilibrium continuum traffic flow model in which traffic sound speed is constant. Hence this model is called the frozen-wave model. This model resembles the Payne–Whitham model but avoids the “back-traveling” of the latter. For this frozen-wave model, the Riemann problem is analyzed for its homogeneous system, two numerical solution methods are developed to solve it, and numerical simulations are carried out under both stable and unstable traffic conditions. These results show that under stable conditions, the model behaves similarly to the Payne–Whitham model. However, under unstable traffic conditions, it has nonphysical solutions or no solutions when a vacuum problem occurs. This study, on the one hand, provides a more complete picture of the properties of this frozen-wave model and reduces the risk of improper applications of it. On the other hand, it also highlights the need to adopt a density-dependent sound speed.

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17

Jiang, Yan Qun, and Shu Guang Zhou. "Macroscopic Simulation of Traffic Flow on Continuum Urban Networks." Applied Mechanics and Materials 641-642 (September 2014): 887–91. http://dx.doi.org/10.4028/www.scientific.net/amm.641-642.887.

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In this paper, a macroscopic model is applied to simulate dynamical features of traffic flow on a continuum urban network. This model is described as the two-dimensional Lighthill-Whitham-Richards model coupled with a reactive dynamic user-optimal route choice model. Numerical results visualize the ability of the model to predict some macroscopic characteristics of traffic flow on networks, i.e. the spatial distribution of flow density and travel cost of users, as well as to capture traffic congestion build-up and dissipation.

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18

Kang, Yirong, and Shuhong Yang. "A new anisotropic continuum traffic flow model with anticipation driving behavior." E3S Web of Conferences 283 (2021): 02036. http://dx.doi.org/10.1051/e3sconf/202128302036.

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Based on the anticipation driving car-following model, a new macro traffic flow model is established in this paper by considering the relationship between micro and macro variables. Therefore, the evolution law of traffic flow with anticipation driving effect can be studied from macroscopic level. By using approaches of linear stability analysis, the linear stability discriminant condition of the new macro model to keep the traffic flow stable against small disturbance is obtained. Numerical experiments verify that the model can not only simulate the unique shock wave, rarefaction wave mutation and the dynamic propagation process of small disturbance, but also improve the stability of traffic flow by introducing the information of anticipation driving behavior.

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19

Zeng, Youzhi, and Ning Zhang. "Continuum Model for Traffic Flow considering Safe Driving Awareness Heterogeneity." Advances in Mathematical Physics 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/603507.

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This paper defines the concepts of region representative vehicle and driver and region representative safe driving awareness and its heterogeneity, and, based on these concepts and a new car-following model proposed, it proposes a new continuum model for traffic flow considering region representative safe driving awareness heterogeneity. Analyses show that the new continuum model follows traffic flow anisotropy principle, and the following insights can be gotten: (1) the bigger the difference of the preceding region representative safe driving awareness coefficient minus the following region representative safe driving awareness coefficient is, the less the probability of the wrong-way travel (the negative velocity) problem in the new continuum model is; (2) when the preceding region representative safe driving awareness coefficient is not less than the following region representative safe driving awareness coefficient, there is no wrong-way travel problem in the new continuum model, and vice versa.

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20

Hittmeir, Sabine, Helene Ranetbauer, Christian Schmeiser, and Marie-Therese Wolfram. "Derivation and analysis of continuum models for crossing pedestrian traffic." Mathematical Models and Methods in Applied Sciences 27, no. 07 (2017): 1301–25. http://dx.doi.org/10.1142/s0218202517400164.

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In this paper, we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded in the transition rates of the microscopic 2D model. We formally derive the corresponding mean-field models and prove existence of global weak solutions for the parabolic model. Moreover we discuss stability of stationary states for the corresponding one-dimensional model. Furthermore we illustrate the rich dynamics of both systems with numerical simulations.

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21

YU, LEI, and ZHONG-KE SHI. "DENSITY WAVE IN A NEW ANISOTROPIC CONTINUUM MODEL FOR TRAFFIC FLOW." International Journal of Modern Physics C 20, no. 11 (2009): 1849–59. http://dx.doi.org/10.1142/s0129183109014771.

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In this paper, we apply a new anisotropic continuum model proposed by Gupta and Katiyar (GK model, for short) [J. Phys. A: Math. Gen.38, 4069 (2005)] to study the density wave of traffic flow. The GK model guarantees the characteristic speeds are always less than or equal to the macroscopic flow speed and overcomes the wrong way travel problem which exists in many high-order continuum models. The stability condition of the GK model is obtained. Applying nonlinear analysis to the GK model, we can obtain the soliton, one type of local density wave, which is induced by the density fluctuation in traffic flow. The soliton wave, which is determined near the neutral stability line by the Korteweg-de Vries (KdV) equation, is discussed in great detail. The numerical results show that local cluster effects which are consistent with the diverse nonlinear phenomena observed in realistic traffic flow can be induced from the GK model.

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22

Cheng, Rongjun, Jufeng Wang, Hongxia Ge, and Zhipeng Li. "Nonlinear analysis of an improved continuum model considering headway change with memory." Modern Physics Letters B 32, no. 03 (2018): 1850037. http://dx.doi.org/10.1142/s0217984918500379.

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Considering the effect of headway changes with memory, an improved continuum model of traffic flow is proposed in this paper. By means of linear stability theory, the new model’s linear stability with the effect of headway changes with memory is obtained. Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the improved traffic flow model, which explores how the headway changes with memory affected each car’s velocity, density and energy consumption. Numerical results show that when considering the effects of headway changes with memory, the traffic jams can be suppressed efficiently. Furthermore, research results demonstrate that the effect of headway changes with memory can avoid the disadvantage of historical information, which will improve the stability of traffic flow and minimize car energy consumption.

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23

Thankappan, Ajitha, Lelitha Vanajakshi, and Shankar C. Subramanian. "SIGNIFICANCE OF INCORPORATING HETEROGENEITY IN A NON-CONTINUUM MACROSCOPIC MODEL FOR DENSITY ESTIMATION." TRANSPORT 29, no. 2 (2014): 125–36. http://dx.doi.org/10.3846/16484142.2014.928789.

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The heterogeneity of traffic and the lack of lane discipline on the roads in India and other developing countries add complexity to the analysis and modeling of traffic. It is generally believed that it is important to take heterogeneity into account in traffic modeling. The aim of the present study is to check the validity of this assumption by analyzing the effect of incorporating heterogeneity in a macroscopic level traffic flow analysis. The application considered is real-time congestion analysis on Indian roads. Traffic density is considered as the congestion indicator. The measurement of density is difficult since it is a spatial parameter. It is usually estimated from other traffic parameters that can be readily measured using available sensors. A model-based estimation scheme using Kalman filtering has been employed to estimate traffic density. A non-continuum macroscopic model was attempted based on the lumped parameter approach. All the traffic variables were quantified without considering traffic lanes in order to take into account the lack of lane discipline. The effect of heterogeneity has been studied by incorporating static values of Passenger Car Units (PCU), dynamic values of Two Wheeler Units (TWU) and considering different classes of vehicles explicitly in the modeling process. The proposed estimation schemes without and with heterogeneity have been compared. The results have been corroborated using data collected from a road stretch in Chennai, India. The study shows that the significance of incorporating heterogeneity into the modeling of mixed traffic at the macroscopic level was not very significant.

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24

Jiang, Rui, and Qing-Song Wu. "The traffic flow controlled by the traffic lights in the speed gradient continuum model." Physica A: Statistical Mechanics and its Applications 355, no. 2-4 (2005): 551–64. http://dx.doi.org/10.1016/j.physa.2005.04.001.

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25

Ang *, K. C., and K. S. Neo. "Real-life application of a simple continuum traffic flow model." International Journal of Mathematical Education in Science and Technology 36, no. 8 (2005): 913–22. http://dx.doi.org/10.1080/00207390500064338.

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26

Ngoduy, D. "DERIVATION OF CONTINUUM TRAFFIC MODEL FOR WEAVING SECTIONS ON FREEWAYS." Transportmetrica 2, no. 3 (2006): 199–222. http://dx.doi.org/10.1080/18128600608685662.

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27

Gupta, Arvind Kumar, and Sapna Sharma. "Nonlinear analysis of traffic jams in an anisotropic continuum model." Chinese Physics B 19, no. 11 (2010): 110503. http://dx.doi.org/10.1088/1674-1056/19/11/110503.

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28

Jiang, Rui, Qing-Song Wu, and Zuo-Jin Zhu. "A new continuum model for traffic flow and numerical tests." Transportation Research Part B: Methodological 36, no. 5 (2002): 405–19. http://dx.doi.org/10.1016/s0191-2615(01)00010-8.

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29

Jiang, Yanqun, S. C. Wong, H. W. Ho, Peng Zhang, Ruxun Liu, and Agachai Sumalee. "A dynamic traffic assignment model for a continuum transportation system." Transportation Research Part B: Methodological 45, no. 2 (2011): 343–63. http://dx.doi.org/10.1016/j.trb.2010.07.003.

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30

Song, Tao, Xing-li Li, Hua Kuang, and Li-yun Dong. "A New Continuum Traffic Model with the Effect of Viscosity." Journal of Hydrodynamics 23, no. 2 (2011): 164–69. http://dx.doi.org/10.1016/s1001-6058(10)60100-x.

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31

Ai, Wen-Huan, Zhong-Ke Shi, and Da-Wei Liu. "Bifurcation analysis of a speed gradient continuum traffic flow model." Physica A: Statistical Mechanics and its Applications 437 (November 2015): 418–29. http://dx.doi.org/10.1016/j.physa.2015.06.004.

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32

Mohan, Ranju, and Gitakrishnan Ramadurai. "Heterogeneous traffic flow modelling using second-order macroscopic continuum model." Physics Letters A 381, no. 3 (2017): 115–23. http://dx.doi.org/10.1016/j.physleta.2016.10.042.

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33

DARBHA, SWAROOP, and K. R. RAJAGOPAL. "LIMIT OF A COLLECTION OF DYNAMICAL SYSTEMS: AN APPLICATION TO MODELING THE FLOW OF TRAFFIC." Mathematical Models and Methods in Applied Sciences 12, no. 10 (2002): 1381–99. http://dx.doi.org/10.1142/s0218202502002161.

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The flow of traffic is usually described using a continuum approach as that of a compressible fluid, a statistical approach via the kinetic theory of gases or cellular automata models. These approaches are not suitable for modeling dynamical systems such as traffic. While such systems are large collections, they are not large enough to be treated as a continuum. We provide a rationale for why they cannot be appropriately described using a continuum model, the kinetic theory of gases, or by appealing to cellular automata models. As an alternative, we develop a discrete dynamical systems approach that is particularly well suited to describe the dynamics of large systems such as traffic.

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Zhai, Cong, and Wei-Tiao Wu. "An extended continuum model with consideration of the self-anticipative effect." Modern Physics Letters B 32, no. 31 (2018): 1850382. http://dx.doi.org/10.1142/s0217984918503827.

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Drivers would adjust the speeds in response to not only the external environment, but also the anticipated traffic condition. In this paper, we propose a new continuum model considering the driver’s self-anticipative effect. Such effect is mainly reflected by the difference between the current speed and optimal speed within the anticipation time step. By applying the linear stability theory, the stability condition of the new model is obtained. Through the nonlinear analysis method, the KdV–Burgers equation of the model is provided. The solution describes the evolution of density waves near the neutral stability region. The simulation example verifies that the self-anticipative effect of the driver contributes to suppressing traffic congestion and reducing exhaust emissions effectively. We thus suggest that the traffic flow stability could be improved in an ad hoc manner.

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35

Yu, Lei. "Nonlinear analysis of a continuum traffic flow model with consideration of the viscous effect." Modern Physics Letters B 32, no. 28 (2018): 1850337. http://dx.doi.org/10.1142/s0217984918503372.

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In this paper, the nonlinear analysis of a viscous continuum traffic flow model is studied. The stability condition of the viscous continuum model is given by using the linear analysis method. The Korteweg–de Vries (KdV) equation is derived to describe the traffic jams. The effect of the viscous term is investigated by numerical simulations. The results show that the existence of the viscous term induces oscillation of traffic flow and the amplitude of the oscillation increases with increasing the coefficient of the viscous term. It is also found that the local clusters are compressed by increasing the coefficient of the viscous term.

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36

Lu, Xuequan, Mingliang Xu, Wenzhi Chen, Zonghui Wang, and Abdennour El Rhalibi. "Adaptive-AR Model with Drivers’ Prediction for Traffic Simulation." International Journal of Computer Games Technology 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/904154.

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We present a novel model called A2R—“Adaptive-AR”—based on a well-known continuum-based model called AR Aw and Rascle (2000) for the simulation of vehicle traffic flows. However, in the standard continuum-based model, vehicles usually follow the flows passively, without taking into account drivers' behavior and effectiveness. In order to simulate real-life traffic flows, we extend the model with a few factors, which include the effectiveness of drivers' prediction, drivers' reaction time, and drivers' types. We demonstrate that our A2R model is effective and the results of the experiments agree well with experience in real world. It has been shown that such a model makes vehicle flows perform more realistically and is closer to the real-life traffic than AR (short for Aw and Rascle and introduced in Aw and Rascle (2000)) model while having a similar performance.

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Du, Y. C., S. C. Wong, and L. J. Sun. "A multi-commodity discrete/continuum model for a traffic equilibrium system." Transportmetrica A: Transport Science 12, no. 3 (2016): 249–71. http://dx.doi.org/10.1080/23249935.2015.1128011.

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Thankappan, Ajitha, Amritha Sunny, Lelitha Vanajakshi, and Shankar C. Subramanian. "A non-continuum lumped-parameter dynamic model applied to Indian traffic." Systems Science & Control Engineering 3, no. 1 (2015): 320–31. http://dx.doi.org/10.1080/21642583.2015.1025149.

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Yu, Lei, Tong Li, and Zhong-ke Shi. "The effect of diffusion in a new viscous continuum traffic model." Physics Letters A 374, no. 23 (2010): 2346–55. http://dx.doi.org/10.1016/j.physleta.2010.03.056.

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Zhai, Cong, and Weitiao Wu. "Analysis of drivers' characteristics on continuum model with traffic jerk effect." Physics Letters A 382, no. 47 (2018): 3381–92. http://dx.doi.org/10.1016/j.physleta.2018.09.029.

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Cortínez, Víctor H., and Patricia N. Dominguez. "An anisotropic continuum model for traffic assignment in mixed transportation networks." Applied Mathematical Modelling 50 (October 2017): 585–603. http://dx.doi.org/10.1016/j.apm.2017.06.004.

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Peng, Guanghan. "A speed gradient viscous continuum model with the consideration of coupling effect for two-lane freeways." International Journal of Modern Physics C 26, no. 02 (2015): 1550014. http://dx.doi.org/10.1142/s012918311550014x.

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In this paper, a speed gradient viscous continuum model is proposed with the consideration of coupling effect for two-lane freeways. Both the speed gradient viscous term and the lane changing term are introduced into the continuity equations. The numerical simulation is carried out to investigate the shock, rarefaction waves, local clusters and changing behaviors. The results show that speed gradient viscous continuum model can describe some particular traffic behaviors in two-lane traffic system.

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Jiao, Yulei, Rongjun Cheng, and Hongxia Ge. "A novel two-lane continuum model considering driver’s expectation and electronic throttle effect." Modern Physics Letters B 35, no. 23 (2021): 2150385. http://dx.doi.org/10.1142/s0217984921503851.

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Considering the effect of driver’s expectation and the electronic throttle (ET), an improved two-lane continuum model is proposed. The linear stability condition of the new model is obtained by using the linear stability theory. The nonlinear analysis method is used to study the evolution process of traffic density wave near the neutral stability curve, and the improved KdV-Burgers equation is obtained. The numerical simulation analysis of the improved traffic flow model is carried out to further study how the changes of the expected effect of drivers affect the vehicle speed, the density of traffic flow, vehicle fuel consumption and exhaust emissions. Numerical results demonstrate that the new continuum model presented herein can well describe the developments of shock waves and rarefaction waves, and considering the factor of driver’s expectation and ET effect has a positive impact on the dynamic characteristic of macroscopic flow.

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Pudjaprasetya, S. R., J. Bunawan, and C. Novtiar. "Traffic Lights or Roundabout? Analysis using the Modified Kinematic LWR Model." East Asian Journal on Applied Mathematics 6, no. 1 (2016): 80–88. http://dx.doi.org/10.4208/eajam.210815.281215a.

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AbstractTraffic flow is treated as a continuum governed by the kinematic LWR model and the Greenshield flux function. The model is modified to describe traffic flow on a road with traffic lights or a roundabout. Parameters introduced determine the traffic flow behaviour and queue formation, and numerical simulations based on the Godunov method are carried out. The numerical procedure is shown to converge, and produces results consistent with previous analytic results.

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Ngoduy, D., Serge P. Hoogendoorn, and H. J. Van Zuylen. "Continuum Traffic Model for Freeway with On- and Off-Ramp to Explain Different Traffic-Congested States." Transportation Research Record: Journal of the Transportation Research Board 1965, no. 1 (2006): 90–102. http://dx.doi.org/10.1177/0361198106196500110.

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46

Cheng, Rongjun, Fangxun Liu, and Hongxia Ge. "A new continuum model based on full velocity difference model considering traffic jerk effect." Nonlinear Dynamics 89, no. 1 (2017): 639–49. http://dx.doi.org/10.1007/s11071-017-3477-2.

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47

Gaddam, Hari Krishna, Asha Kumari Meena, and K. Ramachandra Rao. "KdV–Berger solution and local cluster effect of two-sided lateral gap continuum traffic flow model." International Journal of Modern Physics B 33, no. 15 (2019): 1950153. http://dx.doi.org/10.1142/s0217979219501534.

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This study proposes a new nonlane-based continuum model derived from a two-sided lateral gap-following theory using the relation between microscopic and macroscopic variables. The model considers the effect of lateral gaps of the leading vehicles available on both sides of the following vehicle in multilane scenario. Linear stability analysis is performed to establish the neutral stability condition for the stable traffic flow. Nonlinear analysis is carried out at neutral stability line to derive the KdV–Berger equation, which describes density wave propagation. For that, one of the traveling wave solutions is also obtained. Numerical simulation results show that the two-sided lateral gap in the model improves the stability of the traffic flow by suppressing the traffic jams even at high-density conditions. The results implies that the proposed model is successful in replicating the properties of actual traffic jams in nonlane-based traffic environment.

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48

Calvo, Juan, Juanjo Nieto, and Mohamed Zagour. "Kinetic Model for Vehicular Traffic with Continuum Velocity and Mean Field Interactions." Symmetry 11, no. 9 (2019): 1093. http://dx.doi.org/10.3390/sym11091093.

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This paper is concerned with the modeling and mathematical analysis of vehicular traffic phenomena. We adopt a kinetic theory point of view, under which the microscopic state of each vehicle is described by: (i) position, (ii) velocity and also (iii) activity, an additional varible that we use to describe the quality of the driver-vehicle micro-system. We use methods coming from game theory to describe interactions at the microscopic scale, thus constructing new models within the framework of the Kinetic Theory of Active Particles; the resulting models incorporate some of the symmetries that are commonly found in the mathematical models of the kinetic theory of gases. Short-range interactions and mean field interactions are introduced and modeled to depict velocity changes related to passing phenomena. Our main goal is twofold: (i) to use continuum-velocity variables and (ii) to introduce a non-local acceleration term modeling mean field interactions, related to, for example, the presence of tollgates or traffic highlights.

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Gupta, Arvind Kumar, and Isha Dhiman. "Analyses of a continuum traffic flow model for a nonlane-based system." International Journal of Modern Physics C 25, no. 10 (2014): 1450045. http://dx.doi.org/10.1142/s0129183114500454.

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We develop a heterogeneous continuum model based upon a car-following model for a nonlane-based system taking lateral separation into account. The criterion for linear stability analysis and traveling wave solution of the homogeneous case is studied. The consideration of the lateral separation not only stabilizes the flow but also shrinks the critical region. For heterogeneous case, the fundamental diagram is examined for two different equilibrium speed-density functions and the effect of lane width is investigated for different compositions of heterogeneous traffic. The theoretical findings agree well with the results of numerical simulation which justifies the applicability of the model to a nonlane-based system.

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Holland, Edward N., and Andrew W. Woods. "A continuum model for the dispersion of traffic on two-lane roads." Transportation Research Part B: Methodological 31, no. 6 (1997): 473–85. http://dx.doi.org/10.1016/s0191-2615(97)00009-x.

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Journal articles on the topic 'Continuum traffic model'

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