A car following model in the context of heterogeneous traffic flow involving multilane following behavior. (English) Zbl 07832498
Summary: For improving the stability of heterogeneous traffic flow in smart grids, the Multi-Lane Multi-Vehicle State Information Index Smoothing Fusion Car following model in the context of heterogeneous traffic flow (MLMVISF model) is proposed for CAVs (connected and autonomous vehicles) and HDVs (human driving vehicles). The model takes into account the combined effects of rearview effects, state information (e.g., velocity and acceleration) of multiple preceding vehicles, average velocity information of adjacent lanes, and the perception error headway. Through linear stability analysis, the model’s stability criteria were investigated, and the optimal parameters were determined. MLMVISF model improves heterogeneous traffic flow stability based on linear stability and numerical simulation analysis. MLMVISF improves stability by 15.34 % over the FVD model (Full velocity difference) and 10.43 % over the MVISF model (Multi Vehicle Information Smooth Fusion). The study contributes to the design of automated driving strategies for smart grids.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
heterogeneous traffic flow; multi-lane impact; car following model; linear stability analysisReferences:
| [1] | Ahmed, A.; Ngoduy, D.; Adnan, M.; Baig, M. A.U., On the fundamental diagram and driving behavior modeling of heterogeneous traffic flow using UAV-based data. Transp. Res. Part A-Policy Pract., 100-115 (2021) |
| [2] | Ali, F.; Khan, Z. H.; Khattak, K. S.; Gulliver, T. A.; Khan, A. N., A microscopic heterogeneous traffic flow model considering distance headway. Mathematics, 1, 184 (2023) |
| [3] | Arasan, V. T.; Koshy, R. Z., Methodology for modeling highly heterogeneous traffic flow. J. Transp. Eng. -Asce, 7, 544-551 (2005) |
| [4] | Arasan, V. T.; Arkatkar, S. S., Modelling heterogeneous traffic flow on upgrades of intercity roads. Transport, 2, 129-137 (2010) |
| [5] | Bando, M.; Hasebe, K.; Nakayama, A.; Shibata, A.; Sugiyama, Y., Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., 2, 1035 (1995) |
| [6] | Chen, D.; Sun, D. H.; Liu, H.; Zhao, M.; Li, Y.; Wan, P., Robust control for cooperative driving system of heterogeneous vehicles with parameter uncertainties and communication constraints in the vicinity of traffic signals. Nonlinear Dyn., 2, 1659-1674 (2020) · Zbl 1459.93154 |
| [7] | Chen, Y. D.; Kong, D. W.; Sun, L. S.; Zhang, T.; Song, Y. C., Fundamental diagram and stability analysis for heterogeneous traffic flow considering human-driven vehicle driver’s acceptance of cooperative adaptive cruise control vehicles. Phys. A-Stat. Mech. Its Appl. (2022) |
| [8] | Cheng, R. J.; Lyu, H.; Zheng, Y. X.; Ge, H. X., Modeling and stability analysis of cyberattack effects on heterogeneous intelligent traffic flow. Phys. A-Stat. Mech. Appl. (2022) |
| [9] | Cong, Z.; Weitiao, W., A new car-following model considering driver’s characteristics and traffic jerk. Nonlinear Dyn., 1-15 (2018) |
| [10] | Gong, Y.; Zhu, W. X., Modeling the heterogeneous traffic flow considering the effect of self-stabilizing and autonomous vehicles. Chin. Phys. B, 2 (2022) |
| [11] | Gundaliya, P. J.; Mathew, T. V.; Dhingra, S. L., Heterogeneous traffic flow modelling for an arterial using grid based approach. J. Adv. Transp., 4, 467-491 (2008) |
| [12] | Helbing, D.; Tilch, B., Generalized force model of traffic dynamics. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., 1, 133-138 (1998) |
| [13] | Hua, X. D.; Yu, W. J.; Wang, W., Stability analysis of heterogeneous traffic flow with connected and automated vehicles: joint consideration of communication failures and driver takeover. J. Adv. Transp. (2022) |
| [14] | Huang, L.; Zhai, C.; Wang, H.; Zhang, R.; Qiu, Z.; Wu, J., Cooperative Adaptive Cruise Control and exhaust emission evaluation under heterogeneous connected vehicle network environment in urban city. J. Environ. Manag. (2020) |
| [15] | Imran, W.; Khan, Z. H.; Gulliver, T. A.; Khattak, K. S.; Nasir, H., A macroscopic traffic model for heterogeneous flow. Chin. J. Phys., 419-435 (2020) · Zbl 07829586 |
| [16] | Jiang, R.; Wu, Q.; Zhu, Z., Full velocity difference model for a car-following theory. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys., 1 Pt 2 (2001) |
| [17] | Kanagaraj, V.; Srinivasan, K. K.; Sivanandan, R., Modeling vehicular merging behavior under heterogeneous traffic conditions. Transp. Res. Rec., 140-147 (2010) |
| [18] | Kaur, R.; Sharma, S., Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles. Phys. Lett. A, 22, 1449-1455 (2018) |
| [19] | Kays, H. M.I.; Shimu, T. H.; Hadiuzzaman, M.; Muniruzzaman, S. M.; Rahman, M. M., H-CTM for simulating non-lane-based heterogeneous traffic. Transp. Lett. Int. J. Transp. Res., 7, 382-390 (2019) |
| [20] | Khan, M. U.; Saeed, S.; Nehdi, M. L.; Rehan, R., Macroscopic traffic-flow modelling based on gap-filling behavior of heterogeneous traffic. Appl. Sci., 9, 4278 (2021) |
| [21] | Li, L. H.; Ji, X. K.; Gan, J.; Qu, X.; Ran, B., A macroscopic model of heterogeneous traffic flow based on the safety potential field theory. IEEE Access, 7460-7470 (2021) |
| [22] | Li, T. L.; Hui, F.; Zhao, X. M.; Liu, C.; Ngoduy, D., Modelling heterogeneous traffic dynamics by considering the influence of V2V safety messages. Iet Intell. Transp. Syst., 4, 220-227 (2020) |
| [23] | Lighthill, M. J.; Whitham, G. B., On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A, 1178, 317-345 (1955) · Zbl 0064.20906 |
| [24] | Liu, L.; Zhu, L. L.; Yang, D., Modeling and simulation of the car-truck heterogeneous traffic flow based on a nonlinear car-following model. Appl. Math. Comput., 706-717 (2016) · Zbl 1410.90043 |
| [25] | Mallikarjuna, C.; Rao, K. R., Cellular automata model for heterogeneous traffic. J. Adv. Transp., 3, 321-345 (2009) |
| [26] | Mallikarjuna, C.; Rao, K. R., Heterogeneous traffic flow modelling: a complete methodology. Transportmetrica, 5, 321-345 (2011) |
| [27] | Mohan, R.; Ramadurai, G., Heterogeneous traffic flow modelling using second-order macroscopic continuum model. Phys. Lett. A, 3, 115-123 (2017) · Zbl 1377.90017 |
| [28] | Payne, H. J., Models of freeway traffic and control. Math. Models Public Syst. Simul. Counc., 51-61 (1971) |
| [29] | Richards, P. I., Shock waves on the highway. Oper. Res., 1, 42-51 (1956) · Zbl 1414.90094 |
| [30] | Ruan, T. C.; Zhou, L. J.; Wang, H., Stability of heterogeneous traffic considering impacts of platoon management with multiple time delays. Phys. A-Stat. Mech. Appl. (2021) · Zbl 1540.90068 |
| [31] | Tang, T. Q.; Huang, H. J.; Zhao, S. G.; Shang, H. Y., A new dynamic model for heterogeneous traffic flow. Phys. Lett. A, 29, 2461-2466 (2009) · Zbl 1231.60106 |
| [32] | Thankappan, A.; Vanajakshi, L., A traffic stream model for heterogeneous traffic conditions. Proc. Inst. Civ. Eng. -Transp., 4, 240-247 (2014) |
| [33] | Treiber, M.; Hennecke, A.; Helbing, D., Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., 2 Pt A, 1805-1824 (2000) |
| [34] | Vranken, T.; Schreckenberg, M., Modelling multi-lane heterogeneous traffic flow with human-driven, automated, and communicating automated vehicles. Phys. a-Stat. Mech. Its Appl. (2022) |
| [35] | Wang, H.; Wan, Q.; Wang, W., Asymptotic stability analysis of binary heterogeneous traffic based on car-following model. Discret. Dyn. Nat. Soc. (2016) · Zbl 1417.90054 |
| [36] | Wang, H.; Qin, Y. Y.; Wang, W.; Chen, J., Stability of CACC-manual heterogeneous vehicular flow with partial CACC performance degrading. Transp. B-Transp. Dyn., 1, 788-813 (2019) |
| [37] | Wang, J. F.; Sun, F. X.; Cheng, R. J.; Ge, H. X., An extended heterogeneous car-following model with the consideration of the drivers’ different psychological headways. Phys. A-Stat. Mech. Appl., 1113-1125 (2018) · Zbl 1514.90102 |
| [38] | Wang, S. T.; Zhu, W. X., Modeling the heterogeneous traffic flow considering mean expected velocity field and effect of two-lane communication under connected environment. Phys. A-Stat. Mech. Appl. (2022) |
| [39] | Wang, T.; Cheng, R. J.; Wu, Y., Stability analysis of heterogeneous traffic flow influenced by memory feedback control signal. Appl. Math. Model., 693-708 (2022) · Zbl 1505.90038 |
| [40] | Whitham, G. B.G. B., Linear and nonlinear waves. Linear Nonlinear Waves (1974) · Zbl 0373.76001 |
| [41] | Xie, D. F.; Zhao, X. M.; He, Z. B., Heterogeneous Traffic Mixing Regular and Connected Vehicles: Modeling and Stabilization. IEEE Trans. Intell. Transp. Syst., 6, 2060-2071 (2019) |
| [42] | Yang, D.; Jin, P.; Pu, Y.; Ran, B., Stability analysis of the mixed traffic flow of cars and trucks using heterogeneous optimal velocity car-following model. Phys. A-Stat. Mech. Appl., 371-383 (2014) · Zbl 1395.90099 |
| [43] | Yang, D.; Zhou, X. X.; Su, G.; Liu, S. J., Model and simulation of the heterogeneous traffic flow of the urban signalized intersection with an island work zone. IEEE Trans. Intell. Transp. Syst., 5, 1719-1727 (2019) |
| [44] | Yao, Z. H.; Xu, T. R.; Jiang, Y. S.; Hu, R., Linear stability analysis of heterogeneous traffic flow considering degradations of connected automated vehicles and reaction time. Phys. A-Stat. Mech. Appl. (2021) · Zbl 07534085 |
| [45] | Zhai, C.; Wu, W., Self-delayed feedback car-following control with the velocity uncertainty of preceding vehicles on gradient roads. Nonlinear Dyn., 4, 3379-3400 (2021) |
| [46] | Zhai, C.; Wu, W. T.; Luo, S. W., Heterogeneous traffic flow modeling with drivers’ timid and aggressive characteristics*. Chin. Phys. B, 10 (2021) |
| [47] | Zhai, C.; Wu, W.; Xiao, Y., Cooperative car-following control with electronic throttle and perceived headway errors on gyroidal roads. Appl. Math. Model., 770-786 (2022) · Zbl 1503.90024 |
| [48] | Zhai, C.; Zhang, R.; Peng, T.; Zhong, C.; Xu, H., Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles. Phys. A: Stat. Mech. Appl. (2023) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
