Technical Papers
Jun 3, 2022

A Car-Following Model Considering Driver’s Instantaneous Reaction Delay in Nonlane-Based Traffic Environments

Publication: Journal of Transportation Engineering, Part A: Systems
Volume 148, Issue 8

Abstract

Reaction delay is an indispensable factor in the operation and control process of drivers in a car-following scenario. Utilizing trajectory data obtained from an instrumented vehicle, this paper proposes a data-driven neural network car-following model incorporating instantaneous reaction delay of the drivers in nonlane-based (or disorderly) traffic systems. Considering instantaneous reaction delay as the time interval between relative speed and acceleration, a model is developed where the lateral descriptor of vehicle interaction (or centerline separation, CS) is found as a significant factor in modeling reaction delays in such disordered systems. Interestingly, reaction delays were found to increase with lateral separation between the interacting vehicles. Modeling results further indicate that the car-following model with instantaneous reaction delay outperformed the model with fixed reaction delay. In addition, the proposed model also showed better performance in terms of trajectory reproducing accuracy when compared with the classic car-following models. The results of this work justify the importance of considering CS in the development of algorithms for future autonomous traffic of disorderly traffic environments.

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Data Availability Statement

Some data, models, or code generated or used during the study are available from the corresponding author by request.

References

Ambarwati, L., A. J. Pel, R. Verhaeghe, and B. van Arem. 2014. “Empirical analysis of heterogeneous traffic flow and calibration of porous flow model.” Transp. Res. Part C: Emerging Technol. 48 (Nov): 418–436. https://doi.org/10.1016/j.trc.2014.09.017.
Asaithambi, G., V. Kanagaraj, and T. Toledo. 2016. “Driving behaviors: Models and challenges for non-lane based mixed traffic.” Transp. Dev. Econ. 2 (2): 1–16. https://doi.org/10.1007/s40890-016-0025-6.
Bando, M., K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama. 1995. “Dynamics model of traffic congestion and numerical simulation.” Phys. Rev. E 51 (2): 1035–1042. https://doi.org/10.1103/PhysRevE.51.1035.
Bando, M., T. Kugo, N. Maekawa, and H. Nakano. 1993. “Improving the effective potential.” Phys. Lett. B 301 (1): 83–89. https://doi.org/10.1016/0370-2693(93)90725-W.
Bham, G. H., and R. F. Benekohal. 2004. “A high fidelity traffic simulation model based on cellular automata and car-following concepts.” Transp. Res. Part C: Emerging Technol. 12 (1): 1–32. https://doi.org/10.1016/j.trc.2002.05.001.
Chakroborty, P., and S. Kikuchi. 1999. “Evaluation of the general motors based car-following models and a proposed fuzzy inference model.” Transp. Res. Part C: Emerging Technol. 7 (4): 209–235.https://doi.org/10.1016/S0968-090X(99)00020-0.
Chandler, R. E., R. Herman, and E. W. Montroll. 1958. “Traffic dynamics: Studies in car following.” Oper. Res. 6 (2): 165–184. https://doi.org/10.1287/opre.6.2.165.
Cheng, Q., Z. Liu, Y. Lin, and X. S. Zhou. 2021. “An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship.” Transp. Res. Part B: Methodol. 153 (Nov): 246–271. https://doi.org/10.1016/j.trb.2021.09.004.
Ciuffo, B., and V. Punzo. 2010. “Verification of traffic micro-simulation model calibration procedures: Analysis of goodness-of-fit measures.” In Proc., 89th Annual Meeting of the Transportation Research Record. Washington, DC: Transportation Research Record.
Das, S., and A. K. Maurya. 2018. “Multivariate analysis of microscopic traffic variables using copulas in staggered car-following conditions.” Transportmetrica A: Transp. Sci. 14 (10): 829–854. https://doi.org/10.1080/23249935.2018.1441200.
Das, S., and A. K. Maurya. 2020. “Defining time-to-collision thresholds by the type of lead vehicle in non-lane-based traffic environments.” IEEE Trans. Intell. Transp. Syst. 21 (12): 4972–4982. https://doi.org/10.1109/TITS.2019.2946001.
DeSilva, H., and T. Forbes. 1937. Driver testing results. Cambridge, MA: Harvard Traffic Bureau.
Fan, P., J. Guo, H. Zhao, J. S. Wijnands, and Y. Wang. 2019. “Car-following modeling incorporating driving memory based on autoencoder and long short-term memory neural networks.” Sustainability 11 (23): 6755. https://doi.org/10.3390/su11236755.
Fausett, L. 1994. Fundamentals of neural networks. Englewood Cliffs, NJ: Prentice Hall.
Fung, G. S., N. H. Yung, and G. K. Pang. 2003. “Camera calibration from road lane markings.” Opt. Eng. 42 (10): 2967–2977. https://doi.org/10.1117/1.1606458.
Gazis, D. C., R. Herman, and R. B. Potts. 1959. “Car following theory of steady state traffic flow.” Oper. Res. 7 (4): 499–505. https://doi.org/10.1287/opre.7.4.499.
Ghaffari, A., A. Khodayari, A. Panahi, and F. Alimardani. 2012. “Neural-network-based modeling and prediction of the future state of a Stop & Go behavior in urban areas.” In Proc., IEEE Int. Conf. on Vehicular Electronics and Safety (ICVES 2012), 399–404. New York: IEEE.
Gipps, P. G. 1981. “A behavioural car-following model for computer simulation.” Transp. Res. B: Methodol. 15 (2): 105–111. https://doi.org/10.1016/0191-2615(81)90037-0.
Gunay, B. 2003. “Methods to quantify the discipline of lane-based driving.” Traffic Eng. Control 44 (1): 22–27.
Gunay, B. 2007. “Car following theory with lateral discomfort.” Transp. Res. Part B: Methodol. 41 (7): 722–735. https://doi.org/10.1016/j.trb.2007.02.002.
Hoogendoorn, S. P., and S. Ossen. 2006. “Empirical analysis of two-leader car-following behavior.” Eur. J. Transp. Infrastruct. Res. 6 (3): 229–246. https://doi.org/10.18757/ejtir.2006.6.3.3447.
Huang, X., J. Sun, and J. Sun. 2018. “A car-following model considering asymmetric driving behavior based on long short-term memory neural networks.” Transp. Res. Part C: Emerging Technol. 95 (Oct): 346–362. https://doi.org/10.1016/j.trc.2018.07.022.
Jiang, R., Q. Wu, and Z. Zhu. 2001. “Full velocity difference model for a car-following theory.” Phys. Rev. E 64 (1): 017101. https://doi.org/10.1103/PhysRevE.64.017101.
Jin, S., Z. Y. Huang, P. F. Tao, and D. H. Wang. 2011. “Car-following theory of steady-state traffic flow using time-to-collision.” J. Zhejiang Univ. Sci. A 12 (8): 645–654. https://doi.org/10.1631/jzus.A1000518.
Jin, S., D. Wang, C. Xu, and Z. Huang. 2012. “Staggered car-following induced by lateral separation effects in traffic flow.” Phys. Lett. A 376 (3): 153–157. https://doi.org/10.1016/j.physleta.2011.11.005.
Jin, W. L. 2016. “On the equivalence between continuum and car-following models of traffic flow.” Transp. Res. Part B: Methodol. 93 (Nov): 543–559. https://doi.org/10.1016/j.trb.2016.08.007.
Jin, W. L. 2019. “Nonstandard second-order formulation of the LWR model.” Transportmetrica B: Transp. Dyn. 7 (1): 1338–1355.
Kalogirou, S. A. 2000. “Applications of artificial neural-networks for energy systems.” Appl. Energy 67 (1–2): 17–35. https://doi.org/10.1016/S0306-2619(00)00005-2.
Kanagaraj, V., G. Asaithambi, C. N. Kumar, K. K. Srinivasan, and R. Sivanandan. 2013. “Evaluation of different vehicle following models under mixed traffic conditions.” Procedia-Soc. Behav. Sci. 104 (Dec): 390–401. https://doi.org/10.1016/j.sbspro.2013.11.132.
Karlaftis, M. G., and E. I. Vlahogianni. 2011. “Statistical methods versus neural networks in transportation research: Differences, similarities and some insights.” Transp. Res. Part C: Emerging Technol. 19 (3): 387–399. https://doi.org/10.1016/j.trc.2010.10.004.
Karlik, B., and A. V. Olgac. 2011. “Performance analysis of various activation functions in generalized MLP architectures of neural networks.” Int. J. Artif. Intell. Expert Syst. 1 (4): 111–122.
Khodayari, A., A. Ghaffari, R. Kazemi, and R. Braunstingl. 2011. “Modify car following model by human effects based on locally linear neuro fuzzy.” In Proc., Intelligent Vehicles Symposium (IV), 661–666. New York: IEEE.
Khodayari, A., A. Ghaffari, R. Kazemi, and R. Braunstingl. 2012. “A modified car-following model based on a neural network model of the human driver effects.” IEEE Trans. Syst. Man Cybern. 42 (6): 1440–1449. https://doi.org/10.1109/TSMCA.2012.2192262.
Kikuchi, C., and P. Chakroborty. 1992. “Car-following model based on a fuzzy inference system.” Transp. Res. Rec. 1365 (1): 82–91.
Kometani, E., and T. Sasaki. 1959. “Dynamic behaviour of traffic with a nonlinear spacing-speed relationship.” In Proc., Symp. on Theory of Traffic Flow, 105–119. Amsterdam, Netherlands: Elsevier.
Ma, L., and S. Qu. 2020. “A sequence to sequence learning based car-following model for multi-step predictions considering reaction delay.” Transp. Res. Part C: Emerging Technol. 120 (Nov): 102785. https://doi.org/10.1016/j.trc.2020.102785.
Ma, X., and I. Andréasson. 2006. “Estimation of driver reaction time from car-following data: Application in evaluation of general motor–type model.” Transp. Res. Rec. 1965 (1): 130–141. https://doi.org/10.1177/0361198106196500114.
Mathew, T. V., and K. V. R. Ravishankar. 2012. “Neural network based vehicle-following model for mixed traffic conditions.” Eur. Transp. 52 (Nov): 1–15.
Mehmood, A., and S. M. Easa. 2009. “Modeling reaction time in car-following behaviour based on human factors.” Int. J. Appl. Sci. Eng. Technol. 5 (2): 93–101.
Mo, Z., R. Shi, and X. Di. 2021. “A physics-informed deep learning paradigm for car-following models.” Transp. Res. Part C: Emerging Technol. 130 (Sep): 103240. https://doi.org/10.1016/j.trc.2021.103240.
Moghadam, M. P. A., P. Pahlavani, and S. Naseralavi. 2016. “Prediction of car following behaviour based on the instantaneous reaction time using an ANFIS-CART based model.” Int. J. Transp. Eng. 4 (2): 109–126.
Nagel, K., and M. Schreckenberg. 1992. “A cellular automaton model for freeway traffic.” J. Phys. I 2 (12): 2221–2229. https://doi.org/10.1051/jp1:1992277.
Nair, R., H. S. Mahmassani, and E. Miller-Hooks. 2011. “A porous flow approach to modeling heterogeneous traffic in disordered systems.” Transp. Res. Part B: Methodol. 45 (9): 1331–1345. https://doi.org/10.1016/j.trb.2011.05.009.
Neal, R. M. 1992. “Connectionist learning of belief networks.” Artif. Intell. 56 (1): 71–113. https://doi.org/10.1016/0004-3702(92)90065-6.
Newell, G. F. 2002. “A simplified car-following theory: A lower order model.” Transp. Res. Part B: Methodol. 36 (3): 195–205. https://doi.org/10.1016/S0191-2615(00)00044-8.
Ni, D., J. D. Leonard, C. Jia, and J. Wang. 2016. “Vehicle longitudinal control and traffic stream modeling.” Transp. Sci. 50 (3): 1016–1031. https://doi.org/10.1287/trsc.2015.0614.
Ozaki, H. 1993. “Reaction and anticipation in the car following behaviour.” In Proc., 12th Int. Symp. on Traffic and Transportation Theory, 349–366. Amsterdam, Netherlands: Elsevier.
Panwai, S., and H. Dia. 2007. “Neural agent car-following models.” IEEE Trans. Intell. Transp. Syst. 8 (1): 60–70. https://doi.org/10.1109/TITS.2006.884616.
Papathanasopoulou, V., and C. Antoniou. 2015. “Towards data-driven car-following models.” Transp. Res. Part C: Emerging Technol. 55 (Jun): 496–509. https://doi.org/10.1016/j.trc.2015.02.016.
Papathanasopoulou, V., and C. Antoniou. 2018. “Flexible car–following models for mixed traffic and weak lane–discipline conditions.” Eur. Transp. Res. Rev. 10 (2): 62. https://doi.org/10.1186/s12544-018-0338-0.
Pipes, L. A. 1953. “An operational analysis of traffic dynamics.” J. Appl. Phys. 24 (3): 274–281. https://doi.org/10.1063/1.1721265.
Punzo, V., and M. Montanino. 2016. “Speed or spacing? Cumulative variables, and convolution of model errors and time in traffic flow models validation and calibration.” Transp. Res. Part B: Methodol. 91 (Sep): 21–33. https://doi.org/10.1016/j.trb.2016.04.012.
Qu, D., X. Chen, W. Yang, and X. Bian. 2014. “Modeling of car-following required safe distance based on molecular dynamics.” In Mathematical problems in engineering, 1–7. London: Hindawi. https://doi.org/10.1155/2014/604023.
Ravishankar, K. V. R., and T. V. Mathew. 2011. “Vehicle-type dependent car-following model for heterogeneous traffic conditions.” J. Transp. Eng. 137 (11): 775–781. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000273.
Reuschel, A. 1950. “Fahrzeugbewegungen in der Kolonne.” Osterreichisches Ingenieurwes Arch. 4: 193–215.
Sharma, A., Z. Zheng, and A. Bhaskar. 2019. “Is more always better? The impact of vehicular trajectory completeness on car-following model calibration and validation.” Transp. Res. Part B: Methodol. 120 (Feb): 49–75. https://doi.org/10.1016/j.trb.2018.12.016.
Siuhi, S., and M. Kaseko. 2013. “Nonlinear acceleration and deceleration response behaviour in stimulus-response car-following models.” Adv. Transp. Stud. 31 (Nov): 81–96.
Sivak, M., D. Post, P. Olson, and R. Donohue. 1981. “Driver responses to high-mounted brake lights in actual traffic.” Hum. Factors 23 (2): 231–235. https://doi.org/10.1177/001872088102300210.
Srivaree-Ratana, C., A. Konak, and A. E. Smith. 2002. “Estimation of all-terminal network reliability using an artificial neural network.” Comput. Oper. Res. 29 (7): 849–868. https://doi.org/10.1016/S0305-0548(00)00088-5.
Subramanian, H. 1996. “Estimation of car following models.” Master’s thesis, Dept. of Civil and Environmental Engineering, Massachusetts Institute of Technology.
Toledo, T., H. N. Koutsopoulos, and M. E. Ben-Akiva. 2003. “Modeling integrated lane-changing behavior.” Transp. Res. Rec. 1857 (1): 30–38. https://doi.org/10.3141/1857-04.
Treiber, M., A. Hennecke, and D. Helbing. 2000. “Congested traffic states in empirical observations and microscopic simulations.” Phys. Rev. E 62 (2): 1805–1824. https://doi.org/10.1103/PhysRevE.62.1805.
Treiber, M., and A. Kesting. 2013. “Traffic flow dynamics: Data, models and simulation.” Phys. Today 67 (3): 54.
Treiber, M., A. Kesting, and D. Helbing. 2007. “Influence of reaction times and anticipation on stability of vehicular traffic flow.” Transp. Res. Rec. 1999 (1): 23–29. https://doi.org/10.3141/1999-03.
Wang, X., R. Jiang, L. Li, Y. Lin, X. Zheng, and F. Y. Wang. 2017. “Capturing car-following behaviors by deep learning.” IEEE Trans. Intell. Transp. Syst. 19 (3): 910–920. https://doi.org/10.1109/TITS.2017.2706963.
Wasserman, P. D. 1989. Neural computing: Theory and practice. New York: Van Nostrand Reinhold.
Xu, L., S. Hu, Q. Luo, and L. Zhang. 2015. “Research on car-following model considering lateral offset.” Int. J. Eng. Res. Afr. 13: 71–80. https://doi.org/10.4028/www.scientific.net/JERA.13.71.
Xu, R. G. 2015. “Multiple traffic jams in full velocity difference model with reaction time delay.” Int. J. Simul. Models 14 (2): 325–334. https://doi.org/10.2507/IJSIMM14(2)CO7.
Zheng, J., K. Suzuki, and M. Fujita. 2013. “Car-following behaviour with instantaneous driver–vehicle reaction delay: A neural-network-based methodology.” Transp. Res. Part C: Emerging Technol. 36 (Nov): 339–351. https://doi.org/10.1016/j.trc.2013.09.010.
Zheng, L., P. J. Jin, H. Huang, M. Gao, and B. Ran. 2015. “A vehicle type-dependent visual imaging model for analysing the heterogeneous car-following dynamics.” Transportmetrica B: Transp. Dyn. 4 (1): 68–85. https://doi.org/10.1080/21680566.2015.1055618.
Zheng, Z. 2021. “Reasons, challenges, and some tools for doing reproducible transportation research.” Commun. Transp. Res. 1 (Dec): 100004. https://doi.org/10.1016/j.commtr.2021.100004.
Zhou, M., X. Qu, and X. Li. 2017. “A recurrent neural network based microscopic car following model to predict traffic oscillation.” Transp. Res. Part C: Emerging Technol. 84 (Nov): 245–264. https://doi.org/10.1016/j.trc.2017.08.027.

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Go to Journal of Transportation Engineering, Part A: Systems
Journal of Transportation Engineering, Part A: Systems
Volume 148Issue 8August 2022

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Received: Nov 4, 2021
Accepted: Apr 5, 2022
Published online: Jun 3, 2022
Published in print: Aug 1, 2022
Discussion open until: Nov 3, 2022

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Sanhita Das, Ph.D. [email protected]
Assistant Professor, Dept. of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India (corresponding author). Email: [email protected]
Akhilesh Kumar Maurya, Ph.D. [email protected]
Professor, Dept. of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati 781039, India. Email: [email protected]

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