Study on Vehicle Fuel Consumption and Exhaust Emissions Based on a New Viscous Macroscopic Traffic Flow Model
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 149, Issue 2
Abstract
Based on a conserved higher-order traffic flow model (CHO model), we propose a new viscous macroscopic traffic flow model taking into account the diffusion effect in traffic. The model can reasonably smooth the shock wave so that the acceleration is maintained in a reasonable range. To balance the computational efficiency and accuracy, this viscous macroscopic traffic flow model is integrated with the microscopic vehicle fuel consumption and emission models to estimate vehicle fuel consumption and exhaust emissions. The local discontinuous Galerkin (LDG) method is used to solve the viscous model, and the simulation results are inputted into the microscopic models to calculate vehicle fuel consumption and exhaust emissions. Numerical results illustrate that the proposed viscous model is reasonable and that the designed scheme is feasible and effective. Moreover, we provide concrete suggestions for controlling vehicle fuel consumption and exhaust emissions.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This study was jointly supported by grants from the National Natural Science Foundation of China (72021002, 71890973, 72101185, 11972121, and 71901163).
References
Ahn, K., and H. Rakha. 2008. “The effects of route choice decisions on vehicle energy consumption and emissions.” Transp. Res. Part D: Transp. Environ. 13 (3): 151–167. https://doi.org/10.1016/j.trd.2008.01.005.
Ahn, K., H. Rakha, A. A. Trani, and M. Van Aerde. 2002. “Estimating vehicle fuel consumption and emissions based on instantaneous speed and acceleration levels.” J. Transp. Eng. 128 (2): 182–190. https://doi.org/10.1061/(ASCE)0733-947X(2002)128:2(182).
Ahn, K., A. A. Trani, H. Rakha, and M. Van Aerde. 1999. “Microscopic fuel consumption and emission models.” In Proc., 78th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research Board.
An, F., M. Barth, J. Nobeck, and M. Ross. 1997. “Development of comprehensive modal emissions model operating under hot-stabilized conditions.” In Proc., 76th Annual Meeting of the Transportation Research Board. Washington, DC: Transportation Research Board.
Aw, A., and M. Rascle. 2000. “Resurrection of ‘second order’ models of traffic flow.” SIAM J. Appl. Math. 60 (3): 916–938. https://doi.org/10.1137/S0036139997332099.
Bando, M., K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama. 1995. “Dynamical model of traffic congestion and numerical simulation.” Phys. Rev. E 51 (2): 1035–1042. https://doi.org/10.1103/PhysRevE.51.1035.
Bassi, F., and S. Rebay. 1997. “A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations.” J. Comput. Phys. 131 (2): 267–279. https://doi.org/10.1006/jcph.1996.5572.
Boulter, P. G., T. Barlow, I. S. McCrae, S. Latham, D. Elst, and V. D. Burgwal. 2002. Road traffic characteristics, driving patterns and emission factors for congested situations. Delft, Netherlands: Department Powertrains-Environmental Studies & Testing.
Chang, M. F., and R. Herman. 1981. “Trip time versus stop time and fuel consumption characteristics in cities.” Transp. Sci. 15 (3): 183–209. https://doi.org/10.1287/trsc.15.3.183.
Chowdhury, D., L. Santen, and A. Schadschneider. 2000. “Statistical physics of vehicular traffic and some related systems.” Phys. Rep. 329 (4–6): 199–329. https://doi.org/10.1016/S0370-1573(99)00117-9.
Cockburn, B., S. Y. Lin, and C. W. Shu. 1989. “TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems.” J. Comput. Phys. 84 (1): 90–113. https://doi.org/10.1016/0021-9991(89)90183-6.
Cockburn, B., and C. W. Shu. 1998. “The local discontinuous Galerkin method for time-dependent convection-diffusion systems.” SIAM J. Numer. Anal. 35 (6): 2440–2463. https://doi.org/10.1137/S0036142997316712.
Cockburn, B., and C. W. Shu. 2001. “Runge-Kutta discontinuous Galerkin methods for convection-dominated problems.” J. Sci. Comput. 16 (3): 173–261. https://doi.org/10.1023/A:1012873910884.
Daganzo, C. F. 1995. “Requiem for second-order fluid approximations of traffic flow.” Transp. Res. Part B: Methodol. 29 (4): 277–286. https://doi.org/10.1016/0191-2615(95)00007-Z.
Evans, L., and R. Herman. 1978. “Automobile fuel economy on fixed urban driving schedules.” Transp. Sci. 12 (2): 137–152. https://doi.org/10.1287/trsc.12.2.137.
Gazis, D., R. Herman, and R. Rothery. 1961. “Nonlinear follow the leader models of traffic flow.” Oper. Res. 9 (4): 545–567. https://doi.org/10.1287/opre.9.4.545.
Helbing, D. 1995. “Improved fluid-dynamic model for vehicular traffic.” Phys. Rev. E 51 (4): 3164–3169. https://doi.org/10.1103/PhysRevE.51.3164.
Helbing, D., and B. Tilch. 1998. “Generalized force model of traffic dynamics.” Phys. Rev. E 58 (1): 133–138. https://doi.org/10.1103/PhysRevE.58.133.
Huang, Z., and X. X. Ma. 2009. “Integration of emission and fuel consumption computing with traffic simulation using a distributed framework.” In Proc., 12th Int. IEEE Conf. on Intelligent Transportation Systems, 154–159. New York: IEEE.
IEA (International Energy Agency). 2006. emissions from fuel combustion 1971-2004. Paris: IEA.
Jiang, R., Q. S. Wu, and Z. J. 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.
Jiang, R., Q. S. Wu, and Z. J. Zhu. 2002. “A new continuum model for traffic flow and numerical tests.” Transp. Res. Part B: Methodol. 36 (5): 405–419. https://doi.org/10.1016/S0191-2615(01)00010-8.
Jiang, Y. Q., P. J. Ma, and S. G. Zhou. 2015. “Macroscopic modeling approach to estimate traffic-related emissions in urban areas.” Transp. Res. Part D: Transp. Environ. 60 (4): 41–55. https://doi.org/10.1016/j.trd.2015.10.022.
Kerner, B. S., and P. Konhäuser. 1993. “Cluster effect in initially homogeneous traffic flow.” Phys. Rev. E 48 (4): R2335–R2338. https://doi.org/10.1103/PhysRevE.48.R2335.
Kerner, B. S., and P. Konhäuser. 1994. “Structure and parameters of clusters in traffic flow.” Phys. Rev. E 50 (Apr) 54–83. https://doi.org/10.1103/PhysRevE.50.54.
Kühne, R. D. 1984. “Macroscopic freeway model for dense traffic-stop-start waves and incident detection.” In Proc., 9th Int. Symp. on Transportation and Traffic Theory. Delft, Netherlands: Delft University of Technology.
Kurtze, D., and D. Hong. 1995. “Traffic jams, granular flow, and soliton selection.” Phys. Rev. E 52 (1): 218–221. https://doi.org/10.1103/PhysRevE.52.218.
Lax, P. D. 1973. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Philadelphia: Society for Industrial and Applied Mathematics.
Li, S. F., P. Zhang, and S. C. Wong. 2011. “Conservation form of Helbing’s fluid dynamic traffic flow model.” Appl. Math. Mech. 32 (9): 1109–1118. https://doi.org/10.1007/s10483-011-1485-9.
Lighthill, M. J., and G. B. Whitham. 1955. “On kinematic waves. II. A theory of traffic flow on long crowded roads.” Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 229 (1178): 317–345. https://doi.org/10.1098/rspa.1955.0089.
Lin, Z. Y., S. C. Wong, P. Zhang, and X. N. Zhang. 2020. “Bilevel dynamic continuum model for housing allocation and transportation emission problems in an urban city.” Int. J. Sustainable Transp. 15 (1): 55–69. https://doi.org/10.1080/15568318.2019.1683659.
Maerivoet, S., and B. D. Moor. 2005. “Cellular automata models of road traffic.” Phys. Rep. 419 (1): 1–64. https://doi.org/10.1016/j.physrep.2005.08.005.
Meng, Y. C., Z. Y. Lin, X. Y. Li, D. L. Qiao, M. M. Guo, and P. Zhang. 2022. “Asymptotic traveling wave solutions to anisotropic higher-order traffic flow models with viscosities.” Int. J. Mod. Phys. C 2022 (1): 1–17. https://doi.org/10.1142/S012918312250152.
Newell, G. F. 1961. “Nonlinear effects in the dynamics of car following.” Oper. Res. 9 (2): 209–229. https://doi.org/10.1287/opre.9.2.209.
Nie, Y. M., and Q. F. Li. 2013. “An eco-routing model considering microscopic vehicle operating conditions.” Transp. Res. Part B: Methodol. 55 (Jun): 154–170. https://doi.org/10.1016/j.trb.2013.06.004.
Ntziachristos, L., and Z. Samaras. 2000. COPERT III: Computer program to calculate emissions from road transport, methodology and emission factors. Copenhagen, Denmark: European Environment Agency.
Pan, L., E. J. Yao, D. Mackenzie, and R. Zhang. 2019. “Environmental effects of BEV penetration considering traffic status.” J. Transp. Eng. Part A: Syst. 145 (11): 04019048. https://doi.org/10.1061/JTEPBS.0000275.
Payne, H. J. 1971. “Models of freeway traffic and control.” Math. Models Public Syst. 1 (1): 51–61.
Pipes, L. A. 1953. “An operational analysis of traffic dynamics.” J. Appl. Phys. 24 (3): 274–281. https://doi.org/10.1063/1.1721265.
Qiao, D. L., P. Zhang, S. C. Wong, and K. Choi. 2014. “Discontinuous Galerkin finite element scheme for a conserved higher-order traffic flow model by exploring Riemann solvers.” Appl. Math. Comput. 244 (2): 567–576. https://doi.org/10.1016/j.amc.2014.07.002.
Rakha, H., K. Ahn, K. Moran, B. Saerens, and E. Van den Bulck. 2011. “Simple comprehensive fuel consumption and emissions model based on instantaneous vehicle power.” In Proc., Transportation Research Board 90th Annual Meeting. Washington, DC: Transportation Research Board.
Rakha, H., K. Ahn, and A. A. Trani. 2004. “Development of VT-Micro model for estimating hot stabilized light duty vehicle and truck emissions.” Transp. Res. Part D: Transp. Environ. 9 (1): 49–74. https://doi.org/10.1016/S1361-9209(03)00054-3.
Rascle, M. 2002. “An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model.” Math. Comput. Modell. 35 (5–6): 581–590. https://doi.org/10.1016/S0895-7177(02)80022-X.
Richards, P. I. 1956. “Shock waves on the highway.” Oper. Res. 4 (1): 42–51. https://doi.org/10.1287/opre.4.1.42.
Shi, X., D. Zhao, H. Yao, X. Li, D. Hale, and A. Ghiasi. 2021. “Video-based trajectory extraction with deep learning for High-Granularity Highway Simulation (HIGH-SIM).” Commun. Transp. Res. 1 (21): 100014. https://doi.org/10.1016/j.commtr.2021.100014.
Smoller, J. 1983. Shock waves and reaction-diffusion equations. New York: Springer.
Song, T., X. L. Li, H. Kuang, and L. Y. Dong. 2011. “A new continuum traffic model with the effect of viscosity.” J. Hydrodyn. 23 (2): 164–169. https://doi.org/10.1016/S1001-6058(10)60100-X.
Tan, W., Z. C. Li, and Z. J. Tan. 2017. “Modeling the effects of speed limit, acceleration, and deceleration on overall delay and traffic emission at a signalized intersection.” J. Transp. Eng. Part A: Syst. 143 (12): 04017063. https://doi.org/10.1061/JTEPBS.0000101.
Tang, T. Q., H. J. Huang, and H. Y. Shang. 2015. “Influences of the driver’s bounded rationality on micro driving behavior, fuel consumption and emissions.” Transp. Res. Part D: Transp. Environ. 41 (4): 423–432. https://doi.org/10.1016/j.trd.2015.10.016.
Tang, T. Q., H. J. Huang, and H. Y. Shang. 2017. “An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests.” Physica A 468 (10): 322–333. https://doi.org/10.1016/j.physa.2016.10.092.
Toro, E. F. 1999. Riemann solvers and numerical methods for fluid dynamics: A practical introduction. Berlin: Springer.
Whitham, G. B. 1974. Linear and nonlinear waves. New York: Wiley.
Wu, C. X., P. Zhang, S. C. Wong, D. L. Qiao, and S. Q. Dai. 2013. “Solitary wave solution to Aw-Rascle viscous model of traffic flow.” Appl. Math. Mech. 34 (4): 523–528. https://doi.org/10.1007/s10483-013-1687-9.
Wu, C. X., G. Z. Zhao, and B. Ou. 2011. “A fuel economy optimization system with applications in vehicles with human drivers and autonomous vehicles.” Transp. Res. Part D: Transp. Environ. 16 (7): 515–524. https://doi.org/10.1016/j.trd.2011.06.002.
Xiao, H., H. J. Huang, and T. Q. Tang. 2017. “Analysis of energy consumption and emission of the heterogeneous traffic flow consisting of traditional vehicles and electric vehicles.” Mod. Phys. Lett. B 31 (34): 1750324. https://doi.org/10.1142/S0217984917503249.
Xu, R. Y., P. Zhang, S. Q. Dai, and S. C. Wong. 2007. “Admissibility of a wide cluster solution in anisotropic higher-order traffic flow models.” SIAM J. Appl. Math. 68 (2): 562–573. https://doi.org/10.1137/06066641X.
Xu, Y., and C. W. Shu. 2010. “Local discontinuous Galerkin methods for high-order time-dependent partial differential equations.” Commun. Comput. Phys. 21 (1): 1–15. https://doi.org/10.4208/cicp.OA-2016-0020.
Xue, Y., and S. Q. Dai. 2003. “Continuum traffic model with the consideration of two delay time scales.” Phys. Rev. E 68 (6): 066123. https://doi.org/10.1103/PhysRevE.68.066123.
Yang, L. Z., T. T. Li, S. C. Wong, C. W. Shu, and M. P. Zhang. 2019. “Modeling and simulation of urban air pollution from the dispersion of vehicle exhaust: A continuum modeling approach.” Int. J. Sustainable Transp. 13 (10): 722–740. https://doi.org/10.1080/15568318.2018.1510563.
Yin, J., S. C. Wong, N. N. Sze, and H. W. Ho. 2013. “A continuum model for housing allocation and transportation emission problems in a polycentric city.” Int. J. Sustainable Transp. 7 (4): 275–298. https://doi.org/10.1080/15568318.2011.624842.
Yu, L., T. Li, and Z. K. Shi. 2010. “The effect of diffusion in a new viscous continuum traffic model.” Phys. Lett. A 374 (23): 2346–2355. https://doi.org/10.1016/j.physleta.2010.03.056.
Yu, L., and Z. K. Shi. 2007. “Density waves in traffic flow model with relative velocity.” Eur. Phys. J. B 57 (1): 115–120. https://doi.org/10.1140/epjb/e2007-00160-1.
Zegeye, S. K., B. De Schutter, J. Hellendoorn, E. A. Breunesse, and A. Hegyi. 2013. “Integrated macroscopic traffic flow, emission, and fuel consumption model for control purposes.” Transp. Res. Part C Emerging Technol. 31 (4): 158–171. https://doi.org/10.1016/j.trc.2013.01.002.
Zhang, H. M. 2002. “A non-equilibrium traffic model devoid of gas-like behavior.” Transp. Res. Part B: Methodol. 36 (3): 275–290. https://doi.org/10.1016/S0191-2615(00)00050-3.
Zhang, H. M. 2003. “Driver memory, traffic viscosity and a viscous vehicular traffic flow model.” Transp. Res. Part B: Methodol. 37 (1): 27–41. https://doi.org/10.1016/S0191-2615(01)00043-1.
Zhang, P., D. L. Qiao, L. Y. Dong, S. Q. Dai, and S. C. Wong. 2011. “A number of Riemann solvers for a conserved higher order traffic flow model.” In Proc., 4th Int. Joint Conf. on Computational Sciences and Optimization (CSO), 1049–1053. New York: IEEE.
Zhang, P., and S. C. Wong. 2006. “Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models.” Phys. Rev. E 74 (4): 026109. https://doi.org/10.1103/PhysRevE.74.026109.
Zhang, P., S. C. Wong, and S. Q. Dai. 2009. “A conserved higher-order anisotropic traffic flow model: Description of equilibrium and non-equilibrium flows.” Transp. Res. Part B: Methodol. 43 (5): 562–574. https://doi.org/10.1016/j.trb.2008.10.001.
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.
Zhu, Z. J., and C. Yang. 2013. “Visco-elastic traffic flow model.” J. Adv. Transp. 47 (7): 635–649. https://doi.org/10.1002/atr.186.
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© 2022 American Society of Civil Engineers.
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Received: Apr 29, 2022
Accepted: Sep 26, 2022
Published online: Nov 23, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 23, 2023
ASCE Technical Topics:
- Air pollution
- Emissions
- Energy consumption
- Energy efficiency
- Energy engineering
- Engineering fundamentals
- Environmental engineering
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Highway transportation
- Hydrologic engineering
- Infrastructure
- Model accuracy
- Models (by type)
- Pollution
- Traffic engineering
- Traffic flow
- Traffic management
- Traffic models
- Transportation engineering
- Vehicles
- Viscous flow
- Water and water resources
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Cited by
- Zhiyang Lin, S. C. Wong, Xiaoning Zhang, Peng Zhang, Higher-Order Traffic Flow Model Extended to Road Networks, Journal of Transportation Engineering, Part A: Systems, 10.1061/JTEPBS.TEENG-7556, 149, 4, (2023).