Multi-class AR model: comparison with microsimulation model for traffic flow variables at network level of interest and the two-dimensional formulation

References

• Mohan R, Ramadurai G. State-of-the art of macroscopic traffic flow modelling. Int J Adv Eng Sci Appl Math. 2013;5:158–176.
   Google Scholar
• Lighthill MJ, Whitham GB. On kinematic waves. II, A theory of traffic flow on long crowed roads. Proc Roy Soc A. 1955;229:281–345.
   Google Scholar
• Richards PI. Shockwaves on the highway. Oper Res. 1956;4(1):42–51.
   Web of Science ®Google Scholar
• Payne HJ. Models of freeway traffic and control. La Jolla, CA: Simulation Councils, inc; 1971.
   Google Scholar
• Daganzo CF. Requiem of second-order fluid approximations of traffic flow. Transp Res Part B. 1995b;2(4):277–286.
   Web of Science ®Google Scholar
• Payne HJ. FREEFLO: a macroscopic simualtion model of freeway traffic. Transp Res Rec. 1979;722:68–77.
   Google Scholar
• Zhang HM. A theory of non-equilibrium traffic flow. Transp Res Part B. 1998;32:485–498.
   Web of Science ®Google Scholar
• Aw A, Rascle M. Resurrection of “Second Order” models of traffic flow. SIAM J Appl Math. 2000;60:916–938.
   Web of Science ®Google Scholar
• Jiang R, Wu QS, Zhu ZJ. A new continuum model for traffic flow and numerical tests. Transp Res Part B. 2002;36:405–419.
   Web of Science ®Google Scholar
• Colombo RM. A 2 × 2 hyperbolic traffic flow model. MathComput Modell. 2002;35:683–688.
   Web of Science ®Google Scholar
• Bagnerini P, Rascle M. A multi-class homogenized hyperbolic model of traffic flow. SIAM J Math Anal. 2003;35:949–973.
   Web of Science ®Google Scholar
• Jiang R, Wu QS. Extended speed gradient model for mixed traffic. Transp Res Rec. 2004;1883:78–84.
   Google Scholar
• Tang TQ, Huang HJ, Zhao SG, et al. A new dynamic model for heterogeneous traffic flow. Phys Lett A. 2009;373:2461–2466.
   Web of Science ®Google Scholar
• Berthelin F, Degond P, Delitala M, et al. A model for the formation and evolution of traffic jams. Arch Ration Mech Anal. 2008 Feb;187(2):185–220. Available from.
   Web of Science ®Google Scholar
• Degond P, Delitala M. Modelling and simulation of vehicular traffic jam formation. Kinet Relat Mod. 2008;1:279–293.
   Web of Science ®Google Scholar
• Bellomo N, Dogbe C. On the modelling of traffic and crowds: a survey of models, speculations, and perspectives. SIAM J Appl Math. 2011;53:409–463.
   Google Scholar
• Sun M. Interactions of elementary waves for the Aw-Rascle model. SIAM J Appl Math. 2009;69:1542–1558.
   Web of Science ®Google Scholar
• Tveito A, Winther R. Existence, uniqueness, and continuous dependence for a system of hyperbolic conservation laws modeling polymer flooding. SIAM J Appl Math. 1991;22:905–933.
   Web of Science ®Google Scholar
• Godwik M, HancheOlsan H. Existence of solutions for the Aw-Rascle traffic flow model with vacuum. J Hyperbolic Differ Equ. 2008;5:45–63.
   Web of Science ®Google Scholar
• Herty M, Rascle M. Coupling conditions for a class of ‘second -order’ models for traffic flow. SIAM J Math Anal. 2006;38:595–616.
   Web of Science ®Google Scholar
• Jiang WF, Wang Z. Developing an aw–rascle model of traffic flow. J Eng Math. 2016 Apr;97(1):135–146. DOI:10.1007/s10665-015-9801-2
   Web of Science ®Google Scholar
• Mohan R, Ramadurai G. Heterogeneous traffic flow modelling using second-order macroscopic continuum model. Phys Lett A. 2017;381:115–123.
   Web of Science ®Google Scholar
• Mallikarjuna C, Ramachandra Rao K. Area occupancy characteristics of heterogeneous traffic. Transportmetrica. 2006;2:223–236.
   Web of Science ®Google Scholar
• Arasan VT, Dhivya G., Measuring heterogeneous traffic density. International J Civil and Environmental Eng. 2008;2(10):236–240.
   Google Scholar
• Yan Y, Zhang S, Tang J, et al. Understanding characteristics in multivariate traffic flow time series from complex network structure. Phys A. 2017;477:149–160.
   Web of Science ®Google Scholar
• Li L, Su X, Wang Y, et al. Robust casual dependence mining in big data network and its application to traffic flow predictions. Transp Res Part C. 2015;58:292–307.
   Web of Science ®Google Scholar
• Tang J, Liu F, Zou Y, et al. An improved fuzzy neural network for traffic speed prediction considering periodic characeristic. IEEE Trans Intell Transp Syst. 2017;18(9):2340–2349.
   Web of Science ®Google Scholar
• Asif TM, Dauwels J, Goh YC, et al. Spatiotemporal patterns in large-scale traffic speed prediction. IEEE Trans Intell Transp Syst. 2014;15(2):794–804.
   Web of Science ®Google Scholar
• Vlahogianni IE, Karlaftis GM, Golias CJ. Short-term traffic forecasting: where we are and where we’re going. Transp Res Part C. 2014;43:3–19.
   Web of Science ®Google Scholar
• Leveque JR. Numerical methods for conservation laws. Germany: Birkhauser; 2002.
   Google Scholar
• Steven JG. The Nlopt non-linear optimization package. 2013 Apr 22 [cited 2008]. Available from: http://ab-initio.mit.edu
   Google Scholar