Chun-xiu WU;Tao SONG;Peng ZHANG;S. C. WONG . Phase-plane analysis of conserved higher-order traffic flow model[J]. Applied Mathematics and Mechanics, 2012 , 33(12) : 1505 -1512 . DOI: 10.1007/s10483-012-1640-x

[1] Kerner, B. S. and Konhäuser, P. Structure and parameters of clusters in traffic flow. PhysicalReview E, 50, 54-83 (1994)
[2] Greenberg, J. M. Congestion redux. SIAM Journal on Applied Mathematics, 64(4), 1175-1185(2004)
[3] Siebel, F. and Mauser, W. Synchronized flow and wide moving jams from balanced vehiculartraffic. Physical Review E, 73, 066108 (2006)
[4] Zhang, P.,Wong, S. C., and Dai, S. Q. Characteristic parameters of a wide cluster in a higher-ordertraffic flow model. Chinese Physics Letters, 23, 516-519 (2006)
[5] Zhang, P. and Wong, S. C. Essence of conservation forms in the traveling wave solutions of higherordertraffic flow models. Physical Review E, 74, 026109 (2006)
[6] Xu, R. Y., Zhang, P., Dai, S. Q., and Wong, S. C. Admissiblity of a wide cluster solution in“anisotropic” higher-order traffic flow models. SIAM Journal on Applied Mathematics, 68, 562-573 (2007)
[7] Zhang, P., Wu, C. X., and Wong, S. C. A semi-discrete model and its approach to a solution forwide moving jam in traffic flow. Physica A, 391, 456-463 (2012)
[8] Helbing, D., Hennecke, A., and Treiber, M. Phase diagram of traffic states in the presence ofinhomogeneities. Physical Review Letters, 82, 4360-4363 (1999)
[9] Treiber, M., Kesting, A., and Helbing, D. Three-phase traffic theory and two-phase models witha fundamental diagram in the light of empirical stylized facts. Transportation Research Part B,44, 983-1000 (2010)
[10] Kühne, R. D. Traffic patterns in unstable traffic flow on freeways, highway capacity and level ofservice. Proceedings of the International Symposium on Highway Capacity (ed. Brannolte, U.),Balkema, Rotterdam, 211-223 (1991)
[11] Wilson, R. E. and Berg, P. Existence and classification of traveling wave solutions to second orderhighway traffic models. Traffic and Granular Flow’ 01 (eds. Fukui, M., Sugiyama, Y., Schreckenberg,M., and Wolf, D. E.), Springer, Berlin, 85-90 (2003)
[12] Lee, H. K., Lee, H. W., and Kim, D. Steady-state solutions of hydrodynamic traffic models.Physical Review E, 69, 016118 (2004)
[13] Saavedra, P. and Velasco, R. M. Phase-space analysis for hydrodynamic traffic models. PhysicalReview E, 79, 066103 (2009)
[14] Tomer, E., Safonov, L., and Havlin, S. Presence of many stable non-homogeneous states in aninertial car-following model. Physical Review Letters, 84, 382-385 (2000)
[15] Zhang, P., Wong, S. C., and Dai, S. Q. A conserved higher-order anisotropic traffic flow model:description of equilibrium and non-equilibrium flows. Transportation Research Part B, 43, 562-574(2009)
[16] Lighthill, M. J. and Whitham, G. B. On kinematic waves: II. a theory of traffic flow on longcrowded roads. Proceedings of the Royal Society of London, Series A, 229(1178), 317-345 (1955)
[17] Richards, P. I. Shockwaves on the highway. Operations Research, 4(1), 42-51 (1956)
[18] Zhang, P., Qiao, D. L., Dong, L. Y., Dai, S. Q., and Wong, S. C. A number of Riemann solversfor a conserved higher-order traffic flow model. The Fourth International Joint Conference onComputational Sciences and Optimization, 1049-1053 (2011)
[19] Rascle, M. An improved macroscopic model of traffic flow: derivation and links with the Lighthill-Whitham model. Mathematical and Computer Modelling, 35, 581-590 (2002)
[20] Zhang, H. M. A non-equilibrium traffic model devoid of gas-like behavior. Transportation ResearchPart B, 36, 275-290 (2002)