-
Previous Article
Qualitative analysis of some PDE models of traffic flow
- NHM Home
- This Issue
-
Next Article
Explicit construction of solutions to the Burgers equation with discontinuous initial-boundary conditions
Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models
1. | Temple University, Department of Mathematics, 1805 North Broad Street Philadelphia, PA 19122 |
2. | Department of Mechanical Engineering, University of Alberta, Edmonton, AB, T6G 2G8, Canada |
3. | 4700 King Abdullah University of, Science and Technology, Thuwal 23955-6900, Saudi Arabia |
4. | Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 |
References:
[1] |
J. Stat. Phys, 133 (2008), 1083-1105. |
[2] |
SIAM J. Appl. Math., 60 (2000), 916-938.
doi: 10.1137/S0036139997332099. |
[3] |
Arch. Ration. Mech. Anal., 187 (2008), 185-220.
doi: 10.1007/s00205-007-0061-9. |
[4] |
SIAM J. Appl. Math., 71 (2011), 107-127.
doi: 10.1137/090754467. |
[5] |
Comm. Pure Appl. Math., 47 (1994), 787-830.
doi: 10.1002/cpa.3160470602. |
[6] |
Traffic flow—modelling and simulation. Math. Comput. Modelling, 35 (2002), 683-688.
doi: 10.1016/S0895-7177(02)80029-2. |
[7] |
SIAM J. Appl. Math., 63 (2003), 708-721.
doi: 10.1137/S0036139901393184. |
[8] |
Transp. Res. B, 28 (1994), 269-287.
doi: 10.1016/0191-2615(94)90002-7. |
[9] |
Transp. Res. B, 29 (1995), 79-93.
doi: 10.1016/0191-2615(94)00022-R. |
[10] |
Transp. Res. B, 29 (1995), 277-286.
doi: 10.1016/0191-2615(95)00007-Z. |
[11] |
Transp. Res. B, 40 (2006), 396-403.
doi: 10.1016/j.trb.2005.05.004. |
[12] |
Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 1998. |
[13] |
in preparation, 2012. Google Scholar |
[14] |
Univ. of California Press, Berkeley, CA, 1979. Google Scholar |
[15] |
Phys. Rev. E, 79 (2009), 056113, 13 pp.
doi: 10.1103/PhysRevE.79.056113. |
[16] |
Oper. Res., 7 (1959), 79-85.
doi: 10.1287/opre.7.1.79. |
[17] |
SIAM J. Appl. Math., 62 (2001), 729-745.
doi: 10.1137/S0036139900378657. |
[18] |
SIAM J. Appl. Math., 64 (2004), 1175-1185(electronic).
doi: 10.1137/S0036139903431737. |
[19] |
Proceedings of the Highway Research Record, 14 (1935), 448-477. Google Scholar |
[20] |
D. Helbing, Video of traffic waves,, Website. , (). Google Scholar |
[21] |
Reviews of Modern Physics, 73 (2001), 1067-1141.
doi: 10.1103/RevModPhys.73.1067. |
[22] |
Elsevier, New York, 1971. Google Scholar |
[23] |
Commun. Math. Sci., 1 (2003), 1-12. |
[24] |
in preparation, 2013. Google Scholar |
[25] |
Phys. Rev. Lett., 81 (1998), 3797-3800.
doi: 10.1103/PhysRevLett.81.3797. |
[26] |
Phys. Rev. E, 56 (1997), 4200-4216.
doi: 10.1103/PhysRevE.56.4200. |
[27] |
Phys. Rev. E, 48 (1993), R2335-R2338.
doi: 10.1103/PhysRevE.48.R2335. |
[28] |
Phys. Rev. E, 50 (1994), 54-83.
doi: 10.1103/PhysRevE.50.54. |
[29] |
SIAM J. Appl. Math., 60 (2000), 1749-1766.
doi: 10.1137/S0036139999356181. |
[30] |
Phys. Rev. E, 52 (1995), 5574-5582.
doi: 10.1103/PhysRevE.52.5574. |
[31] |
Phys. Rev. E, 52 (1995), 218-221.
doi: 10.1103/PhysRevE.52.218. |
[32] |
Annales des Ponts., 67 (1993), 24-45. Google Scholar |
[33] |
Second edition, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1992.
doi: 10.1007/978-3-0348-8629-1. |
[34] |
SIAM J. Appl. Math., 61 (2000), 1042-1061(electronic).
doi: 10.1137/S0036139999356788. |
[35] |
Comm. Math. Sci., 3 (2005), 101-118. |
[36] |
Discrete Contin. Dyn. Syst., 24 (2009), 511-521.
doi: 10.3934/dcds.2009.24.511. |
[37] |
Proc. Roy. Soc. A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[38] |
Comm. Math. Phys., 108 (1987), 153-175.
doi: 10.1007/BF01210707. |
[39] |
Traffic Engrg. Control, 31 (1990), 466-470. Google Scholar |
[40] |
J. Phys. I France, 2 (1992), 2221-2229.
doi: 10.1051/jp1:1992277. |
[41] |
In A. Ceder, editor, Proceedings of the 14th International Symposium on Transportation and Trafic Theory, pages 51-79, Jerusalem, 1999. Google Scholar |
[42] |
Operations Research, 9 (1961), 209-229.
doi: 10.1287/opre.9.2.209. |
[43] |
Transp. Res. B, 27 (1993), 289-303.
doi: 10.1016/0191-2615(93)90039-D. |
[44] |
Minnesota Department of Transportation, Mn/DOT traffic data,, Website. , (). Google Scholar |
[45] |
Proc. Simulation Council, 1 (1971), 51-61. Google Scholar |
[46] |
Transp. Res. Rec., 722 (1979), 68-77. Google Scholar |
[47] |
Transportation Planning and Technology, 5 (1979), 131-138.
doi: 10.1080/03081067908717157. |
[48] |
Journal of Applied Physics, 24 (1953), 274-281.
doi: 10.1063/1.1721265. |
[49] |
Operations Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[50] |
in preparation, 2013. Google Scholar |
[51] |
SIAM J. Appl. Math., 66 (2006), 1150-1162(electronic).
doi: 10.1137/050627113. |
[52] |
New Journal of Physics, 10 (2008), 033001.
doi: 10.1088/1367-2630/10/3/033001. |
[53] |
Technical report, Yale Bureau of Highway Traffic, 1961. Google Scholar |
[54] |
Federal Highway Administration US Department of Transportation, Next generation simulation (NGSIM),, Website. , (). Google Scholar |
[55] |
Eur. J. Control, 11 (2005), 301-309.
doi: 10.3166/ejc.11.301-309. |
[56] |
Transp. Res. B, 39 (2005), 141-167.
doi: 10.1016/j.trb.2004.03.003. |
[57] |
Proc. Instn. Civ. Engrs., 3 (1954), 158-171.
doi: 10.1680/ipeds.1954.11628. |
[58] |
Comm. Pure Appl. Math., 12 (1959), 113-158.
doi: 10.1002/cpa.3160120107. |
[59] |
Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. xvi+636 pp. |
[60] |
Transp. Res. B, 36 (2002), 275-290.
doi: 10.1016/S0191-2615(00)00050-3. |
show all references
References:
[1] |
J. Stat. Phys, 133 (2008), 1083-1105. |
[2] |
SIAM J. Appl. Math., 60 (2000), 916-938.
doi: 10.1137/S0036139997332099. |
[3] |
Arch. Ration. Mech. Anal., 187 (2008), 185-220.
doi: 10.1007/s00205-007-0061-9. |
[4] |
SIAM J. Appl. Math., 71 (2011), 107-127.
doi: 10.1137/090754467. |
[5] |
Comm. Pure Appl. Math., 47 (1994), 787-830.
doi: 10.1002/cpa.3160470602. |
[6] |
Traffic flow—modelling and simulation. Math. Comput. Modelling, 35 (2002), 683-688.
doi: 10.1016/S0895-7177(02)80029-2. |
[7] |
SIAM J. Appl. Math., 63 (2003), 708-721.
doi: 10.1137/S0036139901393184. |
[8] |
Transp. Res. B, 28 (1994), 269-287.
doi: 10.1016/0191-2615(94)90002-7. |
[9] |
Transp. Res. B, 29 (1995), 79-93.
doi: 10.1016/0191-2615(94)00022-R. |
[10] |
Transp. Res. B, 29 (1995), 277-286.
doi: 10.1016/0191-2615(95)00007-Z. |
[11] |
Transp. Res. B, 40 (2006), 396-403.
doi: 10.1016/j.trb.2005.05.004. |
[12] |
Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 1998. |
[13] |
in preparation, 2012. Google Scholar |
[14] |
Univ. of California Press, Berkeley, CA, 1979. Google Scholar |
[15] |
Phys. Rev. E, 79 (2009), 056113, 13 pp.
doi: 10.1103/PhysRevE.79.056113. |
[16] |
Oper. Res., 7 (1959), 79-85.
doi: 10.1287/opre.7.1.79. |
[17] |
SIAM J. Appl. Math., 62 (2001), 729-745.
doi: 10.1137/S0036139900378657. |
[18] |
SIAM J. Appl. Math., 64 (2004), 1175-1185(electronic).
doi: 10.1137/S0036139903431737. |
[19] |
Proceedings of the Highway Research Record, 14 (1935), 448-477. Google Scholar |
[20] |
D. Helbing, Video of traffic waves,, Website. , (). Google Scholar |
[21] |
Reviews of Modern Physics, 73 (2001), 1067-1141.
doi: 10.1103/RevModPhys.73.1067. |
[22] |
Elsevier, New York, 1971. Google Scholar |
[23] |
Commun. Math. Sci., 1 (2003), 1-12. |
[24] |
in preparation, 2013. Google Scholar |
[25] |
Phys. Rev. Lett., 81 (1998), 3797-3800.
doi: 10.1103/PhysRevLett.81.3797. |
[26] |
Phys. Rev. E, 56 (1997), 4200-4216.
doi: 10.1103/PhysRevE.56.4200. |
[27] |
Phys. Rev. E, 48 (1993), R2335-R2338.
doi: 10.1103/PhysRevE.48.R2335. |
[28] |
Phys. Rev. E, 50 (1994), 54-83.
doi: 10.1103/PhysRevE.50.54. |
[29] |
SIAM J. Appl. Math., 60 (2000), 1749-1766.
doi: 10.1137/S0036139999356181. |
[30] |
Phys. Rev. E, 52 (1995), 5574-5582.
doi: 10.1103/PhysRevE.52.5574. |
[31] |
Phys. Rev. E, 52 (1995), 218-221.
doi: 10.1103/PhysRevE.52.218. |
[32] |
Annales des Ponts., 67 (1993), 24-45. Google Scholar |
[33] |
Second edition, Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel, 1992.
doi: 10.1007/978-3-0348-8629-1. |
[34] |
SIAM J. Appl. Math., 61 (2000), 1042-1061(electronic).
doi: 10.1137/S0036139999356788. |
[35] |
Comm. Math. Sci., 3 (2005), 101-118. |
[36] |
Discrete Contin. Dyn. Syst., 24 (2009), 511-521.
doi: 10.3934/dcds.2009.24.511. |
[37] |
Proc. Roy. Soc. A, 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[38] |
Comm. Math. Phys., 108 (1987), 153-175.
doi: 10.1007/BF01210707. |
[39] |
Traffic Engrg. Control, 31 (1990), 466-470. Google Scholar |
[40] |
J. Phys. I France, 2 (1992), 2221-2229.
doi: 10.1051/jp1:1992277. |
[41] |
In A. Ceder, editor, Proceedings of the 14th International Symposium on Transportation and Trafic Theory, pages 51-79, Jerusalem, 1999. Google Scholar |
[42] |
Operations Research, 9 (1961), 209-229.
doi: 10.1287/opre.9.2.209. |
[43] |
Transp. Res. B, 27 (1993), 289-303.
doi: 10.1016/0191-2615(93)90039-D. |
[44] |
Minnesota Department of Transportation, Mn/DOT traffic data,, Website. , (). Google Scholar |
[45] |
Proc. Simulation Council, 1 (1971), 51-61. Google Scholar |
[46] |
Transp. Res. Rec., 722 (1979), 68-77. Google Scholar |
[47] |
Transportation Planning and Technology, 5 (1979), 131-138.
doi: 10.1080/03081067908717157. |
[48] |
Journal of Applied Physics, 24 (1953), 274-281.
doi: 10.1063/1.1721265. |
[49] |
Operations Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[50] |
in preparation, 2013. Google Scholar |
[51] |
SIAM J. Appl. Math., 66 (2006), 1150-1162(electronic).
doi: 10.1137/050627113. |
[52] |
New Journal of Physics, 10 (2008), 033001.
doi: 10.1088/1367-2630/10/3/033001. |
[53] |
Technical report, Yale Bureau of Highway Traffic, 1961. Google Scholar |
[54] |
Federal Highway Administration US Department of Transportation, Next generation simulation (NGSIM),, Website. , (). Google Scholar |
[55] |
Eur. J. Control, 11 (2005), 301-309.
doi: 10.3166/ejc.11.301-309. |
[56] |
Transp. Res. B, 39 (2005), 141-167.
doi: 10.1016/j.trb.2004.03.003. |
[57] |
Proc. Instn. Civ. Engrs., 3 (1954), 158-171.
doi: 10.1680/ipeds.1954.11628. |
[58] |
Comm. Pure Appl. Math., 12 (1959), 113-158.
doi: 10.1002/cpa.3160120107. |
[59] |
Pure and Applied Mathematics. Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. xvi+636 pp. |
[60] |
Transp. Res. B, 36 (2002), 275-290.
doi: 10.1016/S0191-2615(00)00050-3. |
[1] |
Stefano Villa, Paola Goatin, Christophe Chalons. Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3921-3952. doi: 10.3934/dcdsb.2017202 |
[2] |
Marco Di Francesco, Simone Fagioli, Massimiliano D. Rosini. Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic. Mathematical Biosciences & Engineering, 2017, 14 (1) : 127-141. doi: 10.3934/mbe.2017009 |
[3] |
Shimao Fan, Michael Herty, Benjamin Seibold. Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model. Networks & Heterogeneous Media, 2014, 9 (2) : 239-268. doi: 10.3934/nhm.2014.9.239 |
[4] |
Boris P. Andreianov, Carlotta Donadello, Ulrich Razafison, Julien Y. Rolland, Massimiliano D. Rosini. Solutions of the Aw-Rascle-Zhang system with point constraints. Networks & Heterogeneous Media, 2016, 11 (1) : 29-47. doi: 10.3934/nhm.2016.11.29 |
[5] |
Marte Godvik, Harald Hanche-Olsen. Car-following and the macroscopic Aw-Rascle traffic flow model. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 279-303. doi: 10.3934/dcdsb.2010.13.279 |
[6] |
Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. Homogenization of second order discrete model with local perturbation and application to traffic flow. Discrete & Continuous Dynamical Systems, 2017, 37 (3) : 1437-1487. doi: 10.3934/dcds.2017060 |
[7] |
Helge Holden, Nils Henrik Risebro. Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flow. Networks & Heterogeneous Media, 2018, 13 (3) : 409-421. doi: 10.3934/nhm.2018018 |
[8] |
Wen Shen. Traveling wave profiles for a Follow-the-Leader model for traffic flow with rough road condition. Networks & Heterogeneous Media, 2018, 13 (3) : 449-478. doi: 10.3934/nhm.2018020 |
[9] |
Wen Shen, Karim Shikh-Khalil. Traveling waves for a microscopic model of traffic flow. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2571-2589. doi: 10.3934/dcds.2018108 |
[10] |
Oliver Kolb, Simone Göttlich, Paola Goatin. Capacity drop and traffic control for a second order traffic model. Networks & Heterogeneous Media, 2017, 12 (4) : 663-681. doi: 10.3934/nhm.2017027 |
[11] |
Michael Burger, Simone Göttlich, Thomas Jung. Derivation of second order traffic flow models with time delays. Networks & Heterogeneous Media, 2019, 14 (2) : 265-288. doi: 10.3934/nhm.2019011 |
[12] |
Luisa Fermo, Andrea Tosin. Fundamental diagrams for kinetic equations of traffic flow. Discrete & Continuous Dynamical Systems - S, 2014, 7 (3) : 449-462. doi: 10.3934/dcdss.2014.7.449 |
[13] |
Raimund Bürger, Christophe Chalons, Rafael Ordoñez, Luis Miguel Villada. A multiclass Lighthill-Whitham-Richards traffic model with a discontinuous velocity function. Networks & Heterogeneous Media, 2021, 16 (2) : 187-219. doi: 10.3934/nhm.2021004 |
[14] |
Michael Herty, Adrian Fazekas, Giuseppe Visconti. A two-dimensional data-driven model for traffic flow on highways. Networks & Heterogeneous Media, 2018, 13 (2) : 217-240. doi: 10.3934/nhm.2018010 |
[15] |
Bertrand Haut, Georges Bastin. A second order model of road junctions in fluid models of traffic networks. Networks & Heterogeneous Media, 2007, 2 (2) : 227-253. doi: 10.3934/nhm.2007.2.227 |
[16] |
Zhaosheng Feng, Goong Chen. Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 763-780. doi: 10.3934/dcds.2009.24.763 |
[17] |
Johanna Ridder, Wen Shen. Traveling waves for nonlocal models of traffic flow. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 4001-4040. doi: 10.3934/dcds.2019161 |
[18] |
Nicolas Forcadel, Wilfredo Salazar, Mamdouh Zaydan. Specified homogenization of a discrete traffic model leading to an effective junction condition. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2173-2206. doi: 10.3934/cpaa.2018104 |
[19] |
Marcello D'Abbicco. Small data solutions for semilinear wave equations with effective damping. Conference Publications, 2013, 2013 (special) : 183-191. doi: 10.3934/proc.2013.2013.183 |
[20] |
Emiliano Cristiani, Elisa Iacomini. An interface-free multi-scale multi-order model for traffic flow. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 6189-6207. doi: 10.3934/dcdsb.2019135 |
2019 Impact Factor: 1.053
Tools
Metrics
Other articles
by authors
[Back to Top]