Multiclass first-order modelling of traffic networks using discontinuous flow-density relationships

References

• Buisson , C , Lebacque , JP and Lesort , JB . 1996 . “ STRADA, a discretized macroscopic model of vehicular traffic flow in complex networks based on the godunov scheme ” . In Symposium on modeling, analysis and simulation 976 – 981 . Lille, , France
   Google Scholar
• Chanut , S . 2005 . “ First order macroscopic traffic flow model for mixed traffic including moving bottleneck effects ” . In Proceedings of the 16th international symposium on transportation and traffic theory, Edited by: Mahmassani , HS . 365 – 386 . Maryland, , USA
   Google Scholar
• Chanut , S and Buisons , C . 2003 . A macroscopic model and its numerical solution for a two-flow mixed traffic with different speeds and lengths . Transportation Research Record , 1852 : 209 – 219 .
   Google Scholar
• Coclite , GM and Piccoli , G . 2005 . Traffic flow on a road network . SIAM Journal of Mathematical Analysis , 36 : 1862 – 1886 .
   Web of Science ®Google Scholar
• Daganzo , CF . 1994 . The cell transmission model, part II: network traffic . Transportation Research B , 28 : 279 – 293 .
   Google Scholar
• Elloumi , N , Hadj-Salem , H and Papageorgiou , M . 1994 . METACOR, a macroscopic modeling tool for urban corridors . Proceedings of the 2nd triennial symposium on transportation analysis , Capri, Italy (CD ROM)
   Google Scholar
• Garavello , M and Piccoli , B . 2006 . Traffic flow on a road network using the Aw-Rascle model . Communications in Partial Differential Equations , 31 : 243 – 275 .
   Web of Science ®Google Scholar
• Godunov , S . 1959 . Finite difference methods for numerical computation of discontinuous solution of the equations of fluid dynamics . Sbornik: Mathematics , 47 : 271 – 306 .
   Google Scholar
• Helbing , D . 1999a . MASTER: macroscopic traffic simulation based on a gas-kinetic non-local traffic model . Transportation Research B , 35 ( 2 ) : 183 – 211 .
   Google Scholar
• Helbing , D , Hennecke , A and Treiber , M . 1999b . Phase diagram of traffic states in the presence of inhomogeneities . Physical Review Letters , 82 ( 21 ) : 4360 – 4363 .
   Web of Science ®Google Scholar
• Helbing , D and Treiber , M . 1998 . Gas-kinetic based traffic flow models explaining observed hysteretic phase transition . Physical Review Letters , 81 : 3042 – 3045 .
   Web of Science ®Google Scholar
• Herty , M , Kirchner , C and Moutari , S . 2006 . Multi-class traffic models on road networks . Communications in Mathematical Sciences , 4 : 591 – 608 .
   Google Scholar
• Herty , M and Rascle , M . 2006 . Coupling conditions for a class of second order models for traffic flow . SIAM Journal of Mathematical Analysis , 38 : 595 – 61 .
   Web of Science ®Google Scholar
• Highway Capacity Manual. 2000 . Washington D.C : Transportation Research Board .
   Google Scholar
• Holden , H and Risebro , N . 1995 . A mathematical model of traffic flow on a network of unidirectional roads . SIAM Journal of Mathematical Analysis , 26 : 999 – 1017 .
   Web of Science ®Google Scholar
• Hoogendoorn , SP and Bovy , PHL . 1999 . “ Proceedings of the 14th international symposium on transportation and traffic theory ” . In Multiclass macroscopic traffic flow modeling: a multilane generalization using gas-kinetic theory Edited by: Ceder , A . 27 – 50 . Jerusalem, , Israel
   Google Scholar
• Jin , WL and Zhang , HM . 2003 . The inhomogeneous kinematic wave traffic flow model as a resonant nonlinear system . Transportation Science , 37 : 294 – 311 .
   Google Scholar
• Kerner , B . 2004 . The physics of traffic , Berlin : Springer .
   Google Scholar
• Lebacque , JP . 1996 . The Godunov scheme and what it means for first-order traffic flow models . Proceedings of the 13th international symposium on transportation and traffic theory , : 647 – 677 .
   Google Scholar
• Lebacque , JP and Khoshyaran , MM . 2005 . “ First-order macroscopic traffic flow models: intersection modeling, network modeling ” . In Proceedings of the 16th international symposium on transportation and traffic theory Edited by: Mahmassani , HS . 365 – 386 . Maryland, , USA
   Google Scholar
• LeVeque , R and Pelanti , M . 2001 . A class of approximate Riemann solvers and their relation to relaxation schemes . Journal of Computational Physics , 172 : 572 – 591 .
   Web of Science ®Google Scholar
• Lighthill , MH and Whitham , GB . 1955 . On kinematic waves 2: a theory of traffic flow on long, crowded roads . Proceedings of the Royal Society of London , 29 ( 1178 ) : 317 – 345 .
   Google Scholar
• Logghe , S . 2003 . “ Dynamic modeling of heterogeneous vehicular traffic ” . In PhD thesis , Belgium : Katholieke University of Leuven .
   Google Scholar
• Mahmassani , H and Jayakrishnan , R . 1991 . System performance and user response under real-time information in a congest traffic corridor . Transportation Research A , 25 : 293 – 307 .
   Google Scholar
• Ngoduy , D . 2006 . Derivation of continuum traffic model for weaving sections on freeways . Transportmetrica , 2 : 199 – 222 .
   Web of Science ®Google Scholar
• Ngoduy , D . 2008 . Operational effects of acceleration lane on main traffic flow at discontinuities . Transportmetrica , 4 : 195 – 207 .
   Web of Science ®Google Scholar
• Ngoduy , D and Liu , R . 2007 . Multiclass first-order simulation model to explain non-linear traffic phenomena . Physica A , 385 : 667 – 682 .
   Web of Science ®Google Scholar
• Richards , PI . 1956 . Shock waves on the highway . Operations Research , 4 : 42 – 51 .
   Web of Science ®Google Scholar
• Sod , GA . 1985 . Numerical methods in fluid dynamics , Cambridge, MA : Cambridge University Press .
   Google Scholar
• Tampere , CMJ . 2004 . “ Human-kinetic multiclass traffic flow theory and modeling ” . In PhD thesis , Netherlands : Delft University of Technology .
   Google Scholar
• Treiber , M and Helbing , D . 1999 . Macroscopic simulation of widely scattered synchronized traffic states . Journal of Physics A: Mathematical and General , 59 : 239 – 253 .
   Google Scholar
• Wong , GCK and Wong , SC . 2002 . A multiclass traffic flow model-an extension of LWR model with heterogeneous drivers . Transportation Research A , 36 : 827 – 841 .
   Google Scholar
• Zhang , P . 2006a . Hyperbolicity and kinematic waves of a class of multi-population partial differential equations . European Journal of Applied Mathematics , 17 : 171 – 200 .
   Web of Science ®Google Scholar
• Zhang , P , Wong , SC and Shu , CW . 2006b . A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway . Journal of Computational Physics , 212 : 739 – 756 .
   Web of Science ®Google Scholar
• Zhang , P , Wong , SC and Xu , ZL . 2008 . A hybrid scheme for solving a multi-class traffic flow with complex wave breaking . Computer Methods in Applied Mechanics and Engineering , 197 : 3816 – 3827 .
   Web of Science ®Google Scholar