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A mixed system modeling two-directional pedestrian flows
A hybrid model for traffic flow and crowd dynamics with random individual properties
1. | Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, D-70569 Stuttgart, Germany |
References:
[1] |
P. Amorim, R. M. Colombo and A. Teixeira, On the numerical integration of scalar conservation laws,, preprint, (2013). Google Scholar |
[2] |
A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow,, SIAM J. Appl. Math., 60 (2000), 916.
doi: 10.1137/S0036139997332099. |
[3] |
N. Bellomo and C. Dogbé, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models,, Math. Models Methods Appl. Sci., 18 (2008), 1317.
doi: 10.1142/S0218202508003054. |
[4] |
N. Bellomo and C. Dogbé, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives,, SIAM Review, 53 (2011), 409.
doi: 10.1137/090746677. |
[5] |
R. M. Colombo, M. Garavello and M. Lécureux-Mercier, A class of non-local models for pedestrian traffic,, Mathematical Models and Methods in the Applied Sciences, 22 (2012).
doi: 10.1142/S0218202511500230. |
[6] |
R. M. Colombo and N. Pogodaev, Confinement strategies in a model for the interaction between individuals and a continuum,, SIAM J. Appl. Dyn. Syst., 11 (2012), 741.
doi: 10.1137/110854321. |
[7] |
M. Crandall and A. Majda, The method of fractional steps for conservation laws,, Numer. Math., 34 (1980), 285.
doi: 10.1007/BF01396704. |
[8] |
E. Cristiani, B. Piccoli and A. Tosin, Multiscale modeling of granular flows with application to crowd dynamics,, Multiscale Model. Simul., 9 (2011), 155.
doi: 10.1137/100797515. |
[9] |
C. F. Daganzo, Requiem for second-order fluid approximations to traffic flow,, Transp. Res. B, 29 (1995), 277.
doi: 10.1016/0191-2615(95)00007-Z. |
[10] |
G. Dal Maso, P. G. Lefloch and F. Murat, Definition and weak stability of nonconservative products,, J. Math. Pures Appl. (9), 74 (1995), 483.
|
[11] |
D. Helbing, Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models,, The European Physical Journal B, 69 (2009), 539.
doi: 10.1140/epjb/e2009-00192-5. |
[12] |
D. Helbing and A. F. Johansson, On the controversy around Daganzo's requiem for and Aw-Rascle's resurrection of second-order traffic flow models,, Modelling and Optimisation of Flows on Networks, (2013), 271.
doi: 10.1007/978-3-642-32160-3_4. |
[13] |
R. L. Hughes, A continuum theory for the flow of pedestrians,, Transportation Research Part B: Methodological, 36 (2002), 507.
doi: 10.1016/S0191-2615(01)00015-7. |
[14] |
S. N. Kružhkov, First order quasilinear equations with several independent variables,, Mat. Sb. (N.S.), 81 (1970), 228.
|
[15] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317.
doi: 10.1098/rspa.1955.0089. |
[16] |
S. Mishra and C. Schwab, Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data,, Math. Comp., 81 (2012), 1979.
doi: 10.1090/S0025-5718-2012-02574-9. |
[17] |
P. I. Richards, Shock waves on the highway,, Operations Res., 4 (1956), 42.
doi: 10.1287/opre.4.1.42. |
[18] |
M. Sabry Hassouna and A. A. Farag, Multistencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 29 (2007), 1563.
doi: 10.1109/TPAMI.2007.1154. |
[19] |
Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S.-i. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam,, New Journal of Physics, 10 (2008).
doi: 10.1088/1367-2630/10/3/033001. |
[20] |
S.-i. Tadaki, M. Kikuchi, F. Minoru, A. Nakayama, K. Nishinari, A. Shibata, Y. Sugiyama, T. Yosida and S. Yukawa, Phase transition in traffic jam experiment on a circuit,, New Journal of Physics, 15 (2013).
doi: 10.1088/1367-2630/15/10/103034. |
show all references
References:
[1] |
P. Amorim, R. M. Colombo and A. Teixeira, On the numerical integration of scalar conservation laws,, preprint, (2013). Google Scholar |
[2] |
A. Aw and M. Rascle, Resurrection of "second order'' models of traffic flow,, SIAM J. Appl. Math., 60 (2000), 916.
doi: 10.1137/S0036139997332099. |
[3] |
N. Bellomo and C. Dogbé, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models,, Math. Models Methods Appl. Sci., 18 (2008), 1317.
doi: 10.1142/S0218202508003054. |
[4] |
N. Bellomo and C. Dogbé, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives,, SIAM Review, 53 (2011), 409.
doi: 10.1137/090746677. |
[5] |
R. M. Colombo, M. Garavello and M. Lécureux-Mercier, A class of non-local models for pedestrian traffic,, Mathematical Models and Methods in the Applied Sciences, 22 (2012).
doi: 10.1142/S0218202511500230. |
[6] |
R. M. Colombo and N. Pogodaev, Confinement strategies in a model for the interaction between individuals and a continuum,, SIAM J. Appl. Dyn. Syst., 11 (2012), 741.
doi: 10.1137/110854321. |
[7] |
M. Crandall and A. Majda, The method of fractional steps for conservation laws,, Numer. Math., 34 (1980), 285.
doi: 10.1007/BF01396704. |
[8] |
E. Cristiani, B. Piccoli and A. Tosin, Multiscale modeling of granular flows with application to crowd dynamics,, Multiscale Model. Simul., 9 (2011), 155.
doi: 10.1137/100797515. |
[9] |
C. F. Daganzo, Requiem for second-order fluid approximations to traffic flow,, Transp. Res. B, 29 (1995), 277.
doi: 10.1016/0191-2615(95)00007-Z. |
[10] |
G. Dal Maso, P. G. Lefloch and F. Murat, Definition and weak stability of nonconservative products,, J. Math. Pures Appl. (9), 74 (1995), 483.
|
[11] |
D. Helbing, Derivation of non-local macroscopic traffic equations and consistent traffic pressures from microscopic car-following models,, The European Physical Journal B, 69 (2009), 539.
doi: 10.1140/epjb/e2009-00192-5. |
[12] |
D. Helbing and A. F. Johansson, On the controversy around Daganzo's requiem for and Aw-Rascle's resurrection of second-order traffic flow models,, Modelling and Optimisation of Flows on Networks, (2013), 271.
doi: 10.1007/978-3-642-32160-3_4. |
[13] |
R. L. Hughes, A continuum theory for the flow of pedestrians,, Transportation Research Part B: Methodological, 36 (2002), 507.
doi: 10.1016/S0191-2615(01)00015-7. |
[14] |
S. N. Kružhkov, First order quasilinear equations with several independent variables,, Mat. Sb. (N.S.), 81 (1970), 228.
|
[15] |
M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads,, Proc. Roy. Soc. London. Ser. A., 229 (1955), 317.
doi: 10.1098/rspa.1955.0089. |
[16] |
S. Mishra and C. Schwab, Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data,, Math. Comp., 81 (2012), 1979.
doi: 10.1090/S0025-5718-2012-02574-9. |
[17] |
P. I. Richards, Shock waves on the highway,, Operations Res., 4 (1956), 42.
doi: 10.1287/opre.4.1.42. |
[18] |
M. Sabry Hassouna and A. A. Farag, Multistencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 29 (2007), 1563.
doi: 10.1109/TPAMI.2007.1154. |
[19] |
Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S.-i. Tadaki and S. Yukawa, Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam,, New Journal of Physics, 10 (2008).
doi: 10.1088/1367-2630/10/3/033001. |
[20] |
S.-i. Tadaki, M. Kikuchi, F. Minoru, A. Nakayama, K. Nishinari, A. Shibata, Y. Sugiyama, T. Yosida and S. Yukawa, Phase transition in traffic jam experiment on a circuit,, New Journal of Physics, 15 (2013).
doi: 10.1088/1367-2630/15/10/103034. |
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