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Preface
Two-way multi-lane traffic model for pedestrians in corridors
1. | 1-University Paris-Sud, Laboratory of Theoretical Physics, Batiment 210, F-91405 ORSAY Cedex, France |
2. | 1-Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse |
3. | 5-Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States |
References:
[1] |
S. Al-nasur and P. Kachroo, "A Microscopic-to-Macroscopic Crowd Dynamic Model," Proceedings of the IEEE ITSC 2006, 2006 IEEE Intelligent Transportation Systems Conference, Toronto, Canada, September, (2006), 17-20. |
[2] |
A. Aw, A. Klar, A. Materne and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63 (2002), 259-278.
doi: 10.1137/S0036139900380955. |
[3] |
A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math., 60 (2000), 916-938.
doi: 10.1137/S0036139997332099. |
[4] |
N. Bellomo and C. Dogbé, On the modelling crowd dynamics: From scaling to second order hyperbolic macroscopic models, Math. Models Methods Appl. Sci., 18 (2008), 1317-1345.
doi: 10.1142/S0218202508003054. |
[5] |
S. Benzoni-Gavage and R. M. Colombo, An $n$-populations model for traffic flow, European J. Appl. Math., 14 (2003), 587-612.
doi: 10.1017/S0956792503005266. |
[6] |
F. Berthelin, P. Degond, M. Delitala and M. Rascle, A model for the formation and evolution of traffic jams, Arch. Rat. Mech. Anal., 187 (2008), 185-220.
doi: 10.1007/s00205-007-0061-9. |
[7] |
F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, J. Royer and M. Rascle, A traffic-flow model with constraints for the modeling of traffic jams, Math. Models Methods Appl. Sci., 18 (2008), 1269-1298.
doi: 10.1142/S0218202508003030. |
[8] |
F. Bouchut, Y. Brenier, J. Cortes and J. F. Ripoll, A hierachy of models for two-phase flows, J. Nonlinear Sci., 10 (2000), 639-660.
doi: 10.1007/s003320010006. |
[9] |
C. Burstedde, K. Klauck, A. Schadschneider and J. Zittarz, Simulation of pedestrian dynamics using a 2-dimensional cellular automaton, Physica A, 295 (2001), 507-525, arXiv:cond-mat/0102397.
doi: 10.1016/S0378-4371(01)00141-8. |
[10] |
C. Chalons, Numerical approximation of a macroscopic model of pedestrian flows, SIAM J. Sci. Comput., 29 (2007), 539-555.
doi: 10.1137/050641211. |
[11] |
R. M. Colombo and M. D. Rosini, Pedestrian flows and nonclassical shocks, Math. Methods Appl. Sci., 28 (2005), 1553-1567.
doi: 10.1002/mma.624. |
[12] |
C. Daganzo, Requiem for second order fluid approximations of traffic flow, Transp. Res. B, 29 (1995), 277-286.
doi: 10.1016/0191-2615(95)00007-Z. |
[13] |
P. Degond and M. Delitala, Modelling and simulation of vehicular traffic jam formation, Kinet. Relat. Models, 1 (2008), 279-293.
doi: 10.3934/krm.2008.1.279. |
[14] |
P. Degond, J. Hua and L. Navoret, Numerical simulations of the Euler system with congestion constraint,, preprint, ().
|
[15] |
P. Degond and M. Tang, All speed scheme for the low Mach number limit of the isentropic Euler equations, Commun. Comput. Phys., 10 (2011), 1-31, arXiv:0908.1929. |
[16] |
R. Y. Guo and H. J. Huang, A mobile lattice gas model for simulating pedestrian evacuation, Physica A, 387 (2008), 580-586.
doi: 10.1016/j.physa.2007.10.001. |
[17] |
S. J. Guy, J. Chhugani, C. Kim, N. Satish, M. C. Lin, D. Manocha and P. Dubey, "Clearpath: Highly Parallel Collision Avoidance for Multi-Agent Simulation," ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA), (2009), 177-187. |
[18] |
D. Helbing, A mathematical model for the behavior of pedestrians, Behavioral Science, 36 (1991), 298-310.
doi: 10.1002/bs.3830360405. |
[19] |
D. Helbing, A fluid-dynamic model for the movement of pedestrians, Complex Systems, 6 (1992), 391-415. |
[20] |
D. Helbing and P. Molnàr, Social force model for pedestrian dynamics, Physical Review E, 51 (1995), 4282-4286.
doi: 10.1103/PhysRevE.51.4282. |
[21] |
D. Helbing and P. Molnàr, Self-organization of complex structures. From individual to collective dynamics, Proceedings of the International Conference held in Berlin, September 24-28, 1995, Edited by Frank Schweitzer. Gordon and Breach Science Publishers, Amsterdam, 1997. |
[22] |
L. F. Henderson, On the fluid mechanics of human crowd motion, Transportation Research, 8 (1974), 509-515.
doi: 10.1016/0041-1647(74)90027-6. |
[23] |
S. Hoogendoorn and P. H. L. Bovy, Simulation of pedestrian flows by optimal control and differential games, Optimal Control Appl. Methods, 24 (2003), 153-172.
doi: 10.1002/oca.727. |
[24] |
R. L. Hughes, A continuum theory for the flow of pedestrians, Transportation Research B, 36 (2002), 507-535.
doi: 10.1016/S0191-2615(01)00015-7. |
[25] |
R. L. Hughes, The flow of human crowds, Ann. Rev. Fluid Mech., 35 (2003), 169-182.
doi: 10.1146/annurev.fluid.35.101101.161136. |
[26] |
A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), 240-282. |
[27] |
R. J. LeVeque, "Finite Volume Methods for Hyperbolic Problems," Cambridge Texts in Mathematics, Cambridge University Press, Cambridge, 2002.
doi: 10.1017/CBO9780511791253. |
[28] |
M. J. Lighthill and J. B. Whitham, On kinematic waves. I: Flow movement in long rivers. II: A theory of traffic flow on long crowded roads, Proc. Roy. Soc., A229 (1955), 281-345. |
[29] |
B. Maury, A. Roudneff-Chupin and F. Santambrogio, A macroscopic crowd motion model of gradient flow type, Math. Models Methods Appl. Sci., 20 (2010), 1787-1821.
doi: 10.1142/S0218202510004799. |
[30] |
B. Maury and J. Venel, A mathematical framework for a crowd motion model, C. R. Acad. Sci. Paris, 346 (2008), 1245-1250. |
[31] |
K. Nishinari, A. Kirchner, A. Namazi and A. Schadschneider, Extended floor field CA model for evacuation dynamics, IEICE Transp. Inf. & Syst., E87-D (2004), 726-732, arXiv:cond-mat/0306262. |
[32] |
J. Ondřej, J. Pettré, A.-H. Olivier and S. Donikian, "A Synthetic-Vision Based Steering Approach for Crowd Simulation," SIGGRAPH '10, 2010. |
[33] |
S. Paris, J. Pettré and S. Donikian, Pedestrian reactive navigation for crowd simulation: A predictive approach, Eurographics, 26 (2007), 665-674. |
[34] |
Pedigree team, Pedestrian flow measurements and analysis in an annular setup,, in preparation., ().
|
[35] |
J. Pettré, J. Ondřej, A.-H. Olivier, A. Cretual and S. Donikian, "Experiment-Based Modeling, Simulation and Validation of Interactions Between Virtual Walkers," SCA '09: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (2009), 189-198. |
[36] |
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85-107, arXiv:0812.4390. |
[37] |
B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal., 199 (2011), 707-738, arXiv:0811.3383. |
[38] |
C. W. Reynolds, "Steering Behaviors for Autonomous Characters," Proceedings of Game Developers Conference 1999, San Jose, California, (1999), 763-782. |
[39] |
V. Shvetsov and D. Helbing, Macroscopic dynamics of multi-lane traffic, Phys. Rev. E, 59 (1999), 6328-6339, arXiv:cond-mat/9906430.
doi: 10.1103/PhysRevE.59.6328. |
[40] |
J. van den Berg and H. Overmars, Planning time-minimal safe paths amidst unpredictably moving obstacles, Int. Journal on Robotics Research, 27 (2008), 1274-1294.
doi: 10.1177/0278364908097581. |
[41] |
W. G. Weng, S. F. Shena, H. Y. Yuana and W. C. Fana, A behavior-based model for pedestrian counter flow, Physica A, 375 (2007), 668-678.
doi: 10.1016/j.physa.2006.09.028. |
[42] |
M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Res. B, 36 (2002), 275-290.
doi: 10.1016/S0191-2615(00)00050-3. |
show all references
References:
[1] |
S. Al-nasur and P. Kachroo, "A Microscopic-to-Macroscopic Crowd Dynamic Model," Proceedings of the IEEE ITSC 2006, 2006 IEEE Intelligent Transportation Systems Conference, Toronto, Canada, September, (2006), 17-20. |
[2] |
A. Aw, A. Klar, A. Materne and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math., 63 (2002), 259-278.
doi: 10.1137/S0036139900380955. |
[3] |
A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math., 60 (2000), 916-938.
doi: 10.1137/S0036139997332099. |
[4] |
N. Bellomo and C. Dogbé, On the modelling crowd dynamics: From scaling to second order hyperbolic macroscopic models, Math. Models Methods Appl. Sci., 18 (2008), 1317-1345.
doi: 10.1142/S0218202508003054. |
[5] |
S. Benzoni-Gavage and R. M. Colombo, An $n$-populations model for traffic flow, European J. Appl. Math., 14 (2003), 587-612.
doi: 10.1017/S0956792503005266. |
[6] |
F. Berthelin, P. Degond, M. Delitala and M. Rascle, A model for the formation and evolution of traffic jams, Arch. Rat. Mech. Anal., 187 (2008), 185-220.
doi: 10.1007/s00205-007-0061-9. |
[7] |
F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, J. Royer and M. Rascle, A traffic-flow model with constraints for the modeling of traffic jams, Math. Models Methods Appl. Sci., 18 (2008), 1269-1298.
doi: 10.1142/S0218202508003030. |
[8] |
F. Bouchut, Y. Brenier, J. Cortes and J. F. Ripoll, A hierachy of models for two-phase flows, J. Nonlinear Sci., 10 (2000), 639-660.
doi: 10.1007/s003320010006. |
[9] |
C. Burstedde, K. Klauck, A. Schadschneider and J. Zittarz, Simulation of pedestrian dynamics using a 2-dimensional cellular automaton, Physica A, 295 (2001), 507-525, arXiv:cond-mat/0102397.
doi: 10.1016/S0378-4371(01)00141-8. |
[10] |
C. Chalons, Numerical approximation of a macroscopic model of pedestrian flows, SIAM J. Sci. Comput., 29 (2007), 539-555.
doi: 10.1137/050641211. |
[11] |
R. M. Colombo and M. D. Rosini, Pedestrian flows and nonclassical shocks, Math. Methods Appl. Sci., 28 (2005), 1553-1567.
doi: 10.1002/mma.624. |
[12] |
C. Daganzo, Requiem for second order fluid approximations of traffic flow, Transp. Res. B, 29 (1995), 277-286.
doi: 10.1016/0191-2615(95)00007-Z. |
[13] |
P. Degond and M. Delitala, Modelling and simulation of vehicular traffic jam formation, Kinet. Relat. Models, 1 (2008), 279-293.
doi: 10.3934/krm.2008.1.279. |
[14] |
P. Degond, J. Hua and L. Navoret, Numerical simulations of the Euler system with congestion constraint,, preprint, ().
|
[15] |
P. Degond and M. Tang, All speed scheme for the low Mach number limit of the isentropic Euler equations, Commun. Comput. Phys., 10 (2011), 1-31, arXiv:0908.1929. |
[16] |
R. Y. Guo and H. J. Huang, A mobile lattice gas model for simulating pedestrian evacuation, Physica A, 387 (2008), 580-586.
doi: 10.1016/j.physa.2007.10.001. |
[17] |
S. J. Guy, J. Chhugani, C. Kim, N. Satish, M. C. Lin, D. Manocha and P. Dubey, "Clearpath: Highly Parallel Collision Avoidance for Multi-Agent Simulation," ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA), (2009), 177-187. |
[18] |
D. Helbing, A mathematical model for the behavior of pedestrians, Behavioral Science, 36 (1991), 298-310.
doi: 10.1002/bs.3830360405. |
[19] |
D. Helbing, A fluid-dynamic model for the movement of pedestrians, Complex Systems, 6 (1992), 391-415. |
[20] |
D. Helbing and P. Molnàr, Social force model for pedestrian dynamics, Physical Review E, 51 (1995), 4282-4286.
doi: 10.1103/PhysRevE.51.4282. |
[21] |
D. Helbing and P. Molnàr, Self-organization of complex structures. From individual to collective dynamics, Proceedings of the International Conference held in Berlin, September 24-28, 1995, Edited by Frank Schweitzer. Gordon and Breach Science Publishers, Amsterdam, 1997. |
[22] |
L. F. Henderson, On the fluid mechanics of human crowd motion, Transportation Research, 8 (1974), 509-515.
doi: 10.1016/0041-1647(74)90027-6. |
[23] |
S. Hoogendoorn and P. H. L. Bovy, Simulation of pedestrian flows by optimal control and differential games, Optimal Control Appl. Methods, 24 (2003), 153-172.
doi: 10.1002/oca.727. |
[24] |
R. L. Hughes, A continuum theory for the flow of pedestrians, Transportation Research B, 36 (2002), 507-535.
doi: 10.1016/S0191-2615(01)00015-7. |
[25] |
R. L. Hughes, The flow of human crowds, Ann. Rev. Fluid Mech., 35 (2003), 169-182.
doi: 10.1146/annurev.fluid.35.101101.161136. |
[26] |
A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160 (2000), 240-282. |
[27] |
R. J. LeVeque, "Finite Volume Methods for Hyperbolic Problems," Cambridge Texts in Mathematics, Cambridge University Press, Cambridge, 2002.
doi: 10.1017/CBO9780511791253. |
[28] |
M. J. Lighthill and J. B. Whitham, On kinematic waves. I: Flow movement in long rivers. II: A theory of traffic flow on long crowded roads, Proc. Roy. Soc., A229 (1955), 281-345. |
[29] |
B. Maury, A. Roudneff-Chupin and F. Santambrogio, A macroscopic crowd motion model of gradient flow type, Math. Models Methods Appl. Sci., 20 (2010), 1787-1821.
doi: 10.1142/S0218202510004799. |
[30] |
B. Maury and J. Venel, A mathematical framework for a crowd motion model, C. R. Acad. Sci. Paris, 346 (2008), 1245-1250. |
[31] |
K. Nishinari, A. Kirchner, A. Namazi and A. Schadschneider, Extended floor field CA model for evacuation dynamics, IEICE Transp. Inf. & Syst., E87-D (2004), 726-732, arXiv:cond-mat/0306262. |
[32] |
J. Ondřej, J. Pettré, A.-H. Olivier and S. Donikian, "A Synthetic-Vision Based Steering Approach for Crowd Simulation," SIGGRAPH '10, 2010. |
[33] |
S. Paris, J. Pettré and S. Donikian, Pedestrian reactive navigation for crowd simulation: A predictive approach, Eurographics, 26 (2007), 665-674. |
[34] |
Pedigree team, Pedestrian flow measurements and analysis in an annular setup,, in preparation., ().
|
[35] |
J. Pettré, J. Ondřej, A.-H. Olivier, A. Cretual and S. Donikian, "Experiment-Based Modeling, Simulation and Validation of Interactions Between Virtual Walkers," SCA '09: Proceedings of the 2009 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (2009), 189-198. |
[36] |
B. Piccoli and A. Tosin, Pedestrian flows in bounded domains with obstacles, Contin. Mech. Thermodyn., 21 (2009), 85-107, arXiv:0812.4390. |
[37] |
B. Piccoli and A. Tosin, Time-evolving measures and macroscopic modeling of pedestrian flow, Arch. Ration. Mech. Anal., 199 (2011), 707-738, arXiv:0811.3383. |
[38] |
C. W. Reynolds, "Steering Behaviors for Autonomous Characters," Proceedings of Game Developers Conference 1999, San Jose, California, (1999), 763-782. |
[39] |
V. Shvetsov and D. Helbing, Macroscopic dynamics of multi-lane traffic, Phys. Rev. E, 59 (1999), 6328-6339, arXiv:cond-mat/9906430.
doi: 10.1103/PhysRevE.59.6328. |
[40] |
J. van den Berg and H. Overmars, Planning time-minimal safe paths amidst unpredictably moving obstacles, Int. Journal on Robotics Research, 27 (2008), 1274-1294.
doi: 10.1177/0278364908097581. |
[41] |
W. G. Weng, S. F. Shena, H. Y. Yuana and W. C. Fana, A behavior-based model for pedestrian counter flow, Physica A, 375 (2007), 668-678.
doi: 10.1016/j.physa.2006.09.028. |
[42] |
M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Res. B, 36 (2002), 275-290.
doi: 10.1016/S0191-2615(00)00050-3. |
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