Traffic jams: Dynamics and control

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 368, Issue 1928, 2010, Pages 4455-4479

  Orosz, Gábor ^a,b   Eddie Wilson, R ^c   Stefan, Gabor ^d,e  

^a University of California   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

^d BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^e INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

Congestion; Driver reaction time; Hopf bifurcation; Stop and go waves; Unstable waves; Vehicular traffic

Indexed keywords

HOPF BIFURCATION;

CONGESTION; DRIVER REACTION; STOP-AND-GO WAVES; UNSTABLE WAVES; VEHICULAR TRAFFIC;

TRAFFIC CONGESTION;

EID: 77958041304     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2010.0205     Document Type: Review

References (77)

1. Aw, A. & Rascle, M. 2000 Resurrection of 'second order' models of traffic flow. SIAM J. Appl. Math. 60, 916-938. (doi:10.1137/S0036139997332099)
2. Bando, M., Hasebe, K., Nakayama, A., Shibata, A. & Sugiyama, Y. 1995 Dynamical model of traffic congestion and numerical simulation. Phys. Rev. E 51, 1035-1042. (doi:10.1103/ PhysRevE.51.1035)
3. Bando, M., Hasebe, K., Nakanishi, K. & Nakayama, A. 1998 Analysis of optimal velocity model with explicit delay. Phys. Rev. E 58, 5429-5435. (doi:10.1103/PhysRevE.58.5429)
4. Benzoni-Gavage, S. & Colombo, R. M. 2003 An n-populations model for traffic flow. Eur. J. Appl. Math. 14, 587-612. (doi:10.1017/S0956792503005266) (Pubitemid 37424462)
5. Berg, F., Mason, A. D. & Woods, A. W. 2000 Continuum approach to car-following models. Phys. Rev. E 61, 1056-1066. (doi:10.1103/FhysRevE.61.1056)
6. Campbell, M., Egerstedt, M., How, J. F. & Murray, R. M. 2010 Autonomous driving in urban environments: approaches, lessons and challenges. Phil. Trans. R. Soc. A 368, 4649-4672. (doi:10.1098/rsta.2010.0110)
7. Carlson, R. C., Fapamichail, I., Fapageorgiou, M. & Messmer, A. 2010 Optimal motorway traffic flow control involving variable speed limits and ramp metering. Transport. Sci. 44, 238-253. (doi:10.1287/trsc.1090.0314)
8. Chandler, R. E., Herman, R. & Montroll, E. W. 1958 Traffic dynamics: studies in car following. Oper. Res. 6, 165-184. (doi:10.1287/opre.6.2.165)
9. Daganzo, C. F. 1995 Requiem for second-order fluid approximations of traffic flow. Transport. Res. B 29, 277-286. (doi:10.1016/0191-2615(95)00007-Z)
10. Daganzo, C. F. 2002a A behavioral theory of multi-lane traffic flow. Fart I. Long homogeneous freeway sections. Transport. Res. B 36, 131-158. (doi:10.1016/S0191-2615(00)00042-4) (Pubitemid 33122545)
11. Daganzo, C. F. 2002b A behavioral theory of multi-lane traffic flow. Fart II. Merges and the onset of congestion. Transport. Res. B 36, 159-169. (doi:10.1016/S0191-2615(00)00043-6) (Pubitemid 33122546)
12. Daganzo, C. F. & Geroliminis, N. 2008 An analytical approximation for the macroscopic fundamental diagram of urban traffic. Transport. Res. B 42, 771-781. (doi:10.1016/j.trb. 2008.06.008)
13. Davis, L. C. 2003 Modification of the optimal velocity traffic model to include delay due to driver reaction time. Physica A 319, 557-567. (doi:10.1016/S0378-4371(02)01457-7)
14. Davis, L. C. 2004 Multilane simulations of traffic phases. Phys. Rev. E 69, 016108. (doi:10.1103/ FhysRevE.69.016108)
15. Dyson, F. 2004 A meeting with Enrico Fermi-how one intuitive physicist rescued a team from fruitless research. Nature 427, 297-297. (doi:10.1038/427297a) (Pubitemid 38133643)
16. Gasser, I. & Werner, B. 2010 Dynamical phenomena induced by bottleneck. Phil. Trans. R. Soc. A 368, 4543-4562. (doi:10.1098/rsta.2010.0118)
17. Gasser, I., Sirito, G. & Werner, B. 2004 Bifurcation analysis of a class of 'car-following' traffic models. Physica D 197, 222-241. (doi:10.1016/j.physd.2004.07.008)
18. Gazis, D. C., Herman, R. & Rothery, R. W. 1961 Nonlinear follow-the-leader models of traffic flow. Oper. Res. 9, 545-567. (doi:10.1287/opre.9.4.545)
19. Gipps, F. G. 1981 A behavioural car-following model for computer simulation. Transport. Res. B 15, 105-111. (doi:10.1016/0191-2615(81)90037-0)
20. Greenshields, B. D. 1935 A study of highway capacity. In Proc. of the 14th Annual Meeting of the Highway Research Board, Washington, DC, pp. 448-477.
21. Greenshields, B. D. 1936 Studying traffic capacity by new methods. J. Appl. Psychol. 20, 353-358. (doi:10.1037/h0063672)
22. Helbing, D. 1995 Theoretical foundation of macroscopic traffic models. Physica A 219, 375-390. (doi:10.1016/0378-4371(95)00174-6)
23. Helbing, D. 2001 Traffic and related self-driven many-particle systems. Rev. Mod. Phys. 73, 1067-1141. (doi:10.1103/RevModFhys.73.1067)
24. Helbing, D. 2009 Derivation of a fundamental diagram for urban traffic flow. Eur. Phys. J. B 70, 229-241. (doi:10.1140/epjb/e2009-00093-7)
25. Helbing, D. & Moussaid, M. 2009 Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model. Eur. Phys. J. B 69, 571-581. (doi:10.1140/epjb/e2009-00042-6)
26. Herman, R., Montroll, E. W., Potts, R. B. & Rothery, R. W. 1959 Traffic dynamics: analysis of stability in car following. Oper. Res. 7, 86-106. (doi:10.1287/opre.7.1.86)
27. Highways Agency, UK. See http://www.highways.gov.uk/.
28. Holland, E. N. 1998 A generalized stability criterion for motorway traffic. Transport. Res. B 32, 141-154. (doi:10.1016/S0191-2615(97)00021-0)
29. Hoogendoorn, S. & Hoogendoorn, R. 2010 Calibration of microscopic traffic-flow models using multiple data sources. Phil. Trans. R. Soc. A 368, 4497-4517. (doi:10.1098/rsta.2010.0189)
30. Igarashi, Y., Itoh, K., Nakanishi, K., Ogura, K. & Yokokawa, K. 2001 Bifurcation phenomena in the optimal velocity model for traffic flow. Phys. Rev. E 64, 047102. (doi:10.1103/PhysRevE.64. 047102)
31. loannou, P. A. & Xu, Z. 1994 Throttle and brake control systems for automatic vehicle following. J. Intell. Transport. Syst. 1, 345-377. (doi:10.1080/10248079408903805)
32. Kerner, B. S. 2004 The physics of traffic: empirical freeway pattern features, engineering applications, and theory. Understanding Complex Systems. Berlin, Germany: Springer.
33. Kerner, B. S. 2008 A theory of traffic congestion at heavy bottlenecks. J. Phys. A 41, 215101. (doi:10.1088/1751-8113/41/21/215101)
34. Kerner, B. S. 2009 Introduction to modern traffic flow theory and control: the long road to three-phase traffic theory. Berlin, Germany: Springer.
35. Kerner, B. S. & Konhauser, P. 1994 Structure and parameters of clusters in traffic flow. Phys. Rev. E 50, 54-83. (doi:10.1103/PhysRevE.50.54)
36. Kesting, A. & Treiber, M. 2008 How reaction time, update time, and adaptation time influence the stability of traffic flow. Comput. Aided Civil Infrastruct. Eng. 23, 125-137. (doi:10.1111/j.1467-8667.2007.00529.x)
37. Kesting, A., Treiber, M. & Helbing, D. 2007 General lane-changing model MOBIL for car-following models. Transport. Res. Rec. 1999, 86-94. (doi:10.3141/1999-10) (Pubitemid 351190535)
38. Kesting, A., Treiber, M. & Helbing, D. 2010 Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity. Phil. Trans. R. Soc. A 368, 4585-4605. (doi:10.1098/rsta.2010.0084)
39. Kometani, E. & Sasaki, T. 1958 On the stability of traffic flow. J. Oper. Res. Soc. Jap. 2, 11-26.
40. Krauss, S., Wagner, P. & Gawron, C. 1997 Metastable states in a microscopic model of traffic flow. Phys. Rev. E 55, 5597-5602. (doi:10.1103/PhysRevE.55.5597)
41. Kurzhanskiy, A. A. & Varaiya, P. 2010 Active traffic management on road networks: a macroscopic approach. Phil. Trans. R. Soc. A 368, 4607-4626. (doi:10.1098/rsta.2010.0185)
42. Laval, J. A. & Leclercq, L. 2010 A mechanism to describe the formation and propagation of stop- and-go waves in congested freeway traffic. Phil. Trans. R. Soc. A 368, 4519-4541. (doi:10.1098/ rsta.2010.0138)
43. Lee, H. Y., Lee, H.-W. & Kim, D. 1998 Origin of synchronized traffic flow on highways and its dynamic phase transitions. Phys. Rev. Lett. 81, 1130-1133. (doi:10.1103/PhysRevLett.81.1130)
44. Lighthill, M. J. & Whitham, G. B. 1955 On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. A 229, 317-345. (doi:10.1098/rspa.1955.0089)
45. Luspay, T. Kulcsar, B., Varga, I. & Bokor, J. 2010 Parameter-dependent modeling of freeway traffic flow. Transport Res. C 18, 471-488. (doi:10.1016/j.trc.2009.09.005)
46. Mason, A. D. & Woods, A. W. 1997 Car-following model of multispecies systems of road traffic. Phys. Rev. E 55, 2203-2214. (doi:10.1103/PhysRevE.55. 2203)
47. Mazloumian, A., Geroliminis, N. & Helbing, D. 2010 The spatial variability of vehicle densities as determinant of urban network capacity. Phil. Trans. R. Soc. A 368, 4627-4647. (doi:10.1098/ rsta.2010.0099)
48. Mueller, E. A. 1970 Aspects of history of traffic signals. IEEE Trans.Veh. Technol. VT19, 6-17. (doi:10.1109/T-VT.1970.23426)
49. MITSIM. Microscopic Traffic Simulator. See http://mit.edu/its/mitsimlab. html.
50. Nagatani, T. 2000 Traffic behaviour in mixture of different vehicles. Physica A 284, 405-420. (doi:10.1016/S0378-4371(00)00263-6)
51. Nagel, K. & Schreckenberg, M. 1992 A cellular automaton model for freeway traffic. J. Phys. I 12, 2221-2229. (doi:10.1051/jp1:1992277)
52. Nagel, K., Wagner, P. & Woesler, R. 2003 Still flowing: approaches to traffic flow and traffic jam modeling. Oper. Res. 51, 681-710. (doi:10.1287/opre.51.5.681.16755)
53. Newell, G. F. 1961 Nonlinear effects in the dynamics of car following. Oper. Res. 9, 209-229. (doi:10.1287/opre.9.2.209)
54. Newell, G. F. 2002 A simplified car-following theory: a lower order model. Transport. Res. B 36, 195-205. (doi:10.1016/S0191-2615(00)00044-8) (Pubitemid 34045951)
55. NGSIM. Next Generation Simulation. See http://www.tfhrc.gov/about/ngsim. htm.
56. Orosz, G. & Stépán, G. 2006 Subcritical Hopf bifurcations in a car-following model with reaction- time delay. Proc. R. Soc. A 462, 2643-2670. (doi:10.1098/rspa.2006.1660) (Pubitemid 44305960)
57. Orosz, G., Wilson, R. E., Szalai, R. & Stépán, G. 2009 Exciting traffic jams: nonlinear phenomena behind traffic jam formation on highways. Phys. Rev. E 80, 046 205. (doi:10.1103/ FhysRevE.80.046205)
58. Orosz, G., Moehlis, J. & Bullo, F. 2010 Robotic reactions: delay-induced patterns in autonomous vehicle systems. Phys. Rev. E 81, 025 204(R). (doi:10.1103/FhysRevE.81.025204)
59. Payne, H. J. 1979 FREFLO: a macroscopic simulation model of freeway traffic. Transport. Res. Rec. 722, 68-77.
60. Pipes, L. A. 1953 An operational analysis of traffic dynamics. J. Appl. Phys. 24, 274-281. (doi:10.1063/1.1721265)
61. Powell, E. A. & Foehler, E. 2008 Rush hour in Pompeii: an archaeologist navigates first-century gridlock. Archaeology 61, 18.
62. Frigogine, I. & Herman, R. 1971 Kinetic theory of vehicular traffic. Amsterdam, The Netherlands: Elsevier.
63. Roose, D. & Szalai, R. 2007 Continuation and bifurcation analysis of delay differential equations. In Numerical continuation methods for dynamical systems (eds B. Krauskopf, H. M. Osinga & J. Galan-Vioque), pp. 359-399. Understanding Complex Systems. Berlin, Germany: Springer.
64. Safonov, L. A., Tomer, E., Strygin, V. V., Ashkenazy, Y. & Havlin, S. 2002 Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic. Chaos 12, 1006-1014. (doi:10.1063/1.1507903) (Pubitemid 36046846)
65. Schonhof, M. & Helbing, D. 2009 Criticism of three-phase traffic theory. Transport. Res. B 43, 784-797. (doi:10.1016/j.trb.2009.02.004)
66. Siebel, F. & Mauser, W. 2006 On the fundamental diagram of traffic flow. SIAM J. Appl. Math. 66, 1150-1162. (doi:10.1137/050627113) (Pubitemid 44231185)
67. Sipahi, R. & Niculescu, S.-I. 2010 Stability of car following with human memory effects and automatic headway compensation. Phil. Trans. R. Soc. A 368, 4563-4583. (doi:10.1098/rsta.2010.0127)
68. Swaroop, D., Hedrick, J. K., Chien, C. C. & loannou, F. A. 1994 A comparison of spacing and headway control laws for automatically controlled vehicles. Veh. Syst. Dyn. 23, 597-625. (doi:10.1080/00423119408969077)
69. Treiber, M., Hennecke, A. & Helbing, D. 2000 Congested traffic states in empirical observations and microscopic simulations. Phys. Rev. E 62, 1805-1824. (doi:10.1103/FhysRevE.62.1805)
70. Varaiya, F. 2008 Congestion, ramp metering and tolls. Phil. Trans. R. Soc. A 366, 1921-1930. (doi:10.1098/rsta.2008.0015) (Pubitemid 351585436)
71. Wagner, F. 2010 Fluid-dynamical and microscopic description of traffic flow: a data-driven comparison. Phil. Trans. R. Soc. A 368, 4481-4495. (doi:10.1098/rsta.2010.0122)
72. Ward, J. A. & Wilson, R. E. 2010 Criteria for convective versus absolute string instability in car-following models. Preprint.
73. Wilson, R. E. 2008 Mechanisms for spatio-temporal pattern formation in highway traffic models. Phil. Trans. R. Soc. A 366, 2017-2032. (doi:10.1098/rsta.2008.0018) (Pubitemid 351585443)
74. Wilson, R. E., Berg, F., Hooper, S. & Lunt, G. 2004 Many-neighbour interaction and non-locality in traffic models. Eur. Phys. J. B 39, 397-408. (doi:10.1140/epjb/e2004-00205-y)
75. Yeo, H. & Skabardonis, A. 2009 Understanding stop-and-go traffic in view of asymmetric traffic theory. In Transportation and traffic theory 2009: Golden jubilee, 18th Int. Symp. of Traffic Theory and Transportation (eds W. H. K. Lam, S. C. Wong & H. K. LO), pp. 99-116. Berlin, Germany: Springer.
76. Zhang, J. & loannou, F. A. 2006 Longitudinal control of heavy trucks in mixed traffic: environmental and fuel economy considerations. IEEE Trans. Intell. Transport. Syst. 7, 92-104. (doi:10.1109/TITS.2006.869597)
77. Zhou, J. & Feng, H. 2005 Range policy of adaptive cruise control vehicles for improved flow stability and string stability. IEEE Trans. Intell. Transport. Syst. 6, 229-237. (doi:10.1109/ TITS.2005.848359)