A review of mathematical models for the flow of traffic and some recent results

Nonlinear Analysis, Theory, Methods and Applications

Volumn 69, Issue 3, 2008, Pages 950-970

  Darbha, S ^a   Rajagopal, K R ^a   Tyagi, V ^a  

^a Texas AandM University   (United States)

Author keywords

Congestion; Density; Dynamical system; Intelligent transportation system; Macroscopic models; Microscopic models

Indexed keywords

DYNAMICAL SYSTEMS; KINETIC THEORY OF GASES; MATHEMATICAL MODELS; PROBLEM SOLVING; REAL TIME SYSTEMS;

INTELLIGENT TRANSPORTATION SYSTEM; MACROSCOPIC MODELS; MICROSCOPIC MODELS; REAL TIME DATA;

FLOW OF GASES;

EID: 44649110151     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.02.123     Document Type: Article

References (65)

1. In: Gartner N., Messer C., and Rathi A. (Eds). Monograph on Traffic Flow Theory (1997), Transportation Research Board
2. Abdel-Aty M.A., Kitamura R., and Jovanis P. Exploring route choice behavior using GIS-based alternative routes and hypothetical travel time information input. Transport. Res. Record 1493 (1995) 74-80
3. B. van Arem, J.H. Hogema, M.J.W.A. Vanderschuren, An assessment of the impact of Autonomous Intelligent Cruise Control, TNO Report No: INRO-WG 1995-17a, 1995
4. Bellomo N., Marasco A., and Romano A. From the modelling of drivers' behavior to hydrodynamic models and problems of traffic flow. Nonlinear Anal. RWA 3 (2002) 330-363
5. A. Bose, P. Ioannou, Analysis of Traffic Flow with Mixed Manual and Semi-Automated Vehicles, USC Report, CATT 99-01-10
6. Brackstone M., and McDonald M. Car following - a historical review. Transport. Res. Part F 2 (1999) 181-196
7. Chandler R.E., Herman R., and Montroll E.W. Traffic dynamics: Studies in car following. Oper. Res. 6 (1958) 165-184
8. Chapman S., and Cowling T.G. The Mathematical Theory of Non-Uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases. 3rd edition (1990), Cambridge University Press
9. Chen C., Jia Z.F., and Varaiya P. Causes and cures of highway congestion. IEEE Control Systems Mag. (2001) 26-32
10. Chu K.-C. Decentralized control of high speed vehicular strings. Transport. Sci. 8 (1974) 361-384
11. Edie L.C. Car following and steady state theory for non-congested traffic. Oper. Res. 9 (1960) 66-76
12. Garrard W.L., Caudill R.J., Kornhauser A.L., McKinnon D., and Brown S.J. State-of-the-art longitudinal control of automated guideway transit vehicles. High Speed Ground Transport. J. 12 2 (1978)
13. C.C. Chien, Y. Zhang, A. Stotsky, S.R. Dharmasena, P. Ioannou, Macroscopic Roadway Traffic Controller Design, California PATH Report, UCB-ITS-PRR-95-28, 1995
14. Daganzo C.F. Requiem for second-order fluid approximations of traffic flow. Transport. Res. B 29B (1995) 277-286
15. Darbha S., and Rajagopal K.R. A non-continuum approach to modelling the flow of traffic. Math. Modelling Methods Appl. Sci. 12 10 (2002) 1381-1399
16. Del Castillo J.M., Pintado P., and Benitez F.G. The reaction time of drivers and the stability of traffic flow. Transport. Res.-B. 28B (1994) 35-60
17. Drew D.R. Traffic Flow Theory and Control (1968), McGraw-Hill
18. Finch G. Congestion pricing: reducing traffic jams through economics. Public Roads 60 2 (1996) 4-5
19. R.J. Forbes, Notes on the history of ancient roads and their construction, NV Noord-Hoolandsche-Vitevers-MIJ, Amsterdam, 1934
20. E.R. Foster, A constant separation control law for use in automated guideway transit, in: Proc. of 29th IEEE Vehicular Technology Conference, 1979, pp. 358-361
21. Gazis D.C., Herman R., and Potts R. Car-following theory of steady state traffic flow. Oper. Res. 7 (1959) 499-595
22. Gazis D.C., Herman R., and Rothery R.W. Nonlinear follow the leader models of traffic flow. Oper. Res. 7 (1961) 499-505
23. Gibbons J.H. Federal strategy for transportation research and development. In: Sussman J. (Ed). Forum on Future Directions in Transportation R & D (1995), National Academy Press, Washington, DC
24. Gipps P.B. A behavioral car-following model for computer simulation. Transport. Res. 20 B (1981) 403-414
25. T.L. Greenlee, H.J. Payne, Freeway ramp metering strategies for responding to incidents, in: Proc. of IEEE Conference on Decision and Control, 1977, pp. 982-987
26. Greenshields B.D. A study in highway capacity. Highway Res. Rec. 14 (1934) 468
27. Shaival Gupta, D. Swaroop, Intelligent cruise control systems and traffic flow behavior, Appendix M, Evaluation of Intelligent Cruise Control System, vol. II (Appendices), DOT-VNTSC-NHTSA-3, DOT HS 808 969, Final Report, October 1999
28. Huandra R., and Swaroop D. Design of an intelligent cruise control system based on a traffic flow specification. Vehicle Syst. Dynam. J. 30 5 (1998) 319-344
29. Ioannou P., and Chien C. Autonomous intelligent cruise control. IEEE Trans. Vehicular Technol. 42 (1993) 657-672
30. Paul J. Telecommunications and alternative work schedules: Options for managing transit travel demand. Urban Affairs Quart. 19 (1983) 167-189
31. E. Kometani, T. Sasaki, Dynamic behavior of traffic with a nonlinear spacing-speed relationship, in: Proceedings of the Symposium on Theory of Traffic Flow held at General Motors Research Laboratories, 1959, pp. 105-119
32. Lighthill M.J., and Witham G.B. On kinematic waves II: A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London, Series A. 229 (1955) 317-345
33. J.L. Madre, Y. Bussiere, J. Armoogum, Demographic dynamics of mobility in urban areas: A case study of paris and grenoble, in: Proc. of the 7th World Conference on Transportation Research, vol. 1, 1995, pp. 287-303
34. May A.D. Traffic Flow Theory Fundamentals (1990), Prentice Hall
35. Michalopoulos P.G., Lin J., and Beskos D.E. Integrated modeling and numerical treatment of traffic flow. Appl. Math. Model. 11 (1987) 447-457
36. Muralikrishnan J., and Rajagopal K.R. Review and uses and modeling of bitumen from ancient to modern times. Appl. Mech. Rev. 56 (2003) 149-214
37. Milne-Thomson L.M. Theoretical Hydrodynamics (1996), Dover
38. Newell G.F. A simplified car-following theory: A lower order model. Transport. Res.- B 36 (2002) 196-205
39. Newell G.F. Mathematical Models for Freely-Flowing Highway Traffic. J. Oper. Res. Soc. Amer. 3 2 (1995) 176-186
40. Newell G.F. Nonlinear effects in the dynamics of car-following. Oper. Res. 9 (1961) 209-229
41. Palmquist U. Intelligent cruise control and roadside information. IEEE Micro 13 1 (1993) 20-28
42. Papageorgiou M. Lecture Notes in Control and Information Sciences vol. 50 (1983), Springer Verlag
43. Papageorgiou M., Blosseville J., and Hadj-Salem H. Macroscopic modelling of traffic flow on the boulevard peripherique in Paris. Transport. Res.-A 24 (1990) 345-359
44. Papageorgiou M. Some remarks on macroscopic traffic flow modeling. Transport. Res.-A 32 5 (1998) 323-329
45. Payne H.J. Models of freeway traffic and control. Simul. Council Proc. 1 (1971) 51-61
46. H.J. Payne, A critical review of a macroscopic freeway model, in: Engineering Foundation Conference on Research Directions in Computer Control of Urban Traffic Systems, 1979, pp. 251-265
47. Payne H.J., Thompson W.A., and Isaksen L. Design of a traffic-responsive control system for a Los Angeles freeway. IEEE Trans. Syst. Man Cybern. SMC-3 (1973) 213-224
48. Pipes L.A. An operational analysis of traffic dynamics. J. Appl. Phys. 24 (1953) 274-281
49. Prigogine I., and Herman R. Kinetic Theory of Vehicular Traffic (1971), Elsevier
50. Prigogine I., and Andrews C.F. A Boltzmann-like approach for traffic flow. Oper. Res. 8 6 (1960) 789-797
51. Rajamani R., and Shladover S.E. An experimental comparative study of autonomous and cooperative vehicle-follower control systems. Transport. Res. Part C : Emerging Technol. 9 1 (2001) 15-31
52. Richards P.I. Shock waves on the highway. Oper. Res. (1956) 42-51
53. D. Swaroop, String stability of interconnected systems: An application to platooning in automated highway systems, Ph.D. Dissertation, Department of Mechanical Engineering, U. C. Berkeley, December 1994
54. Wagner P., Nagel K., and Wolf D.E. Realistic multi-lane traffic rules for cellular automata. Physica A 234 (1997) 687-698
55. IVHS America, A strategic plan for intelligent vehicle-highway systems in the United States, Report No. IVHS-AMER-92-3, May 1992
56. David Schrank, Shawn Turner, Timothy Lomax, Trends in Urban Roadway Congestion - 1982-1991, vol. 1, TTI Research Report # 1131-1136, 1994
57. J. Markowitz, TravInfo: The San Francisco bay area intermodal traveler information system, in: Proc. of Wescon, 1993, pp. 339-344
58. Tabor D. Gases, Liquids and Solids: And Other States of Matter (1991), Cambridge University Press
59. B.S.Y. Rao, P. Varaiya, Potential benefits of roadside intelligence for flow control in IVHS, in: Proc. of American Control Conference, 1994, pp. 418-422
60. Saxton L., and Schenck C. Diversion and corridor control systems in western europe. In World Survey on Current Research and Development on Roads and Road Transport (1977), International Road Federation, Washington, D.C 692-723
61. S. Sheikholeslam, C.A. Desoer, Longitudinal control of a platoon of vehicles, in: Proc. of American Control Conference, May 1990, pp. 291-296
62. Shladover S.E. Review of the state of development of advanced vehicle control systems (AVCS). Vehicle Syst. Dynam. 24 (1995) 551-595
63. Treyford R.S. Testing dynamic advisory speeds under adaptive signal control. Australian Road Res. 38 2 (1987) 243-255
64. Tyagi V., Darbha S., and Rajagopal K.R. Development and corroboration of a non-continuum model of the flow of traffic. Nonlinear Anal. Hybrid Systems 2 (2008) 590-612
65. V. Tyagi, A non-continuum approach to model the flow of traffic, Ph.D. Dissertation, Department of Mechanical Engineering, Texas A&M University, February 2007