Stability analysis of the classical car-following model

Transportation Research Part B: Methodological

Volumn 31, Issue 6, 1997, Pages 441-462

  Zhang, Xiaoyan ^a   Jarrett, David F ^b  

^a EDINBURGH NAPIER UNIVERSITY   (United Kingdom)

^b MIDDLESEX UNIVERSITY   (United Kingdom)

Author keywords

Car following model; Nonlinear dynamical system; Stability analysis; Traffic flow

Indexed keywords

ASYMPTOTIC STABILITY; AUTOMOBILES; INTEGRATION; LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR EQUATIONS;

CAR FOLLOWING MODEL; NONLINEAR DYNAMICAL SYSTEM; STABILITY ANALYSIS;

TRAFFIC CONTROL;

METHODOLOGY; PLANNING METHOD; ROAD TRANSPORT; TRANSPORT PLANNING;

EID: 0031278159     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0191-2615(97)00006-4     Document Type: Article

References (18)

1. Bender, J. G. and Fenton, R. E. (1970) On the flow capacity of automated highways. Transportation Science 4(1), 52-63.
2. Chandler, R. E., Herman, R. and Montroll, E. W. (1958) Traffic dynamics: studies in car following. Operations Research 6, 165-184.
3. Disbro, J. E. and Frame, M. (1990) Traffic flow theory and chaotic behaviour. Transportation Research Record 1225, 109-115.
4. Driver, R. D. (1977) Ordinary and Delay-differential Equations. Springer-Verlag, Berlin, Heidelberg, New York.
5. Farmer, J. D. (1982) Chaotic attractors of an infinite-dimensional dynamical system. Physica 7D, 366-393.
6. Ferrari, P. (1994) The instability of motorway traffic. Transportation Research-B 28, 175-186.
7. Gazis, D. C., Herman, R. and Rothery, R. W. (1961) Nonlinear follow-the-leader models of traffic flow. Operations Research 9(4), 545-567.
8. Györi, I. and Ladas, G. (1991) Oscillation Theory of Delay Differential Equations: with Applications. Clarendon Press, Oxford.
9. Hale, J. K. and Lunel, S. M. V. (1993) Introduction to Functional Differential Equations. Springer-Verlag, London.
10. Herman, R., Montroll, E. W., Potts, R. B. and Rothery, R. W. (1959) Traffic dynamics: analysis of stability in car following. Operations Research 7, 86-106.
11. Jarrett, D. F. and Zhang, X. (1993) The dynamic behaviour of road traffic flow: stability or chaos? In BCS Displays Group: Application of Fractals and Chaos, eds A. J. Crilly, R. A. Earnshaw and H. Jones, pp. 237-248, Springer-Verlag, Berlin, Heidelberg.
12. Kirby, H. R. and Smith, M. J. (1991) Can chaos theories have transport applications. 23rd Annual Conference of the Universities Transport Study Group. University of Nottingham (unpublished).
13. Kuang, Y. (1993) Delay Differential Equations with Applications in Population Dynamics. Academic Press Inc., New York.
14. Ozaki, H. (1993) Reaction and anticipation in the car-following behaviour. Transportation and Traffic Theory. Proceedings of the 12th International Symposium on the Theory of Traffic Flow and Transportation, eds C. F. Daganzo, pp. 349-362, Elsevier, New York.
15. Ran, B., Huang, W. and Leight, S. (1996) Some solution strategies for automated highway exit bottleneck problems. Transportation Research-C 4(3), 167-179.
16. The Department of Transport and the Central Office of Information (1988) The Highway Code. HMSO, London.
17. Unwin, E. A. and Duckstein, L. (1967) Stability of reciprocal-spacing type car-following models. Transportation Science 1, 95-109.
18. Wilhelm, W. E. and Schmidt, J. W. (1973) Review of car following theory. Transportation Engineering Journal (ASCE) 99(TE4), 923-933.