Car-following models: Fifty years of linear stability analysis - a mathematical perspective

Transportation Planning and Technology

Volumn 34, Issue 1, 2011, Pages 3-18

  Wilson, R E ^a   Ward, J A ^b  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b UNIVERSITY OF LIMERICK   (Ireland)

Author keywords

Car following models; Highway traffic modelling; Linear stability

Indexed keywords

CAR-FOLLOWING MODELS; HIGHWAY TRAFFIC; LINEAR STABILITY; LINEAR STABILITY PROPERTIES; PLATOON STABILITIES; STRING STABILITY; UNIFORM FLOW;

STABILITY CRITERIA;

LINEAR STABILITY ANALYSIS;

AUTOMOBILE; LINEARITY; MODELING; STABILITY ANALYSIS; TRANSPORTATION PLANNING;

EID: 78650039514     PISSN: 03081060     EISSN: 10290354     Source Type: Journal    
DOI: 10.1080/03081060.2011.530826     Document Type: Article

References (19)

1. Bando, M., et al., 1995. Dynamical model of traffic congestion and numerical simulation. Physical Review E, 51, 1035-1042.
2. Bender, C.M. and Orszag, S.A., 1999. Advanced mathematical methods for scientists and engineers. Berlin: Springer-Verlag.
3. Brackstone, M. and McDonald, M., 1999. Car following: a historical review. Transportation Research F, 1-2, 181-196.
4. Gasser, I., Sirito, G., and Werner, B., 2004. Bifurcation analysis of a class of car-following traffic models. Physica D, 197, 277-296.
5. Gazis, D.C., Herman, R., and Rothery, R.W., 1961. Nonlinear follow-the-leader models of traffic flow. Operations Research, 9, 545-567.
6. Helbing, D., 2001. Traffic and related self-driven many-particle systems. Reviews of Modern Physics, 73, 1067-1141.
7. Herman, R., et al., 1959. Traffic dynamics: analysis of stability in car-following. Operations Research, 7, 86-106.
8. Kometani, E. and Sasaki, T., 1958. On the stability of traffic flow. Journal of Operations Research - Japan, 2, 11-26.
9. Lighthill, M.J. and Whitham, G.B., 1955. On kinematic waves. II: a theory of traffic on long crowded roads. Proceedings of the Royal Society Part A, 229, 317-345.
10. Mitarai, N. and Nakanishi, H., 2000. Convective instability and structure formation in traffic flow. Journal of the Physical Society of Japan, 69, 3752-3761.
11. Orosz, G., Wilson, R.E., and Krauskopf, B., 2004. Global bifurcation investigation of an optimal velocity traffic model with driver reaction time. Physical Review E, 70, Art no. 026207.
12. Pipes, L., 1953. An operational analysis of traffic dynamics. Journal of Applied Physics, 24, 274-281.
13. Schönhof, M. and Helbing, D., 2007. Empirical features of congested traffic states and their implications for traffic modelling. Transportation Science, 41, 135-166.
14. Treiber, M., Hennecke, A., and Helbing, D., 2000. Congested traffic states in empirical observations and microscopic simulations. Physical Review E, 62, 1805-1824.
15. Treiber, M., Kesting, A., and Helbing, D., 2010. Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transportation Research B, 44, 983-1000.
16. Ward, J.A., 2009. Heterogeneity, lane-changing and instability in traffic: a mathematical approach. Thesis (PhD). University of Bristol.
17. Ward, J.A. and Wilson, R.E., 2010. Criteria for convective versus absolute string instability in car-following models. Bristol: Department of Engineering Mathematics, University of Bristol.
18. Wilson, R.E., 2001. An analysis of Gipps's car-following model of highway traffic. IMA Journal of Applied Mathematics, 66, 509-537.
19. Wilson, R.E., 2008. Mechanisms for spatiotemporal pattern formation in highway traffic models. Philosophical Transactions of the Royal Society Part A, 366, 2017-2032.