Logistic modeling of the equilibrium speed-density relationship

Transportation Research Part A: Policy and Practice

Volumn 45, Issue 6, 2011, Pages 554-566

  Wang, Haizhong ^a   Li, Jia ^a   Chen, Qian Yong ^b   Ni, Daiheng ^a  

^a University of Massachusetts   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Fundamental diagram; Generalized logistic curve; Logistic speed density model

Indexed keywords

SPEED;

FUNDAMENTAL DIAGRAM; GRAPHICAL REPRESENTATIONS; LOGISTIC CURVES; SPEED-DENSITY; SPEED-DENSITY RELATIONSHIPS; STATISTICAL APPROACH; TRAFFIC FLOW ANALYSIS; TRANSPORTATION ENGINEERING;

TRAFFIC CONTROL;

ACCURACY ASSESSMENT; DIAGRAM; EMPIRICAL ANALYSIS; EQUILIBRIUM; LOGISTICS; NUMERICAL MODEL; STATISTICAL ANALYSIS; TRAFFIC MANAGEMENT;

EID: 84866299506     PISSN: 09658564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tra.2011.03.010     Document Type: Article

References (30)

1. Coscia C., Canavesio V. First-order macroscopic modeling of human crowd dynamics. Math Models Methods Appl Sci 2008, 18:1217-1247.
2. Coscia V., Delitala M., Frasca P. On the mathematical theory of vehicular traffic flow models ii. discrete velocity kinetic models. Int J Non-Linear Mech 2007, 42:411-421.
3. Del Castillo F.G.B.J.M. On the functional form of the speed-density relationship - I: general theory. Transportation Research Part B: Methodological 1995, 29B:373-389.
4. Del Castillo F.G.B.J.M. On the functional form of the speed-density relationship - II: empirical investigation. Transportation Research Part B: Methodological 1995, 29B:391-406.
5. Drake J.L.S.J.S., May A.D. A statistical analysis of speed-density hypotheses. Highway Research Record 1967, 156:53-87.
6. Drew D.R. Traffic Flow Theory and Control 1968, McGraw-Hill Book Company, Chapter 12.
7. Easingwood C.J. Early product life cycle forms for infrequently purchased major products. International Journal of Research in Marketing 1987, 4:3-9.
8. Edie L.C. Car-following and steady-state theory for noncongested traffic. Operations Research 1961, 9:66.
9. Greenberg H. An analysis of traffic flow. Operation Research 1959, 7:79-85.
10. Greenshields B.D. A study in highway capacity. Highway Research Board Proceedings 1935, 14:448-477.
11. Huet M.-A.P.E.J.S., Bouvier A. Statistical Tools for Nonlinear Regression A Pracital Guide With S-PLUS and R Examples 2004, Springer. Second ed.
12. Jayakrishnan A.C.R., Tsai Wei K. A dynamic traffic assignment model with traffic flow relationships. Transportation Research Part C 1995, 3C(1):51-72.
13. Kerner B.S., Konhäuser P. Structure and parameters of clusters in traffic flow. Physical Review E 1994, 50(1):54-83. 10.1103/PhysRevE.50.54.
14. Ledvij, M., Curve fitting made easy. The Industrial Physicist.
15. Lighthill M.J., Whitham G.B. On kinematic waves. II. A theory of traffic flow on long crowded roads. Royal Society of London Proceedings Series A 1955, 229:317-345.
16. Lighthill M.J., Whitham G.B. On kinematic waves. I. Flood movement in long rivers. Royal Society of London Proceedings Series A 1955, 229:281-316.
17. Lu Sun J.Z. Development of multiregime speed-density relationship by cluster analysis. Transportation Research Record 2005, 193:64-71.
18. MacNicholas, M.J., 2008. A simple and pragmatic representation of traffic flow. In: Symposium on The Fundamental Diagram: 75 years, Transportation Research Board, Woods Hole, MA.
19. Manual, H.C., 2000. Highway Capacity Manual, Transportation Research Board, Washington, DC, fourth edition Edition, ISBN 0-309-06681-6.
20. Marchetti C. Human population dynamics revisited with the logistic model: how much can be modeled and predicted?. Technological Forecasting and Social Change 1996, 52:1-30.
21. May A.D. Traffic Flow Fundamentals 1990, Prentice Hall.
22. Nelder J.A. The fitting of a generalization of the logistic curve. Biometrics 1961, 17:89-100.
23. Newell G.F. Nonlinear effects in the dynamics of car following. Operation Research 1961, 9:209.
24. Paul J.R.D., Gottschalk G. The five-parameter logistic: a characterization and comparison with the four-parameter logistic. Analytical Biochemistry 2005, 343:54-65.
25. Pipes L.A. Car following models and the fundamental diagram of road traffic. Transportation Research 1967, 1:21-29. 10.1016/0041-1647(67)90092-5.
26. Rouse, D.I., 1991. Stochastic modeling of plant disease epidemic processes. Handbook of Applied Mycology Sail and Plants 1.
27. Stukel T.A. Generalized logistic models. Journal of the American Statistical Association 1988, 83(402):426-431.
28. Underwood, R.T., 1961. Speed, volume, and density relationship: quality and theory of traffic flow. Yale Bureau of Highway Traffic 141-188 (New Haven, Connecticut).
29. Van Aerde, M., 1995. Single regime speed-flow-density relationship for congested and uncongested highways. In: The 74th TRB Annual Conference, Washington DC, Transportation Research Board.
30. Yi, J., Lin, H., Alvarez, L., Horowitz, R., 2002. Stability of macroscopic traffic flow modeling through wavefront expansion. In: American Control Conference, 2002. Proceedings of the 2002, vol. 2. pp. 1484-1490 <>. doi:10.1109/ACC.2002.1023231.