A generic characterization of equilibrium speed-flow curves

Transportation Science

Volumn 42, Issue 2, 2008, Pages 220-235

  Li, Z F Michael ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Highway capacity; Speed density relations; Speed flow relations; Vehicular traffic flow

Indexed keywords

CHARACTERIZATION; CURVES (ROAD); DENSITY FUNCTIONAL THEORY; HIGHWAY ENGINEERING; RATIONAL FUNCTIONS; TRAFFIC CONGESTION; TRAFFIC CONTROL; TRANSPORTATION;

EMPIRICAL INVESTIGATION; HIGHWAY CAPACITY; HIGHWAY CAPACITY MANUAL; RATIONAL GENERATING FUNCTIONS; SPEED FLOW; SPEED-DENSITY; SPEED-DENSITY RELATIONSHIPS; VEHICULAR TRAFFIC FLOW;

SPEED;

EID: 70449707296     PISSN: 00411655     EISSN: 15265447     Source Type: Journal    
DOI: 10.1287/trsc.1070.0201     Document Type: Article

References (67)

1. Akçelik, R. 1974. Traffic signals and route control in urban areas. Ph. D. thesis (unpublished), Institute for Transport Studies, University of Leeds, Leeds, UK.
2. Akçelik, R., R. Roper, M. Besley. 1999. Fundamental relationships for freeway traffic flows. Research Report 341, ARRB Transport Research Ltd., Melbourne, Australia.
3. Banks, J. H. 1989. Freeway speed flow concentration relationships: More recent evidence and interpretations. Transportation Res. Record 1225 53-60.
4. Banks, J. H. 1991a. Two-capacity phenomenon at freeway bottlenecks: A basis for ramp metering? Transportation Res. Record 1320 83-90.
5. Banks, J. H. 1991b. The two-capacity phenomenon: Some theoretical issues. Transportation Res. Record 1320 234-241.
6. Cassidy, M. J. 1998. Bivariate relations in nearly stationary highway traffic. Transportation Res. Part B 32 49-59.
7. Cassidy, M. J., R. L. Bertini. 1999. Some traffic features at freeway bottlenecks. Transportation Res. Part B 33 25-42.
8. Cassidy, M. J., M. Mauch. 2001. An observed traffic pattern in long freeway queues. Transportation Res. Part A 35 149-162.
9. Chin, H. C., A. D. May. 1991. Examination of the speed-flow relationship at the Caldecott Tunnel. Transportation Res. Record 1320 75-82.
10. Daganzo, C. F. 1995. Requiem for second-order approximation of traffic flow. Transportation Res. Part B 29 277-286.
11. Del Castillo, J. M., F. G. Benitez. 1995. On the functional form of the speed-density relationship-I: General theory, II: Empirical investigation. Transportation Res. Part B 29 373-406.
12. Dick, A. C. 1966. Speed/flow relationships within an urban area. Traffic Engrg. Control 8 393-396.
13. Drake, L. S., J. L. Schofer, A. D. May. 1967. A statistical analysis of speed-density hypotheses. Highway Res. Record 154 53-87.
14. Drew, D. R. 1965. Deterministic aspects of freeway operations and control. Highway Res. Record 99 48-58.
15. Drew, D. R. 1968. Traffic Flow Theory and Control. McGraw-Hill, New York.
16. Duncan, N. C. 1976. A note on speed/flow/concentration relations. Traffic Engrg. Control 17 34-35.
17. Duncan, N. C. 1979. A further look at speed/flow/concentration. Traffic Engrg. Control 20 482-483.
18. Duncan, N. C., A. W. Christie, M. Marlow. 1980. Traffic speed in towns: Further analysis of the urban congestion surveys. Traffic Engrg. Control 21 576-579.
19. Edie, L. C. 1961. Car-following and steady-state theory for noncongested traffic. Oper. Res. 9 66-76.
20. Einbeck, J., G. Tutz. 2006. Modelling beyond regression functions: An application of multimodal regression to speed-flow data. Appl. Statist. 55 (Part 4) 461-475.
21. Franklin, R. E. 1961. The structure of a traffic shock wave. Civ. Engrg. Publ. Wks. Rev. 56 1186-1188.
22. Gazis, D. C., R. Herman, R. Potts. 1959. Car-following theory of steady-state traffic flow. Oper. Res. 7 499-505.
23. Gazis, D. C., R. Herman, R. Rothery. 1961. Non-linear follow-theleader models of traffic flow. Oper. Res. 9 545-567.
24. Gerlough, D. L., M. J. Huber. 1975. Traffic flow theory: A monograph. Special Report 165, Transportation Research Board, Washington, D. C.
25. Greenberg, H. 1959. An analysis of traffic flow. Oper. Res. 7 79-85.
26. Greenshields, B. D. 1935. A study of traffic capacity. Highway Res. Board Proc. 14 448-477.
27. Haight, F. A. 1960. The volume density relation in the theory of road traffic. Oper. Res. 8 572-573.
28. Haight, F. A. 1963. Mathematical Theories of Traffic Flow. Academic Press, New York.
29. Hall, F. L., L. M. Hall. 1990. Capacity and speed flow analysis of the QEW in Ontario. Transportation Res. Record 1287 108-118.
30. Hall, F. L., B. L. Allen, M. A. Gunter. 1986. Empirical analysis of freeway flow-density relationships. Transportation Res. Part A 20 197-210.
31. Hall, F. L., V. F. Hurdle, J. H. Banks. 1992. A synthesis of recent work on the nature of speed-flow and flow-occupancy (or density) relationships on freeways. Transportation Res. Record 1365 12-17.
32. Jin, W. L., H. M. Zhang. 2003. The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model. Transportation Res. Part B 37 207-223.
33. Kockelman, K. M. 2001. Modeling traffic's flow-density relation: Accommodation of multiple flow regimes and traveler types. Transportation 28 363-374.
34. Li, M. Z. F. 1999. Estimating congestion toll by using traffic count data-Singapore's area licensing scheme. Transportation Res. Part E 35 1-10.
35. Li, M. Z. F. 2002. The role of speed-flow relationship in congestion pricing implementation with an application to Singapore. Transportation Res. Part B 36 731-754.
36. Li, T., H. M. Zhang. 2001. The mathematical theory of an enhanced nonequilibrium traffic flow model. J. Networks Spatial Econom. 1 167-177.
37. Lighthill, M. J., G. B. Whitham. 1955. On kinematic waves II: A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London 229A (1178) 317-345.
38. May, A. D. 1990. Traffic Flow Fundamentals. Prentice-Hall, Englewood Cliffs, NJ.
39. May, A. D., H. E. M. Keller. 1967. Non-linear car-following models. Highway Res. Records 199 19-32.
40. May, A. D., H. E. M. Keller. 1968. Evaluation of single- and multiregime traffic flow models. W. Leutzbach, P. Baron, eds. Proc. 4th Internat. Sympos. Theory of Traffic Flow, Karlsruhe, Germany, 37-48.
41. Meng, Q., W. Xu, H. Yang. 2005. A trial-and-error procedure for implementing a road-pricing scheme. Transportation Res. Record 1923 103-109.
42. Munjal, P. K., L. A. Pipes. 1971. Propagation of on-ramp density perturbation on unidirectional, and two and three-lane freeways. Transportation Res. 5 241-255.
43. Nagel, K., P. Wagner, R. Woesler. 2003. Still flowing: Approaches to traffic flow and traffic jam modeling. Oper. Res. 51 (5) 681-710.
44. Newell, G. F. 1955. Mathematical models of freely flowing highway traffic. Oper. Res. 3 176-186.
45. Newell, G. F. 1961. Nonlinear effects in the dynamics of carfollowing. Oper. Res. 9 209-229.
46. Newell, G. F. 1993. A simplified theory of kinematic waves in highway traffic. I: General theory. II: Queueing at freeway bottlenecks. III: Multi-destination flows. Transportation Res. Part B 27 281-313.
47. Newell, G. F. 2003. A simplified car-following theory: A low order model. Transportation Res. Part B 36 195-205.
48. Payne, H. J. 1971. Models of freeway traffic and control. G. A. Bekey, ed. Mathematical Models of Public Systems, no. 28. Simulation Council Proc., Simulation Councils, La Jolla, CA, 51-60.
49. Pipes, L. A. 1953. An operational analysis of traffic dynamics. J. Appl. Phys. 24 274-281.
50. Pipes, L. A. 1967. Car following models and the fundamental diagram of road traffic. Transportation Res. 1 21-29.
51. Polus, A., J. Craus, M. Livneh. 1991. Flow and capacity characteristics on two-lane rural highways. Transportation Res. Record 1320 128-134.
52. Richards, P. I. 1956. Shock waves on the highways. Oper. Res. 4 42-51.
53. Singh, R. 1999. Improved speed-flow relationships: Application to transportation planning models. R. Donnelly, ed. 7th TRB Conf. Appl. Transportation Planning Methods, Boston, Transportation Research Board, Washington, D. C., 340-349.
54. Thomson, J. M. 1967. Speeds and flows of traffic in central London: 2. Speed-flow relations. Traffic Engrg. Control 8 (12) 721-725.
55. Transportation Research Board. 2000. Highway Capacity Manual (HCM) 2000. National Research Council, Washington, D. C.
56. Underwood, R. T. 1961. Speed, Volume and Density Relationships- Quality and Theory of Traffic Flow. Yale Bureau of Highway Traffic, New Haven, CT, 141-188.
57. Walters, A. A. 1961. The theory and measurement of private and social cost of highway congestion. Econometrica 29 676-699.
58. Wardrop, J. G. 1952. Some theoretical aspects of road traffic research. Proc. Inst. Civil Engineers 1 (3, Part II) 325-362.
59. Wardrop, J. G. 1968. Journey speed and flow in central urban areas. Traffic Engrg. Control 9 (11) 528-532.
60. Wardrop, J. G., G. Charlesworth. 1954. A method of estimating speed and flow of traffic from a moving vehicle. Proc. Inst. Civil Engineers 3 (1, Part II) 158-171.
61. Whitham, G. B. 1974. Linear and Nonlinear Waves. John Wiley and Sons, New York.
62. Willams, J. C., H. S. Mahmassani, R. Herman. 1987. Urban traffic network flow models. Transportation Res. Record 1112 78-88.
63. Yang, H., Q. Meng, D. H. Lee. 2004. Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions. Transportation Res. Part B 38 477-493.
64. Zhang, H. M. 1998. A theory of nonequilibrium traffic flow. Transportation Res. Part B 32 485-498.
65. Zhang, H. M. 1999. An analysis of the stability and wave properties of a new continuum theory. Transportation Res. Part B 33 387-398.
66. Zhang, H. M. 2000. Structural properties of solutions arising from a nonequilibrium traffic flow theory. Transportation Res. Part B 34 583-603.
67. Zhao, Y., K. M. Kockelman. 2006. On-line marginal cost pricing across networks: Incorporating heterogeneous users and stochastic equilibrium. Transportation Res. Part B 40 424-435.