A stochastic model of traffic flow: Theoretical foundations

Transportation Research Part B: Methodological

Volumn 46, Issue 1, 2012, Pages 156-174

  Jabari, Saif Eddin ^a   Liu, Henry X ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Cell transmission; Counting processes; Fluid limit; Random time headways; Stochastic traffic flow

Indexed keywords

AUTOMOBILE DRIVER SIMULATORS; CONTINUOUS TIME SYSTEMS; DYNAMICS; STOCHASTIC SYSTEMS; STREET TRAFFIC CONTROL; TRAFFIC CONTROL; TRANSPORTATION;

CELL TRANSMISSIONS; COUNTING PROCESS; FLUID LIMITS; RANDOM TIME HEADWAYS; STOCHASTIC TRAFFIC FLOWS;

STOCHASTIC MODELS;

COMPUTER SIMULATION; ESTIMATION METHOD; NUMERICAL MODEL; STOCHASTICITY; TRAFFIC MANAGEMENT; UNCERTAINTY ANALYSIS;

EID: 80755184698     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2011.09.006     Document Type: Article

References (33)

1. Bellman R. The stability of solutions of linear differential equations. Duke Mathematical Journal 1943, 10(4):643-647.
2. Boel R., Mihaylova L. A compositional stochastic model for real-time freeway traffic simulation. Transportation Research Part B 2006, 40(4):319-334.
3. Branston D. Models of single lane time headway distributions. Transportation Science 1976, 10(2):125-148.
4. Bui, D., Nelson, P., Narasimhan, S., 1992. Computational realizations of the entropy condition in modeling congested traffic flow. Federal Highway Administration Report FHWA/TX-92/1232-7.
5. Chen H., Yao D. Fundamentals of Queueing Networks 2001, Springer, New York.
6. Cowan R. Useful headway models. Transportation Research 1975, 9(6):371-375.
7. Daganzo C. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B 1994, 28(4):269-287.
8. Daganzo C. A finite difference approximation of the kinematic wave model of traffic flow. Transportation Research Part B 1995, 29(4):261-276.
9. Daganzo C. The cell transmission model, part II: network traffic. Transportation Research Part B 1995, 29(2):79-93.
10. Davis G., Kang J. Estimating destination-specific traffic densities on urban freeways for advanced traffic management. Transportation Research Record: Journal of the Transportation Research Board 1994, 1457:143-148.
11. Gazis D., Knapp C. On-line estimation of traffic densities from time-series of flow and speed data. Transportation Science 1971, 5(3):283-301.
12. Gazis D., Liu C. Kalman filtering estimation of traffic counts for two network links in tandem. Transportation Research Part B 2003, 37(8):737-745.
13. Godunov S. A difference scheme for numerical computation of discontinuous solutions of hydrodynamic equations. Mathematics of the Sbornik 1959, 47(3):271-306.
14. Helbing D. Traffic and related self-driven many-particle systems. Reviews of Modern Physics 2001, 73(4):1067-1141.
15. Holden H., Risebro N. Conservation laws with a random source. Applied Mathematics and Optimization 1997, 36(2):229-241.
16. Hoogendoorn S., Bovy P. New estimation technique for vehicle-type-specific headway distributions. Transportation Research Record: Journal of the Transportation Research Board 1998, 1646:18-28.
17. Kang, J., 1995. Estimation of destination-specific traffic densities and identification of parameters on urban freeways using Markov models of traffic flow. Ph.D. thesis, University of Minnesota.
18. Lebacque J. The Godunov scheme and what it means for first order traffic flow models. Proceedings of the 13th International Symposium on Transportation and Traffic Theory 1996, 647-677. Elsevier, Lyon, France. J.B. Lesort (Ed.).
19. LeVeque R. Numerical Methods for Conservation Laws 1992, Birkhäuser, Berlin. second ed.
20. Lighthill, M., Whitham, G., 1955. On kinematic waves. I: flood movement in long rivers, II.A theory of traffic flow on long crowded roads. In: Proceedings of the Royal Society (London) A229. pp. 281-345.
21. Oksendal B. Stochastic Differential Equations 2007, Springer, Berlin. sixth ed.
22. Osher S. Riemann solvers, the entropy condition, and difference approximations. SIAM Journal on Numerical Analysis 1984, 21(2):217-235.
23. Paveri-Fontana S. On Boltzmann-like treatments for traffic flow: a critical review of the basic model and an alternative proposal for dilute traffic analysis. Transportation Research 1975, 9(4):225-235.
24. Prigogine I., Andrews F. A Boltzmann-like approach for traffic flow. Operations Research 1960, 8(6):789-797.
25. Prigogine I., Herman R. Kinetic Theory of Traffic Flow 1971, Elsevier, New York.
26. Resnick S. Adventures in Stochastic Processes 1992, Birkhäuser, Boston.
27. Richards P. Shock waves on the highway. Operations Research 1956, 4(1):42-51.
28. Skorokhod A. Limit theorems for stochastic processes. Theory of Probability and Its Applications 1956, 1(3):261-290.
29. Sumalee A., Zhong R., Pan T., Szeto W. Stochastic cell transmission model (SCTM): a stochastic dynamic traffic model for traffic state surveillance and assignment. Transportation Research Part B 2011, 45(3):507-533.
30. Szeto M., Gazis D. Application of Kalman filtering to the surveillance and control of traffic systems. Transportation Science 1972, 6(4):419-439.
31. Wang Y., Papageorgiou M. Real-time freeway traffic state estimation based on extended Kalman filter: a general approach. Transportation Research Part B 2005, 39(2):141-167.
32. Wang Y., Papageorgiou M., Messmer A. Real-time freeway traffic state estimation based on extended Kalman filter: a case study. Transportation Science 2007, 41(2):167-181.
33. Whitt W. Stochastic Process Limits 2002, Springer, New York.