The distribution of congestion on a class of stochastic kinematic wave models

Transportation Science

Volumn 48, Issue 2, 2014, Pages 217-224

  Laval, Jorge A ^a   Chilukuri, Bhargava R ^a  

^a Georgia Institute of Technology   (United States)

Author keywords

Kinematic wave model; Stochastic traffic flow

Indexed keywords

KINEMATICS; STOCHASTIC SYSTEMS; TRAFFIC CONGESTION; WHITE NOISE;

BOTTLENECK PROBLEM; FUNDAMENTAL DIAGRAM; INITIAL DENSITY; KINEMATIC WAVE MODELS; RIEMANN PROBLEM; STOCHASTIC SOLUTION; STOCHASTIC TRAFFIC FLOWS; TIME-SPACE;

STOCHASTIC MODELS;

EID: 84902650196     PISSN: 00411655     EISSN: 15265447     Source Type: Journal    
DOI: 10.1287/trsc.2013.0462     Document Type: Article

References (35)

1. Antia HM, Basu S (2000) Temporal variations of the rotation rate in the solar interior. Astrophysics J. 541(1):442-448.
2. Avellaneda M, Weinan E (1995) Statistical properties of shocks in Burgers turbulence. Comm. Math. Phys. 172(1):13-38.
3. Barles G, Souganidis P (2000) On the large time behavior of solutions of Hamilton-Jacobi equations. SIAM J. Math. Anal. 31(4):925-939.
4. Barlovic R, Huisinga T, Schadschneider A, Schreckenberg M (2002) Open boundaries in a cellular automaton model for traffic flow with métastable states. Phys. Rev. E 66(4, Pt. 2):1-11.
5. Barlovic R, Santen L, Schadschneider A, Schreckenberg M (1998) Metastable states in cellular automata for traffic flow. Eur. Physical J. B 5:793-800.
6. Benz A (2002) Plasma Astrophysics: Kinetic Processes in Solar and Stellar Coronae, 2nd ed., Vol. 279. Astrophysics and Space Science Library (Kluwer, Dordrecht, The Netherlands).
7. Burgers JM (1974) The Nonlinear Diffusion Equation: Asymptotic Solutions and Statistical Problems (D. Reidel Pub. Co., Dordrecht, The Netherlands).
8. Dafermos CM (2000) Hyperbolic Conservation Laws in Continuum Physics (Springer, Berlin).
9. Daganzo CF (1994) The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Res. Part B 28(4):269-287.
10. Daganzo CF (2005a) A variational formulation of kinematic wave theory: Basic theory and complex boundary conditions. Transportation Res. Part B 39(2):187-196.
11. Daganzo CF (2005b) A variational formulation of kinematic waves: Solution methods. Transportation Res. Part B: Methodological 39(10):934-950.
12. Del Castillo JM (2001) Propagation of perturbations in dense traffic flow: A model and its implications. Transportation Res. Part B 35(2):367-390.
13. Godunov S (1959) A difference scheme for numerical computation of discontinuous solutions of equations of fluid dynamics. Mathematicheskii Sbornik 89(47):271-306.
14. Helbing D, Treiber M (1998) Gas-kinetic-based traffic model explaining observed hysteresis phase transition. Phys. Rev. Lett. 81(14):3042-3045.
15. Helbing D, Hennecke A, Shvetsov V, Treiber M (2001) Master: Macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transportation Res. Part B 35:183-211.
16. Holden H, Risebro NH (1997) Conservation laws with a random source Appl. Math. Optim. 36(2):229-241.
17. Hopf E (1969/1970) On the right weak solution of the Cauchy problem for a quasilinear equation of first order. J. Math. Mech. 19:483-487.
18. Khoshyaran M, Lebacque P (2007) A stochastic macroscopic traffic model devoid of diffusion. Appert-Rolland C, Lassarr S, Gondret P, Dauchot O, Sykes C, eds. Traffic and Granular Flow '07 (Springer, New York), 139-150.
19. Kim T, Zhang HM (2008) A stochastic wave propagation model. Transportation Res. Part B 42:619-634.
20. Lax PD (1957) Hyperbolic systems of conservation laws II. Sarnak P, Majda A, eds. Communications on Pure and Applied Mathematics (Wiley Periodicals, New York), 537-566.
21. Nagel K, Schreckenberg M (1992) A cellular automaton model for freeway traffic. J. Phys. I 2(2):2221-2229.
22. Newell GF (2002) A simplified car-following theory: A lower order model. Transportation Res. Part B 36(3):195-205.
23. Ngoduy D (2008) Operational effect of acceleration lane on main traffic flow at discontinuities. Transportmetrica 4(3):195-207.
24. Ngoduy D, Hoogendoorn S, Van Zuylen H (2006) New continuum traffic model for freeway with on- and off-ramp to explain different traffic congested states. Transportation Res. Record 1965(1):91-102.
25. Olejnik OA (1957) Discontinuous solutions of non-linear differential equations. Am. Math. Soc. Transl. II. Ser. 26:95-172. [Translated by George Biriuk.]
26. Rezakhanlou F, Tarver JE (2000) Homogenization for stochastic Hamilton-Jacobi equations. Arch. Rational Mech. Anal. 151(4):277-309.
27. Rorro M (2005) Numerical approximation of the effective Hamiltonian and of the Aubry set for first order Hamilton-Jacobi equations. Ugo B, Piermarco C, Dolcetta Italo C, Maurizio F, Benedetto P, eds. Proc. Sci. CSTNA 2005(SISSA):016.
28. Rorro M (2006) An approximation scheme for the effective Hamiltonian and applications. Appl. Numer. Math. 56(9):1238-1254.
29. Ryan R (1998) Large-deviation analysis of Burgers turbulence with white-noise initial data. Comm. Pure Appl. Math. 51(1):47-75.
30. Shvetsov V, Helbing D (1999) Macroscopic dynamics of multilane traffic. Phys. Rev. E 59(6):6328-6339.
31. Sinai YG (1992) Statistics of shocks in solutions of inviscid Burgers equation. Comm. Math. Phys. 148(3):601-621.
32. Sopasakis A (2004) Stochastic noise approach to traffic flow modeling. Physica A: Statist. Mech. Appl. 342(3-4):741-754.
33. Souganidis PE (1999) Stochastic homogenization of Hamilton-Jacobi equations and some applications. Asymptotic Anal. 20(1):1-11.
34. Sumalee A, Zhong RX, Pan TL, Szeto WY (2011) Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment. Transportation Res. Part B: Methodological 45(3):507-533.
35. Wehr J, Xin J (1997) Front speed in the Burgers equation with a random flux. J. Statist. Phys. 88(3-4):843-871.