Analysis of Kinematic Waves Arising in Diverging Traffic Flow Models
Published Online:1 Apr 2014https://doi.org/10.1287/trsc.2013.0499
References
- (2000) On the convergence of Godunov scheme for nonlinear hyperbolic systems. Chinese Ann. Math. Ser. B 21(3):269–284.Crossref, Google Scholar
- (1998) Unstable Godunov discrete profiles for steady shock waves. SIAM J. Numer. Anal. 35(6):2272–2297.Crossref, Google Scholar
- (2003) Freeway on-ramp metering, delay savings, and diverge bottleneck. Transportation Res. Record: J. Transportation Res. Board 1856:1–5.Crossref, Google Scholar
- (2005) Traffic flow on a road network. SIAM J. Math. Anal. 36(6):1862–1886.Crossref, Google Scholar
- (2004) Modern numerical methods for fluid flow. Unpublished manuscript.Google Scholar
- (1928) Über die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen 100(1):32–74.Crossref, Google Scholar
- (1999) Remarks on traffic flow modeling and its applications. Brilon W, Huber F, Schreckenberg M, Wallentowitz H, eds. Traffic and Mobility: Simulation, Economics, Environment (Springer-Verlag, Berlin, Heidelberg), 105–115.Crossref, Google Scholar
- (1994) The cell transmission model: A dynamic representation of highway traffic consistent with hydrodynamic theory. Transportation Res. Part B 28(4):269–287.Crossref, Google Scholar
- (1995) The cell transmission model II: Network traffic. Transportation Res. Part B 29(2):79–93.Crossref, Google Scholar
- (1997) A continuum theory of traffic dynamics for freeways with special lanes. Transportation Res. Part B 31(2):83–102.Crossref, Google Scholar
- (1999) Possible explanations of phase transitions in highway traffic. Transportation Res. Part A 33(5):365–379.Google Scholar
- (1997) A simple physical principle for the simulation of freeways with special lanes and priority vehicles. Transportation Res. Part B 31(2):103–125.Crossref, Google Scholar
- (1995) On the functional form of the speed-density relationship—II: Empirical investigation. Transportation Res. Part B 29(5):391–406.Crossref, Google Scholar
- (1980) Stable and entropy satisfying approximations for transonic flow calculations. Math. Comput. 34(149):45–75.Crossref, Google Scholar
- (1990) Behavioral model of freeway exiting. Transportation Res. Record 1281:16–27.Google Scholar
- Federal Highway Administration (2004) Traffic flow theory: A state of the art report. Transportation Research Board, Washington, DC.Google Scholar
- (1935) A study in highway capacity. Highway Res. Board Proc. 14:448–477.Google Scholar
- (1995) A mathematical model of traffic flow on a network of unidirectional roads. SIAM J. Math. Anal. 26(4):999–1017.Crossref, Google Scholar
- (2010) Continuous kinematic wave models of merging traffic flow. Transportation Res. Part B 44(8–9):1084–1103.Crossref, Google Scholar
- (2003a) The inhomogeneous kinematic wave traffic flow model as a resonant nonlinear system. Transportation Sci. 37(3):294–311.Link, Google Scholar
- (2003b) On the distribution schemes for determining flows through a merge. Transportation Res. Part B 37(6):521–540.Crossref, Google Scholar
- (2004) A multicommodity kinematic wave simulation model of network traffic flow. Transportation Res. Record: J. Transportation Res. Board 1883:59–67.Crossref, Google Scholar
- (2009) Supply-demand diagrams and a new framework for analyzing the inhomogeneous Lighthill-Whitham-Richards model. Proc. 18th Internat. Sympos. Transportation Traffic Theory, Hong Kong, 603–635.Crossref, Google Scholar
- (1972) Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves (SIAM, Philadelphia).Google Scholar
- (1996) The Godunov scheme and what it means for first order traffic flow models. Proc. 13th Internat. Sympos. Transportation Traffic Theory (Elsevier Science, Lyon, France), 647–677.Google Scholar
- (2005) First order macroscopic traffic flow models: Intersection modeling, network modeling. Proc. 16th Internat. Sympos. Transportation Traffic Theory (Pergamon, Oxford, UK), 365–386.Google Scholar
- (1955) On kinematic waves: II. A theory of traffic flow on long crowded roads. Proc. Royal Soc. London A 229(1178):317–345.Crossref, Google Scholar
- (1996) Modelling of freeway merging and diverging flow dynamics. Appl. Math. Model. 20(6):459–469.Crossref, Google Scholar
- (2002) The bottleneck mechanism of a freeway diverge. Transportation Res. Part A 36(6):483–505.Google Scholar
- (1999) Delays caused by a queue at a freeway exit ramp. Transportation Res. Part B 33(5):337–350.Crossref, Google Scholar
- (2006) Continuum traffic model for freeway with on- and off-ramp to explain different traffic-congested states. Transportation Res. Record: J. Transportation Res. Board 1965:91–102.Crossref, Google Scholar
- (1990) Dynamic modelling, assignment and route guidance in traffic networks. Transportation Res. Part B 24(6):471–495.Crossref, Google Scholar
- (2008) Studies of emergency evacuation strategies based on kinematic wave models of network vehicular traffic. Proc. 11th Internat. IEEE Conf. Intelligent Transportation Systems, Beijing, 222–227.Crossref, Google Scholar
- (1956) Shock waves on the highway. Oper. Res. 4(1):42–51.Link, Google Scholar
- (1982) A transportation network evacuation model. Transportation Res. Part A 16(3):209–218.Crossref, Google Scholar
- (1984) On the relation between the upwind-differencing schemes of Godunov, Engquist-Osher and Roe. SIAM J. Sci. Statist. Comput. 5(1):1–20.Crossref, Google Scholar

