Analysis of Traffic Statics and Dynamics in Signalized Networks: A Poincaré Map Approach

Published Online:https://doi.org/10.1287/trsc.2017.0740

References

  • Buisson C, Ladier C (2009) Exploring the impact of homogeneity of traffic measurements on the existence of macroscopic fundamental diagrams. Transportation Res. Record: J. Transportation Res. Board 2124:127–136.CrossrefGoogle Scholar
  • Cassidy MJ (1998) Bivariate relations in nearly stationary highway traffic. Transportation Res. Part B 32(1):49–59.CrossrefGoogle Scholar
  • Courant R, Friedrichs K, Lewy H (1928) Über die partiellen differenzengleichungen der mathematischen physik. Mathematische Annalen 100(1):32–74.CrossrefGoogle Scholar
  • 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.CrossrefGoogle Scholar
  • Daganzo CF (1995) The cell transmission model, part II: Network traffic. Transportation Res. Part B 29(2):79–93.CrossrefGoogle Scholar
  • Daganzo CF, Geroliminis N (2008) An analytical approximation for the macroscopic fundamental diagram of urban traffic. Transportation Res. Part B 42(9):771–781.CrossrefGoogle Scholar
  • Daganzo CF, Gayah VV, Gonzales EJ (2011) Macroscopic relations of urban traffic variables: Bifurcations, multivaluedness and instability. Transportation Res. Part B 45(1):278–288.CrossrefGoogle Scholar
  • El Aroudi A, Debbat M, Martinez-Salamero L (2007) Poincaré maps modeling and local orbital stability analysis of discontinuous piecewise affine periodically driven systems. Nonlinear Dynam. 50(3):431–445.CrossrefGoogle Scholar
  • Epperson JF (2013) An Introduction to Numerical Methods and Analysis, 2nd ed. (John Wiley & Sons, Hoboken, NJ).Google Scholar
  • Farhi N, Goursat M, Quadrat J (2011) The traffic phases of road networks. Transportation Res. Part C 19(1):85–102.CrossrefGoogle Scholar
  • Gan Q-J (2014) Macroscopic modeling and analysis of urban vehicular traffic. Unpublished doctoral dissertation, University of California, Irvine.Google Scholar
  • Gayah VV, Daganzo C (2011a) Effects of turning maneuvers and route choice on a simple network. Transportation Res. Record: J. Transportation Res. Board 2249:15–19.CrossrefGoogle Scholar
  • Gayah VV, Daganzo CF (2011b) Clockwise hysteresis loops in the macroscopic fundamental diagram: An effect of network instability. Transportation Res. Part B 45(4):643–655.CrossrefGoogle Scholar
  • Geroliminis N, Daganzo CF (2008) Existence of urban-scale macroscopic fundamental diagrams: Some experimental findings. Transportation Res. Part B 42(9):759–770.CrossrefGoogle Scholar
  • Geroliminis N, Sun J (2011) Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transportation Res. Part B 45(3):605–617.CrossrefGoogle Scholar
  • Godfrey J (1969) The mechanism of a road network. Traffic Engrg. Control 11(7):323–327.Google Scholar
  • Haberman R (1977) Mathematical Models (SIAM, Philadelphia).Google Scholar
  • Helbing D (2009) Derivation of a fundamental diagram for urban traffic flow. Eur. Phys. J. B 70(2):229–241.CrossrefGoogle Scholar
  • Herman R, Prigogine I (1979) A two-fluid approach to town traffic. Science 204:148–151.CrossrefGoogle Scholar
  • Ji Y, Daamen W, Hoogendoorn S, Hoogendoorn-Lanser S, Qian X (2010) Investigating the shape of the macroscopic fundamental diagram using simulation data. Transportation Res. Record: J. Transportation Res. Board 2161:40–48.CrossrefGoogle Scholar
  • Jin W-L (2012) A link queue model of network traffic flow. arXiv:1209.2361.Google Scholar
  • Jin W-L (2013) Stability and bifurcation in network traffic flow: A Poincaré map approach. Transportation Res. Part B 57:191–208.CrossrefGoogle Scholar
  • Jin W-L, Gan Q-J, Gayah VV (2013) A kinematic wave approach to traffic statics and dynamics in a double-ring network. Transportation Res. Part B 57:114–131.CrossrefGoogle Scholar
  • Knoop V, Hoogendoorn S, Van Lint JW (2012) Routing strategies based on macroscopic fundamental diagram. Transportation Res. Record: J. Transportation Res. Board 2315:1–10.CrossrefGoogle Scholar
  • La Salle J (1976) The Stability of Dynamical Systems (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Leclercq L, Geroliminis N (2013) Estimating MFDs in simple networks with route choice. Procedia-Soc. Behavioral Sci. 80:99–118.CrossrefGoogle Scholar
  • Papageorgiou M, Diakaki C, Dinopoulou V, Kotsialos A, Wang Y (2003) Review of road traffic control strategies. Proc. IEEE 91(12):2043–2067.CrossrefGoogle Scholar
  • Schrank D, Eisele B, Lomax T (2012) TTI’s 2012 urban mobility report. Texas A&M Transportation Institute. Texas A&M University System, College Station.Google Scholar
  • Sorensen P, Wachs M, Min EY, Kofner A, Ecola L (2008) Moving Los Angeles: Short-Term Policy Options for Improving Transportation (RAND Corporation, Santa Monica, CA).CrossrefGoogle Scholar
  • Sun Z, Ge SS (2011) Stability Theory of Switched Dynamical Systems (Springer-Verlag, London).CrossrefGoogle Scholar
  • Teschl G (2012) Ordinary Differential Equations and Dynamical Systems, Vol. 140 (American Mathematical Society, Providence, RI).CrossrefGoogle Scholar
  • Webster FV (1958) Traffic signal settings. Road Research Laboratory Technical Paper 39, H.M. Stationary Office, London.Google Scholar
  • Wiggins S (2003) Introduction to Applied Nonlinear Dynamical Systems and Chaos, Vol. 2 (Springer Science & Business Media, New York).Google Scholar
  • Wu X, Liu HX, Geroliminis N (2011) An empirical analysis on the arterial fundamental diagram. Transportation Res. Part B 45(1):255–266.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.