Day-to-day vehicular flow dynamics in intelligent transportation network

Hsun-Jung Cho*, Ming Chorng Hwang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


In this paper, a flow evolution model is developed by using the dynamical system approach for a vehicular network equipped with predicted travel information. The concerned system variables, path flow, and predicted minimal travel time of an origin-destination (OD) pair, are measured on the peak-hour-average base for each day. The time change rates of these two variables are formulated as a system of ordinary differential equations under the assumption of daily learning and adaptive processes for commuters. By incorporating the total perceived travel time loss (or saving) into the proposed models, time change rates of path flows are generated with a flow-related manner to prevent path flow dynamics from being insensible to traffic congestion which had been formulated in the existing studies. Heterogeneous models with various user adjusting sensitivities and predicted travel information are also presented. Equilibrium solutions of the proposed network dynamics satisfy the Wardrop user equilibria and are proved to be asymptotically stable by using the stability theorem of Lyapunov. The issue of existence and uniqueness of solutions is proved both on the lemma of Lipschitz condition and the fundamental theorem of ordinary differential equations. In addition, some simple examples are demonstrated to show the asymptotic behaviors of the proposed models numerically.

Original languageEnglish
Pages (from-to)501-522
Number of pages22
JournalMathematical and Computer Modelling
Issue number4-5
StatePublished - 1 Feb 2005


  • Day-to-day network dynamics
  • Dynamic traffic assignment
  • Lyapunov function
  • Nonlinear dynamical system

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