On the Existence of Stationary States in General Road Networks

The daily driving experience and empirical observations suggest that traffic patterns in a road network are relatively stationary during peak periods. In numerous transportation network studies, there has been an implicit conjecture that stationary states exist in a network when origin demands, route choice proportions, and destination supplies are constant. In this study, the author first rigorously formulate the conjecture within the framework of a network kinematic wave theory with an invariant junction model. After defining stationary states, the author derives a system of algebraic equations in 3-tuples of stationary link flow-rates, demands, and supplies. The author then introduce a new definition of junction critical demand levels based on effective demands and supplies. With a map in critical demand levels, the author show that its fixed points and, therefore, stationary states exist with the help of Brouwer's fixed point theorem. For two simple road networks, the author shows that the map is well-defined and can be used to solve stationary states with a brute-force method. Finally the author summarizes the study and present some future extensions and applications.


  • English

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  • Accession Number: 01571161
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Jul 24 2015 3:23PM