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Approximating Traffic Flow by a Schrödinger Equation - Introduction of Non-Reflecting Boundary Conditions

In: Traffic and Granular Flow ’03

Author

Listed:
  • R. Woesler

    (German Aerospace Center, Institute of Transportation Research)

  • K.-U. Thiessenhusen

    (German Aerospace Center, Institute of Transportation Research)

  • R.D. Kühne

    (German Aerospace Center, Institute of Transportation Research)

Abstract

Summary We show that some simple urban traffic flow equations can be approximated by equations which are equivalent to a Schrödinger equation. For a simulation of the Schrödinger equation as well as for analytical computations it is useful that waves of traffic which travel along a road are not reflected at the boundaries of the simulated region. We present the non-reflecting boundary condition for a corresponding one-dimensional Schrödinger equation, and show simulation results for a wave package of traffic moving towards such a boundary.

Suggested Citation

  • R. Woesler & K.-U. Thiessenhusen & R.D. Kühne, 2005. "Approximating Traffic Flow by a Schrödinger Equation - Introduction of Non-Reflecting Boundary Conditions," Springer Books, in: Serge P. Hoogendoorn & Stefan Luding & Piet H. L. Bovy & Michael Schreckenberg & Dietrich E. Wolf (ed.), Traffic and Granular Flow ’03, pages 223-228, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-28091-0_20
    DOI: 10.1007/3-540-28091-X_20
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