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

Abstract

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. Numerous ways to describe traffic flow are known. A simple way to approximate urban traffic with one-dimensional lanes is to use the following macroscopic equations.