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Properties of the LWR model with time delay

  • * Corresponding author: Elisa Iacomini

    * Corresponding author: Elisa Iacomini 
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  • In this article, we investigate theoretical and numerical properties of the first-order Lighthill-Whitham-Richards (LWR) traffic flow model with time delay. Since standard results from the literature are not directly applicable to the delayed model, we mainly focus on the numerical analysis of the proposed finite difference discretization. The simulation results also show that the delay model is able to capture Stop & Go waves.

    Mathematics Subject Classification: 35L65, 90B20, 65M06.


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  • Figure 1.  Comparison between density profiles computed with (right) and without(left) CFL condition in case of a rarefaction wave

    Figure 2.  Comparison between density profiles computed with (right) and without (left) CFL condition in a shock framework

    Figure 3.  Test 0: Comparing the density evolution computed by the delayed model (left) and the LWR model (right)

    Figure 4.  Test 0: Comparison between density profiles corresponding to different grid steps size

    Figure 5.  Test 0: Density evolution and profile, at time $ T = \frac{1}{3}T_f $, in case of a too high delay

    Figure 6.  Test 1: Reproducing the simulation presented in [7], with $ \rho^0(x,1) $ on the left and $ \rho^0(x,2) $ on the right

    Figure 7.  Test 2: Density values in the $ (x,t) $-plane (left) and density profile at time $ T = T_f $ (right)

    Figure 8.  Test 2: Density values in the $ (x,t) $-plane with low delay term, $ T_\Delta = 4 \Delta t $, (left) and density profile at $ T = T_f $ (right)

    Figure 9.  Triggering of Stop & Go waves: Density values in the $ (x,t) $-plane

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