Figures (2)  Tables (3)

    • Figure 1. 

      The probability distribution of traffic flow patterns.

    • Figure 2. 

      The four motorways of Amsterdam.

    • Models Criterion A1 A2 A4 A8
      HA RMSE (vehs/h) 404.84 348.96 357.85 218.72
      MAPE (%) 16.87 15.53 16.72 16.24
      KF RMSE (vehs/h) 332.03 239.87 250.51 187.48
      MAPE (%) 12.46 10.72 12.62 12.63
      ANN RMSE (vehs/h) 299.64 212.95 225.86 166.50
      MAPE (%) 12.61 10.89 12.49 12.53
      SAE RMSE (vehs/h) 295.43 209.32 226.91 167.01
      MAPE (%) 11.92 10.23 11.87 12.03
      GSA-ELM RMSE (vehs/h) 287.89 203.04 221.39 163.24
      MAPE (%) 11.69 10.25 11.72 12.05
      PSOGSA-ELM RMSE (vehs/h) 288.03 204.09 220.52 163.92
      MAPE (%) 11.53 10.16 11.67 12.02
      LSTM RMSE (vehs/h) 289.56 204.71 224.49 165.13
      MAPE (%) 12.38 10.56 11.99 12.48
      NiLSTM RMSE (vehs/h) 285.54 203.69 223.72 163.25
      MAPE (%) 12.00 10.14 11.57 11.76
      $ {\overline{\delta }}_{relax} $-LSTM RMSE (vehs/h) 280.54 195.28 220.08 161.69
      MAPE (%) 11.48 10.02 11.51 11.54

      Table 1. 

      The comparison of the $ {\overline{\delta }}_{relax} $-LSTM model with five baseline models on the four baseline datasets, with boldface representing the best performance.

    • Hyperparameter value Value
      Hidden layers 1
      Hidden units 256
      Batch size 32
      Input length 12
      Epochs 200

      Table 2. 

      The hyperparameters for the LSTM, NiLSTM, and $ {\overline{\delta }}_{relax} $- LSTM network.

    • Dataset λ1 λ2 δ1 δ2 c1 c2
      A1 0.6 0.4 0.3 10 0 −1
      A2 0.8 0.2 30 0.3 5 0
      A4 1 0 0.7 30 0 −0.5
      A8 0.6 0.4 0.3 15 0 −1

      Table 3. 

      The parameter settings of $ \mathcal{L} $ for the $ {\overline{\delta }}_{relax} $-LSTM network.