Figures (8)  Tables (5)

    • Figure 1. 

      LSTM unit.

    • Figure 2. 

      Attention pooling module for hierarchical LSTM. Note the distinct treatment of cell states (dashed red path) incorporating both layers, vs hidden states using only the lower layer.

    • Figure 3. 

      Hierarchical Attention LSTM (HierAttnLSTM).

    • Figure 4. 

      Monthly and daily travel time pattern in PEMS district 4 data.

    • Figure 5. 

      Travel state data autocorrelation analysis.

    • Figure 6. 

      Spatial temporal traffic flow prediction results compared to ground truth.

    • Figure 7. 

      Distribution of traffic flow prediction errors.

    • Figure 8. 

      One week travel time prediction samples on self-downloaded PEMS-BAY dataset.

    • Model 3 step (15-min) 6 step (30-min) 9 step (45-min) 12 step (60-min)
      MAE RMSE MAE RMSE MAE RMSE MAE RMSE
      HierAttnLSTM 9.079 22.766 8.933 22.574 9.076 22.884 9.168 22.844
      AGCRN[55] 18.132 29.221 18.834 30.464 19.377 31.310 19.851 31.965
      GWNET[22] 17.692 28.516 18.574 29.888 19.247 30.895 19.956 31.848
      MTGNN[54] 17.925 28.837 18.760 30.296 19.349 31.334 20.135 32.510
      GMAN[27] 18.790 29.549 19.538 30.805 20.189 31.765 20.865 32.575
      STGCN[56] 19.146 30.301 20.133 31.886 20.830 33.056 21.567 34.200
      GRU[57] 22.441 36.286 22.506 36.342 22.571 36.415 22.583 36.447
      Seq2Seq[58] 22.585 36.475 22.581 36.348 22.762 36.554 23.163 36.988
      DCRNN[21] 19.581 31.125 21.467 34.067 23.152 36.665 24.864 39.228
      STG2Seq[60] 23.006 35.973 23.251 36.227 23.744 36.822 24.935 38.330
      AE[59] 23.999 37.942 24.024 37.990 24.401 38.446 25.025 39.289
      ASTGCN[23] 20.530 31.755 22.971 35.033 24.982 38.170 27.495 41.776
      TGCN[61] 21.678 34.635 23.962 37.777 26.340 41.045 29.062 44.794
      Proposed model results are highlighted in bold.

      Table 1. 

      PEMSD4 traffic flow forecasting.

    • Model 3 step (15-min) 6 step (30-min) 9 step (45-min) 12 step (60-min)
      MAE RMSE MAE RMSE MAE RMSE MAE RMSE
      HierAttnLSTM 8.375 20.356 9.204 22.518 9.427 22.715 9.215 22.320
      GWNET[22] 13.486 21.615 14.349 23.375 15.039 24.773 15.672 25.855
      AGCRN[55] 14.146 22.241 14.962 24.055 15.675 25.445 16.427 26.557
      MTGNN[54] 14.001 21.988 14.883 23.624 15.707 24.873 16.583 26.128
      STGCN[56] 15.166 23.615 16.188 25.401 16.971 26.556 17.819 27.818
      GMAN[27] 15.158 23.021 15.924 24.553 16.725 25.738 17.837 27.141
      DCRNN[21] 15.139 23.476 16.619 25.982 17.960 28.009 19.345 30.058
      Seq2Seq[58] 19.186 31.220 19.326 31.446 19.618 31.772 19.894 32.117
      GRU[57] 19.992 32.276 20.126 32.569 20.274 32.853 20.461 33.200
      STG2Seq[60] 18.217 27.334 19.479 29.289 20.432 30.617 21.445 32.130
      ASTGCN[23] 16.433 24.878 18.547 27.919 20.357 30.206 22.284 32.706
      AE[59] 22.266 35.562 22.209 35.557 22.335 35.696 22.865 36.269
      TGCN[61] 17.348 25.934 19.109 28.846 21.007 31.524 23.417 34.694
      Proposed model results are highlighted in bold.

      Table 2. 

      PEMSD8 traffic flow forecasting.

    • Model 3 step (15-min) 6 step (30-min) 9 step (45-min) 12 step (60-min)
      MAE RMSE MAE RMSE MAE RMSE MAE RMSE
      GWNET[22] 1.317 2.782 1.635 3.704 1.802 4.154 1.914 4.404
      MTGNN[54] 1.331 2.797 1.657 3.760 1.831 4.214 1.954 4.489
      DCRNN[21] 1.314 2.775 1.652 3.777 1.841 4.301 1.966 4.600
      AGCRN[55] 1.368 2.868 1.686 3.827 1.845 4.265 1.966 4.587
      STGCN[56] 1.450 2.872 1.768 3.742 1.941 4.140 2.057 4.355
      GMAN[27] 1.521 2.950 1.828 3.733 1.998 4.107 2.115 4.321
      ASTGCN[23] 1.497 3.024 1.954 4.091 2.253 4.708 2.522 5.172
      HierAttnLSTM 2.493 5.163 2.496 5.177 2.779 5.494 2.587 5.340
      GRU[54] 2.491 5.204 2.508 5.288 2.535 5.384 2.575 5.510
      Seq2Seq[58] 2.443 5.108 2.446 5.144 2.493 5.259 2.581 5.470
      AE[59] 2.570 5.302 2.573 5.288 2.627 5.392 2.724 5.608
      STG2Seq[60] 2.192 4.231 2.424 4.826 2.604 5.266 2.768 5.650
      TGCN[61] 2.633 5.288 2.739 5.525 2.906 5.875 3.103 6.314
      Proposed model results are highlighted in bold.

      Table 3. 

      PEMS-BAY traffic speed forecasting.

    • Model Parameter count Size (MB)
      MSTGCN 169596 0.65
      DCRNN 372483 1.42
      GWNET 410484 1.57
      HierAttnLstm(64) 415107 1.58
      ASTGCN 556296 2.12
      AGCRN 745160 2.84
      HierAttnLstm(128) 806917 3.08
      STGCN 1476003 5.63

      Table 4. 

      PEMS-BAY traffic speed forecasting.

    • Model 15 min 30 min 45 min
      MAE RMSE MAE RMSE MAE RMSE
      Stacked LSTM 0.247 0.445 0.272 0.517 0.286 0.557
      Stacked BiLSTM 0.278 0.470 0.296 0.541 0.314 0.583
      HierAttnLSTM 0.195 0.339 0.235 0.424 0.268 0.49
      Proposed model results are highlighted in bold.

      Table 5. 

      Ablation analysis on travel time prediction at different horizons.