# Multimodal Dynamic Journey-Planning +
## 4 Experimental Evaluation
### Experimental Results
The implementations of HLCSA and HLRaptor tested in our experimental study were taken from [33]. The average number of journeys which need to be computed in the profile solution set is about 14. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Map**} & \multirow{2}{*}{**Algorithm**} & \multirow{2}{*}{**Object**} & \multicolumn{4}{c}{**Travel Modes**} & \multicolumn{2}{c}{**Query [ms]**} \\ \cline{3-10}  & & & & **Public Transport** & **Walk** & **EV/Car** & **Cycle** & **L-Walk** & **U-Walk** \\ \hline \multirow{4}{*}{**Dataset**} & TE-QH-ALT[10] & EA & \(\bullet\) & & & & 6.28 & \\  & DTM-QH-ALT[10] & EA & \(\bullet\) & & & & 11.66 & \\  & MDTM-QH-ALT & EA & \(\bullet\) & & & & 5.71 & \\  & MDTM-QH-ALT & EA & \(\bullet\) & \(\bullet\) & \(\bullet\) & 8.15 & 103.46 \\ \hline \multirow{4}{*}{**Dataset**} & TE-QH-ALT[10] & EA & \(\bullet\) & & & & 5.09 & \\  & DTM-QH-ALT[10] & EA & \(\bullet\) & & & & 9.81 & \\  & MDTM-QH-ALT & EA & \(\bullet\) & & & & 4.01 & \\  & MDTM-QH-ALT & EA & \(\bullet\) & \(\bullet\) & \(\bullet\) & 6.02 & 107.93 \\  & McMDTM-QH-ALT-1.0 & MC & \(\bullet\) & \(\bullet\) & \(\bullet\) & 6.22 & 215.27 \\  & McMDTM-QH-ALT-1.2 & MC & \(\bullet\) & \(\bullet\) & \(\bullet\) & 15.40 & 360.56 \\  & MCR-ht [7.8] & MC & \(\bullet\) & \(\bullet\) & \(\bullet\) & 361.23 \\  & MR-oo-10[7.8] & MC & \(\bullet\) & \(\bullet\) & & 21.47 & \\  & PrMDTM-QH-ALT & PF(2h) & \(\bullet\) & \(\bullet\) & & 162.76 & 1182.12 \\  & HLCSA[29] \(\dagger\) & PF(2h) & \(\bullet\) & \(\bullet\) & & & 1096.97 \\  & HLRaptor[29]\(\dagger\) & PF(2h) & \(\bullet\) & \(\bullet\) & & & 733.64 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison between query algorithms. L-Walk (U-Walk) denotes a query algorithm with limited (unlimited) walking. McMDTM-QH-ALT-1.0 (McMDTM-QH-ALT-1.2) denotes McMDTM-QH-ALT with \(r_{mc}=1\) (\(r_{mc}=1.2\)). Bullets (\(\bullet\)) indicate the options taken into account. EA denotes an earliest arrival journey. MC denotes a multicriteria journey on arrival time and number of transfers (and walking duration for MCR-ht). PF denotes profiles with earliest arrival journeys with respect to the departure domain. (\(\dagger\)) These results apply to a smaller London instance consisting of 19,746 stops and 4,695,285 elementary connections. For evaluating updates (occurring after a delay), 10,000 elementary connections were randomly selected for each input instance, and for each elementary connection we randomly generated a delay affecting the corresponding train or bus, chosen with uniform probability distribution between 1 and 360 min. In the experimental evaluation we have included the update algorithms TE-UH for TE-red [10], DTM-U for DTM [10], and the new algorithm MDTM-U for MDTM. The experimental results of the update algorithms are reported in Table 8. The update times measure the average computational times for updating the graph when a delay in a transportation vehicle itinerary has to be absorbed. In DTM-U, only (at most) two arc weights and a few node time references need to be changed in the original graph to keep the EA queries correct. Although MDTM-U has an additional computation cost to maintain the earliest arrival index table for any node time reference update, the time of MDTM-U is competitive to that of the DTM-U. The updating algorithm in both cases takes less than 164 us. That is due to the fact that the number of stations where something changes, as a consequence of a delay, is small with respect to the size of the whole set of stations \(|\Phi|\).