# Planning-Level Optimisation of Headway Regularity
## 5 Sensitivity Analysis  
As the optimisation procedure yields different results for peak and off-peak periods, which can be distinguished by the headway and the transport demand, these parameters were considered in the sensitivity analysis. First, the sensitivity of the optimisation procedure was examined by simulating a change in transport demand by decreasing/increasing the number of passengers boarding and alighting at each stop by 10% and 20%, resulting in the five cases shown in Table 3. For each case, the impact of transport demand on travel time and headway regularity was analysed. The sensitivity of headway regularity to changes in transport demand is obtained by the difference between the PRDM of radial lines and diametrical lines (Table 4). As can be  
Figure 8: Difference in the average passenger travel time. \begin{table}
\begin{tabular}{c c} \hline \hline
**Case** & **Percentage Decrease/Increase in the Number of Passengers** \\ \hline
1 & \(-20\%\) \\
2 & \(-10\%\) \\
3 & \(0\%\) \\
4 & \(+10\%\) \\
5 & \(+20\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Passenger boarding and alighting at stops per case. seen from Figure 9, changes in transport demand have a significant impact on the headway regularity. In the example depicted on the graph, for a primary headway disturbance of 3 min after optimisation, a \(-0.184\) reduction in PRDM is achieved in CASE 1, while \(-0.219\), \(-0.262\), \(-0.306\) and \(-0.358\) reductions are obtained for the remaining four cases. For the same values of primary headway disturbance, by increasing the transport demand, a better headway regularity is achieved, i.e., the optimisation procedure results in a greater PRDM reduction. Figure 10 and Table 5 show that changes in transport demand also have a significant impact on passenger travel time. For example, if a primary disruption of 3 min occurs after optimisation, passengers will experience a \(-0.59\) reduction in travel time in CASE 1, while \(-0.80\), \(-1.08\), \(-1.31\) and \(-1.58\) reductions are achieved in CASE 2-5. Correspondingly, with an increase in transport demand on the same line and with the same values of primary headway disruption, greater savings in passenger travel time are achieved. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variant**} & \multirow{2}{*}{**Case**} & \multicolumn{6}{c}{**Primary Headway Disturbance (min)**} \\ \cline{3-8}  & & & **0** & **1** & **2** & **3** & **4** \\ \hline \multirow{4}{*}{**PPDM**} & 1 & 0 & 0.282 & 0.556 & 0.821 & 1.094 \\  & 2 & 0 & 0.256 & 0.600 & 0.891 & 1.208 \\  & 3 & 0 & 0.352 & 0.652 & 0.996 & 1.269 \\  & 4 & 0 & 0.370 & 0.722 & 1.057 & 1.400 \\  & 5 & 0 & 0.413 & 0.783 & 1.153 & 1.531 \\ \hline \multirow{4}{*}{**PPDM**} & 1 & 0 & 0.212 & 0.434 & 0.637 & 0.850 \\  & 2 & 0 & 0.204 & 0.451 & 0.672 & 0.911 \\  & 3 & 0 & 0.265 & 0.486 & 0.733 & 0.946 \\  & 4 & 0 & 0.265 & 0.521 & 0.751 & 0.998 \\  & 5 & 0 & 0.291 & 0.547 & 0.795 & 1.06 Based on the aforementioned analysis, it can be concluded that the transport demand and the effects of the optimisation procedure (travel time and headway regularity) are positively correlated. Specifically, increasing the primary headway disturbance increases the sensitivity of the optimisation procedure to the transport demand. As a part of the sensitivity analysis, a simulation of headway was also carried out. Five cases were created for this purpose (Table 6) and the impact of the headway on travel time and headway regularity was analysed for each case. The sensitivity of headway regularity to changes in headway is obtained by the difference between the PRDM of radial lines and diametrical lines (Table 7). It is evident from Figure 11 that changes in headway duration have a significant impact on the headway regularity.