## 6 Results: Application of the Sensitivity Analysis on the \"Traffic Jam Chauffeur\"
### Sensitivity Analysis of AV to Events and Distribution Function
#### 6.2.1 Sensitivity Analysis of AV to Events  
For each logical situation, a list of events is associated with it. In order to identify this list, we will rely on the types of events that the AV may face in TJC conditions, the limits of the associated ODD and the value ranges of the logical situations. To illustrate this, let us consider Table 7, which shows the sensitivity of the logical situation Y8 as defined in the Appendix A. The events for this situation are as follows:  
1. Events impacting the concrete level concern the ranges to which at least one of the components of the AV is sensitive. Ranges A1_2, A2_2 and A4_2 are concerned. Their sensitivities are defined in Table 8. We note \(e_{ji}\) an event i of the logical situation j and S(\(e_{ji}\)) its sensitivity. \(\Delta\)(Ax_y) is an event concerning a change of value within the same range of values Ax_y. 2. Events impacting the logical level consist of a change in the range of values of the logical situation considered and concern what we have called the level 1 neighborhood. By analyzing the eight logical situations, those that differ from Y8 by a single range of values are: Y4, Y6 and Y7 (they represent the level 1 neighborhood of Y8). Sincesuch an event triggers a transition from one logical situation to another, the gradient (i.e., the absolute value of the difference in sensitivity between the initial and final situation) is used to obtain the sensitivity. Table 9 gives the events and their sensitivity in the case of logical situation Y8. \(\Delta\)(Ax_y, Ax_z) is a range change event. 3. The events impacting the functional level trigger a transition of the AV out of the \"Car following\" situation. Considering the conditions of validity of the \"Car following\" situation and the constraints of the ODD mentioned in paragraph 4.2, the modifications of the value ranges (and thus the events) that make it leave the \"Car following\" situation are among others: \(\mathrm{e_{8.7}}=\Delta\)(A1_1, A1_0) (switching from two lanes to one lane: end of Ego lane) \(\mathrm{e_{8.8}}=\Delta\)(A1_2, A1_0) (switching from 3+ lanes to one lane: end of Ego lane) \(\mathrm{e_{8.9}}=\Delta\)(A5_1, A5_2) (switching from Speed_OtherVehicle.1.Low to Speed_Other Vehicle.1.High)  
The range A1_0 does not affect any technology (sensitivity contribution = 0) but its occurrence implies a change of lane for the Ego (addition of a factor of 1 to the sensitivity) and thus causes a change of functional situation; therefore, a sensitivity of 1 is obtained. The sensitivities of these events are shown in Table 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Techno 1** & **Techno 2** & **Techno 3** & **Techno 4** & **Techno 5** & **Decision** & **Actual** \\  & **(Radar)** & **(Lidar)** & **(Ultrasonic)** & **(Stereo Camera)** & **(Mono Camera)** & **Decision** & **Actual** \\ \hline \multicolumn{2}{c}{Y8} & & & & & \\ \hline A1\_2 & & & 0.2 & 0.2 & 1 & \\ \hline A2\_2 & & & 0.2 & 0.2 & & \\ \hline A3\_1 & & & & & & \\ \hline A4\_2 & 0.2 & 0.2 & 0.2 & 0.2 & 1 & 1 \\ \hline A5\_1 & & & & & & \\ \hline Sensitivity of & 0.2 & 0.2 & 0.2 & 1 & 1 & 1 \\ \hline Sensitivity of & & & & & & \\ \(\mathrm{Y_{8}}\) & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 7: Sensitivity of the logical situation Y8. \begin{table}
\begin{tabular}{c c c c} \hline  & **Y4** & **Y6** & **Y7** \\ \cline{2-4} Y8 & Event impacting the logical level & \(\mathrm{e_{8,4}}=\Delta\)(A1_2, A1_1) & \(\mathrm{e_{8,5}}=\Delta\)(A4_2, A4_1) & \(\mathrm{e_{8,6}}=\Delta\)(A2_2, A2_1) \\ \cline{2-4} Sensitivity of the event & \(\mathrm{S(e_{8,4})}=\left|\,2.6-1.6\,1\right|=1\) & \(\mathrm{S(e_{8,5})}=\left|\,2.6-1.4\,1\right|=1.2\) & \(\mathrm{S(e_{8,6})}=\left|\,2.6-2.6\,1\right|=0\) \\ \hline \end{tabular}
\end{table} 
Table 9: Sensitivities of events impacting the logical level for Y8. About the range A5_2, its occurrence leads to a violation of one of the TJC conditions, which is that the speed must be less than a maximum value of 60 km/h (Table 1).