## 2 Related Work
### Full Course Yellow Phases  
A regular yellow flag indicates minor danger in a sector of the race track, for example, a slow car. The effect on the race is negligible. Full course yellow phases indicate a significant danger and therefore have a bigger impact. They limit the speed of the drivers, which increases the lap times. In Formula 1, FCY phases are differentiated into virtual safety car (VSC) and safety car (SC) phases. The race control decides, depending on the danger for the race participants and marshals, which variant is deployed. A VSC prescribes a minimum lap time \(t_{\text{lap,vsc}}\) for every driver. Figure 4 indicates, that \(t_{\text{lap,vsc}}\) is about 140% of the fastest unaffected lap time of a race \(t_{\text{lap,min}}\). Since every driver has to keep to it immediately, the time intervals between the drivers remain more or less constant. During an SC phase, drivers must also reduce their speed, similar to a VSC phase. Additionally, a physical car drives out of the pit lane onto the race track in front of the race leader. It drives much slower than the race cars and must not be overtaken. Therefore, it increases the lap times further to \(t_{\text{lap,sc}}\approx 1.6\cdot t_{\text{lap,min}}\) as soon as the drivers reach it on the track, cp. Figure 4. As a result, the gaps between the drivers vanish. A crucial element for race strategy is that the relative time loss for driving through the pit lane is significantly reduced during VSC and SC phases since it depends on how long it takes to pass the pit lane on the race track in comparison to driving through it. Under SC or VSC conditions, the cars drive slower on the track while driving through the pit lane is always speed limited and, therefore, not affected. It can be seen in Figure 4 that the lap times vary considerably during SC and VSC phases. Therefore, when calculating the average lap time increases mentioned in the previous paragraph, we apply the following criteria in order to consider only representative lap times. For SC phases, we use those laps in which the SC has already been on track for more than 1.5 laps before the lap and which are not the last lap of the phase. For VSC phases, the lap must be fully covered by the phase. Generally, only the lap times of the drivers on positions 1-3 are used. The values are averaged over all seasons 2014-2019. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Driver** & **Team** & **Accidents** & **Failures** \\ \hline [PERSON] & Mercedes & 0 & 0 \\ [PERSON] & Mercedes & 1 & 1 \\ [PERSON] & Ferrari & 1 & 2 \\ [PERSON] & Ferrari & 2 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of accidents and (technical) failures for the drivers of Mercedes and Ferrari in the 2019 season (data from [10]). [PERSON] [7] models an SC by increasing the lap time of every driver for five laps by 20%. [PERSON] [5] simulates SC phases for six laps. He distinguishes between run-up phase (20% lap time increase) and following phase (40% lap time increase). Additionally, he reduces tire wear during an SC phase. [PERSON] [6] is the only author distinguishing between VSC and SC phases. The VSC is modeled by a lap time increase of 20%. The SC implementation is similar to [PERSON] [5] except for the reduced tire wear, which is neglected. However, [PERSON] [6] takes into account the reduced time loss of pit stops during FCY phases \(t_{\text{pit,in-lap/out-lap,fcy}}\):  
\[t_{\text{pit,in-lap/out-lap,fcy}}=0.5\cdot t_{\text{pit,in-lap/out-lap}}. \tag{9}\]  
When comparing the implementations in the literature with reality, it becomes clear that several aspects are not modeled accurately. Firstly, FCY phases in the presented approaches always start and end exactly on a completed lap, which is not the case in reality. Secondly, in reality, VSC and SC always appear at the same point in race time \(t_{\text{race}}\) for every driver, which is different from appearing at certain race progress, especially if some slower drivers are lapped during the race.