## 4 Experimental Results  
As mentioned previously, this study aims to quantify the relationship between speed limit adherence within different population sizes and the subsequent impact on collisions. The experiments will conduct multiple model execution scenarios under nine conditions, refer to Table 3. The goal is to quantitatively identify the best and worst-case scenarios concerning the number of collisions in an urban street network. More specifically, low, mid and full adherence to speed limits will be compared across low, mid and high traffic density (number of vehicles); these are identified as the independent variables, while the dependent variable is the number of collisions. All other parameters will remain constant  
Figure 3: Urban Street Network of Morley, UK (data source: [64]). to ensure a heterogeneous population of vehicles across all experiments. The model is still in its infancy and can be thought of as a proof of concept. Thus, factors such as weather and time of day have not yet been implemented but will be considered for future extensions. The main variables of interest at this current time for this study are adherence to speed limit, vehicle density and collisions. As described in the background section, the relationship between collision rate and traffic density has been theorised but not empirically verified. Since collisions in the real world can be caused by many factors, we will focus on collisions caused by speeding. Our question is: do higher traffic densities suppress the higher collision rates caused by speeding in an urban environment? Each experiment ran five times with different random seeds for five minutes due to the computational demand required to render 3D agents. Final collision values were averaged across runs and normalised by the number of vehicles, with the standard deviation displayed in the error bars. The results are shown in Figure 4.  
Firstly, it is important to note the size of the error. While some variance in model runs is expected, the extent of the overlap between scenarios makes drawing firm conclusions from these experimental results difficult. However, in future studies, this will be taken into account. While keeping account of this variance, it is still clear that there is a greater difference in collision rates between 50 and 100 vehicles than between 100 and 200. This suggests that there exists a critical density at which the number of collisions begins to scale linearly with traffic density; prior to this critical point, an increase in vehicles results in a disproportion  
Figure 4: Number of collisions (normalised by number of vehicles) against the percentage of non-adherence to speed limits, refer to Supplementary Materials for data used. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Independent Variable Measure** & **Low Adherence** & **Mid Adherence** & **High Adherence** \\ \hline Low traffic density & 50 vehicles (25\%) and & 50 vehicles (25\%) and & 50 vehicles (25\%) and \\  & 15 adherence (30\%) & 30 adherence (60\%) & 50 adherence (100\%) \\ \hline Mid traffic density & 100 vehicles (50\%) and & 100 vehicles (50\%) and & 100 vehicles (50\%) and \\  & 30 adherence (30\%) & 60 adherence (60\%) & 100 adherence (100\%) \\ \hline High traffic density & 200 vehicles (100\%) and & 200 vehicles (100\%) and & 200 vehicles (100\%) and \\  & 60 adherence (30\%) & 120 adherence (60\%) & 200 adherence (100\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiment conditions. ately large increase in collisions. Similar patterns were found in empirical data collected in the subsequent studies [7; 8; 9]. In Figure 4, we see little evidence of reduction (either proportional or absolute) in the number of collisions as traffic density increases. Higher traffic density also does not appear to suppress the effects of low-speed limit adherence on collisions. As can be seen from the trend lines in Figure 4, collisions increase at a near-identical rate as a function of the percentage of non-adherence.