## 4 Methods
### Upgrading the Formerly Developed Safety Indicators  
In the developed modeling framework, traffic safety can be characterized using additional methods and indicators. In this subsection, we present the further development of our previous indicators (\(\overline{VN}\), \(\sigma_{VN}\)) and the development of a new safety assessment concept (\(CF\)). It should be noted that during the evaluation of the numerical examples, we also applied the previously introduced \(CM\) and \(\sigma_{VV}\) indicators in their unchanged form. The network level average speed (\(\overline{VN}\)) was calculated as the mean, and the inhomogeneity of speed values (\(\sigma_{VN}\)) was calculated as the empirical standard deviation of the average speeds of vehicles in the network [47]. With a different approach, similar values can be expressed based on the speed data of all vehicles in the consecutive time steps over the investigated time interval. By applying the instantaneous speed values, the distance travelled by the vehicles in the network and the length of time spent there can be taken into account. As a result, the individual vehicles are not considered with the same weight and the estimation can be made more precise. Based on the above presented considerations, the modified formulas of \(\overline{VN}\) and \(\sigma_{VN}\) are presented in Equations (7) and (8). Notation \(orig(k)\) and \(dest(k)\) indicate the origin and destination locations of vehicle \(k\) assigned from matrices \(\textbf{ORIG}\in R^{m\times o}\) and \(\textbf{DEST}\in R^{m\times o}\), respectively. \[\overline{VN}=\frac{\sum_{k,j,l,d=1}^{m,(t-1),\rho,o}x_{k,j,i}*x_{k,j+1,i}*d_{ i,q}}{\sum_{k=1}^{m}\left(t-1-\sum_{j=1}^{(t-1)}x_{k,j,dest(k)}-\sum_{j=1}^{(t-1)}x_{ k,j+1,orig(k)}\right)} \tag{7}\]  
That is, the lengths of the road sections that each vehicle travelled was added in the numerator. Then it was divided by a sum that added the number of time steps elapsed between the start of each vehicle from its origin and the arrival to its destination. To determine the correct number of the considered time steps, the sum of time steps spent in the origin location, and the sum of time steps spent in the destination location were subtracted from the total number of the investigated (\(t-1\)) time steps inside the summation. In this way, the average speed at the network level was undefined if none of the vehicles left its origin location for the entire investigated timeframe. A lower value of indicator \(\overline{VN}\) implies a safer flow of traffic in the case of equally efficient transport management processes by the lower average speeds of the vehicles. The indicator \(\sigma_{VN}\) characterized the level of safety based on the differences in the speed data of the vehicles in the different time steps. \[\sigma_{VN}=\sqrt{\frac{\sum_{k,j,i,q=1}^{m,(t-1),\rho,o}\left(x_{k,j,i}*x_{k, j+1,q}*d_{i,q}-\overline{VN}\right)^{2}}{x_{k,j,i}=1}}\] \[x_{k,j+1,q}=1\] \[x_{k,j,dest(k)}\
eq 1\] \[\frac{x_{k,j+1\,orig(k)}\
eq 1}{\sum_{k=1}^{m}\left(t-1-\sum_{j=1}^{(t -1)}x_{k,j,dest(k)}-\sum_{j=1}^{(t-1)}x_{k,j+1,orig(k)}\right)} \tag{8}\]  
While using the regular formula of standard deviation, the time steps spent in the origin/destination locations were excluded (only the active vehicles were considered). The indicator refers to the similarity of the speed data of the different vehicles over the considered time steps. Thus, a lower value of indicator \(\sigma_{VN}\) implies a safer flow of traffic due to a smaller difference between the speed data of the individual vehicles. As a new method for determining road safety in the autonomous transport system, we propose the investigation of close following vehicle manoeuvres on the network. According to the concept of the developed binary integer model, it was allowed for a vehicle to arrive at a location that was left by another vehicle at the same time step.