## 5 Simulation Results
When \(\rho_{max}\) reaches 45, the number of vehicles saturates, as it has already reached the maximum number of vehicles that simultaneously occupied the emergency lane. The simulation results clearly indicate that the number of vehicles can be easily increased, however, increasing the \(\rho_{max}\) value increases the overall signalization traffic in the communication network and it could potentially increase the  
Figure 6: **(a)** The number of informed destination vehicles as a function of the maximum message rate, \(\rho_{max}\). **(b)** The minimum end-to-end delay as a function of the maximum message rate, \(\rho_{max}\). **(c)** The maximum end-to-end delay as a function of the maximum message rate, \(\rho_{max}\). All panels were obtained by simulating the Zilina scenario. To facilitate the identification of the overall trend in panels (**b**,**c**), we show the line obtained by the ordinary least squares regression method. end-to-end delays experienced by the PEEV-WS. In Figure 6b,c, we examine the minimum and the maximum end-to-end delay, i.e., the minimum and the maximum value of end-to-end delays across all PEEV-WS messages, as a function of \(\rho_{max}\). In both cases, we find an increasing trend, however, considering the required reaction time, the increase in the end-to-end delay is not substantial. To assess the system performance in the transport domain, the empirical reaction time available to drivers is evaluated. The available reaction time strongly depends on the distance between the EV and the involved vehicle at the time when the EV initiates the message transmission. Its value is naturally low for the vehicles close to the EV and it is different for every combination of transmission start time and vehicle positions. For this reason, we evaluate the system performance for individual vehicles considering the emergency scenarios Zilina and Bratislava. The delivery time of the first message can be found in Figure 7. The time of the delivery of the first message is the difference between the time when the first message was received and the time when the first message was sent. Please note, if some messages are not delivered, then the time of delivery does not coincide with the end-to-end delay of messages. If the distance between the EV and vehicle was less than 1000 m, the time of the first message delivery was negligible as in most cases one hop was sufficient. When more hops were needed the delivery time increased, nevertheless, it did not exceed 1.5 s, which is an acceptable value, considering the required reaction time. The three vehicles in Figure 7a with times of message delivery greater than 1 s, correspond to the cases when the first sent message did not reach the destination vehicle and the message was retransmitted during the following time interval. For simplicity reasons, the time needed to present the content of the received communication message to the driver and the time a driver needs to learn the message content was neglected as it can vary depending on the utilized human-machine interface implementation. Hence, the available reaction time depends on the distance from the EV to the vehicle at the time when the first message was delivered, on the relative speed of the vehicles, and on the action taken by the vehicle driver. To estimate the lower and the upper bound of the available reaction time, we assume two hypothetical options for how the situation could unfold after the driver receives the first message informing about the approaching EV. The first option is when the driver immediately stops the vehicle on the roadside not to be in the way of the EV (as it is currently required by the Slovak legislation). The second option is when the vehicle changes lane and EV, as well as the vehicle, continue without changing speed. In both cases, we can easily estimate the time when the EV will reach the vehicle and hence estimate the available reaction time.