# The Impact of Spoofing Attacks in Connected Autonomous Vehicles under Traffic Congestion Conditions
## 4 Evaluation
### Effects of Spoofing Attack  
The effects of the spoofing attack on the platoon's movement are shown in the following experiments, in which speed and acceleration are compared against the two limit values of vehicle density: 10 and 25 vehicles/km. In Figures 5-8, acceleration and velocity are displayed for a platoon of vehicles with size 10. Figure 4: At the next crossroads, the vehicles from the node “Node 2” (in blue) and below are dynamically separated from the influence of the Victim node “Node 1” (in red) and continue their course on an alternative route. The green shows the notification of nodes in serial mode for “Change Route()”. Figure 5: Speed of platoon of vehicles in normal scenario. Moreover, in Figures 9-12, acceleration and velocity are displayed for a platoon of vehicles with size 25. The majority of published papers use _driving volatility measures_ as the dominant safety measure to assess CAV behavior variation [20]. All variations in CAV behaviors, that is, sharp fluctuations in movement factors such as acceleration, deceleration, and speed, are expressed through volatility. The term _volatility_ expresses a trade-off between security risks  
Figure 8: Acceleration of platoon of vehicles in spoofing attack scenario with a density of 10 vehicles/km. Figure 6: Speed of platoon of vehicles in spoofing attack scenario with a density of 10 vehicles/km. Figure 7: Acceleration of platoon of vehicles in normal scenario. and lower comfort. Hence, the volatility metric is a prior indicator for a future potential crash. A measure of volatility based on [8] is \(CoV\), which is given by the ratio of the standard deviation of the vector of the acceleration or the speed to the mean of the same vector showing relative dispersion in Equation (1). \[CoV=\frac{S.D}{\hat{g}} \tag{1}\]  
where standard deviation is represented by \(S.D\) and speed and acceleration-deceleration mean is represented by \(\hat{g}\). Conducting statistical analysis of the above results, according to 120 s in total observations (i.e., every 1 s of the total 120 s of the simulation time), we observe the \(CoV\) values for acceleration within the range values of \(10,15,20,25\) vehicles/km in Table 2 and the \(CoV\) values for the speed within the same range values in Table 3. The main conclusion we draw regarding the _volatility_ based metric is that, under the spoofing attack, the speed's \(CoV\) increases by about 12.1%, as well as the absolute value of the acceleration \(CoV\), but to a lesser extent. This is because, during the spoofing attack, the victim-vehicle and those behind it slow down sharply, resulting in a negative average acceleration value, and variations in the deceleration values were considerably higher as compared to the acceleration values. This also indicates increased risk of rear-end collisions. Finally, below these vehicle range values, the coefficients remain constant, which is due to this range being quite limited. Figure 10: Speed of platoon of vehicles in spoofing attack scenario with a density of 25 vehicles/km. Figure 9: Speed of platoon of vehicles with 25 vehicles/km in normal scenario. Figure 13 illustrates the comparison of the mean value of PDR for all the vehicles present in the area in the range of values defined in Table 1. It also shows the average total distance traveled by each vehicle during the simulation on a logarithmic scale, because the difference between normal scenario and spoofing attack scenario was quite large. We observe that both PDR and total distance distribution approximate an exponential distribution with a very small parameter. Similarly, the same parameter's distributions (PDR and the total distance) for the case of the spoofing attack we have implemented approach the cumulative distribution function (CDF) of an exponential distribution with a very small parameter. Therefore, the spoofing attack results in all vehicles traveling shorter