# Resolving Persistent Packet Collisions through Broadcast Feedback in Cellular V2X Communication +
## 4 Consecutive Error Prevention Performance: Evaluation
### Number of Packet Collisions  
Figure 9a shows the number of collision events. Again, the y-axis is in log scale. As can be predicted, the number of collision events in the SPS + alternating scheme is orders of magnitudes higher than in SPS and SPS + colFeedback, as it fragments an SPS collision event into multiple single-packet collisions. In contrast, the SPS + colFeedback scheme is generally comparable to the original SPS because it modifies only the length of the event by terminating it through a prompt reselection. However, it is visibly higher than in SPS for the highest traffic density, \(\rho=250\). This is because resource reselections performed upon collision events increase the unpredictability for SPS [8], hence increased collisions especially for the high traffic density. However, when the traffic density is low, it has a positive effect of decreasing the overall number of collision events thanks to fast reselections away from the collision resources, which can more evenly spread the packet transmissions across the resource plane. Figure 9b sums up Figures 8 and 9a. It shows the total number of collided packets, which is the product of the number of collision events and the number of individual collisions in each event. Notice that the SPS + alternating scheme does not reduce the number of collisions compared to SPS, but increases it. It is because the scheme selects two resources upon reselection, which can be easily shown to increase the collision probability. Recollect that in SPS, a packet collision event mostly takes place when two (or more) vehicles re-select the frequency resource almost at the same time because otherwise, vehicles know the resources that neighboring vehicles will use through the chain reservation using the RRI field in the received SCI. Two (or more vehicles) finishing using the current frequency resource and concurrently re-selecting a new resource do not notify each other about their resource choice for the next run. Thus, they may select the same resource, i.e., a resource collision. As the SPS resource selection procedure, common to both methods (SPS, SPS + alternating), randomly selects the next resource from the 20% (in LTE [11]; configurable in NR [2]) of the least utilized resources in the selection window, one can easily derive the collision probability of SPS and SPS + alternating. Assume for simplicity that there are \(r\) resources in the same selection window that \(v\) (\(\geq\) 2) vehicles reselect their  
Figure 9: Performance comparison: (**a**) number of consecutive collision events; (**b**) number of individual collisions, y-axis in log scale. next resource from. In SPS, the probability that there is a collision in a resource that a vehicle selects is given in Equation (9). \[P_{col}^{(SPS)}=1-\left(1-\frac{1}{r}\right)^{v-1} \tag{9}\]  
In SPS + alternating, the probability that there is a collision in at least one of the two selected resources is given as in Equation (10) and it is larger than the native SPS collision probability. \[P_{col}^{(SPS+alt)}=1-\left(1-\frac{1}{r}\right)^{v}\left(1-\frac{2}{r}\right) ^{v-1}>P_{col}^{(SPS)} \tag{10}\]  
Figure 10 exemplifies how SPS + alternating increases the collision probability with some selected values of \(r\) and \(v\). In essence, the probability of a vehicle selecting a resource that other vehicles may have selected increases. Although it may help mitigate the long invisibility problem due to persistent collision, it is at the cost of the increased packet collisions. In contrast, Figure 9b shows that the SPS + colFeedback scheme has more than an order of magnitude smaller number of collided packets than SPS. This is because the number of colliding packets is reduced from \(\mathbb{E}[min\{l_{1},\ l_{2}\}]\) = 27.78 packets (Equation (6)) to less than two packets per event (Figure 8). In summary, the collision feedback scheme successfully solves the persistent collision problem, while decimating the absolute number of collided packets.