# Investigating and Modeling of Cooperative Vehicle-to-Vehicle Safety Stopping Distance
## 4 Communication-Assisted Stopping Distance
### Theoretical Model for Consecutive Losses  
The following section outlines the main findings of the work, where the analysis is conducted as to multiple consecutive packet losses, and a model is designed and assessed to show impacts of consecutive losses. The losses we observed in our field tests, can be split into single losses or consecutive losses (burst losses). These types losses can occur due to circumstances, such as channel fluctuations, obstacles in the way, weather changes, or the hidden node problem. The use of UDP in our testbed means there is no acknowledgement of a packet being received, and this means that, if a packet is lost, the sender is not aware of this. UDP is the closest representation of a broadcast type communication used for CAMs/BSMs.  
We believe this assists in identifying the reliability requirements for DSRC and highlights the importance of maintaining highly reliable systems. We have also chosen to monitor this over different data rates to analyze impacts by the Inter Packet Gap (IPG). The IPG will be abbreviated to \(\mathrm{T_{PI}}\), which is the Packet Interval Time. The number of losses we chose to use will be shown later, but it will be stated that these losses are based upon real world field tests conducted.  
We developed a model that shows the theoretical loss on the stopping distance that consecutive packet losses could have. This model is based upon the field work for stopping distance, along with an equation that calculates the loss of stopping distance per packet, which includes the packet sending interval. Equation (4) shows the model formula, and Table  
time and packet interval would need to be included, which are used to represent the packet being received successfully, and this is shown in Equation (5).  
\[\begin{split} R_{\text{SD}}&=\Big{\{}(T_{E2E}V)+[\frac{W }{2 gC_{\text{ae}}}ln(1+\frac{C_{\text{ae}}V^{2}}{\eta_{\text{b}}\mu W+f_{r}cos \theta+Wsin\theta})]\Big{\}}\\ &\quad-\bigg{(}\Big{\{}V[PaL(T_{E2E}+T_{\text{PI}})]\Big{\}}+ \Big{[}V(T_{E2E}+T_{\text{PI}}+PT_{E2E})\Big{]}\bigg{)}.\end{split} \tag{5}\]  
We chose to use the second model as this paper is focused on the impacts of how packet loss can alter the stopping distance when relying on communications, and this equation highlights that impact. The model works by utilizing Equation (3) to find the normalized stopping distance for a vehicle and then we subtract the distance lost via consecutive losses. The losses can be seen in the second part of Equation (5). The result of this equation will leave us with the distance remaining to a collision or stopping distance remaining. We know that, after losing the consecutive packets, the vehicle will still need to stop in order to show the full distance required to stop, and the Equation (5) sign could switch. This would then represent the stopping distance, plus the distance lost through consecutive loss, to leave us with total stopping distance. In our case, we are showing how lead and following autonomous vehicles communicate, with the following vehicle adhering to a communication-assisted stopping distance. We then analyze how this stopping distance is impacted with the addition of consecutive packet loss, and this is shown for different speeds and data rates. For our results, we show the stopping distance when 0 packets are lost, and we then show how the stopping distance is reduced with each consecutive loss. This highlights how the reduction in reliability leads to reduced stopping distance and, hence, a higher chance of collisions with the lead vehicle. As the reduction value reaches 0, we deem this to be the point at which lead and follow vehicle will be occupying the same space or that a collision may have occurred. We also show a negative value, which would mean the follow vehicle has gone past the lead vehicle, and this would be classified as a collision; we show this to identify the impact of reliability.