# Investigating and Modeling of Cooperative Vehicle-to-Vehicle Safety Stopping Distance
## 6 Simulation of Density Losses
### Node Density Simulation  
With the safety distance calculated, the number of nodes in range can now be predicted for each traveling speed. This will be based upon the calculated safety distance and 5 m set as a car length. Due to the use of omnidirectional antennas, it is known the radiation pattern is a circle with the center point being the antenna. To communicate to vehicle of interest, the radius will be the safety distance plus one full car length. As this is a circle pattern, the diameter is simply shown Equation (15). However, we also know that a vehicle is approximately 5 m, and a centrally placed antenna would limit the circumference; to compensate, we add an additional 5 m to the diameter to represent the vehicle of interest, shown as \(V_{\mathrm{L}}\). This equation will only be applicable in our simulation as we are only considering average  
Figure 12: Safety distance variations. vehicle sizes, and, to more appropriately represent other vehicles, such as a bus or lorry, a custom radius distance would be applicable. \[d=(r*2)+V_{\text{L}}\,. \tag{15}\]  
With the diameter calculated from the safety distance, we can now predict the number of nodes within this diameter. For example, at 30 mph and using the PATH, safety distance of 20.2 m is 45.4 m. We then calculate how many nodes will be present in the communication range. This can be simplified down to number of cars per lane, safety distance per car, and the number of lanes to give an approximate minimum value. For our number of nodes, we consider all vehicles maintaining the 20.2-m spacing, with an approximate length of 5 m per vehicle. Therefore, in one lane of traffic, two nodes will be within range. This will be then multiplied by number of lanes, leading to the classification that 9 nodes will be within range, including the central node. This is, however, the best-case scenario; a worst-case scenario would be that the minimum safety distance is not adhered to, and cars could be packed tightly together. This leads to 11 cars per lane being within communication range, which results in a total of 33 at 30 mph. This is shown in Equation (16) for best case and Equation (17) for maximum nodes, where \(d\) represents diameter of communication, \(r\) represents radius of communication, \(L\) is used to show number of lanes, and \(d_{\text{c}}\) shows length of vehicle. \[Nodes_{\text{avg}}=((d/(r+d_{\text{c}}))+1)*L, \tag{16}\]  
\[Nodes_{\text{max}}=(d/d_{\text{c}})*L. \tag{17}\]  
Figure 13 shows the result of the node calculation, and it shows that the ADAS has a vastly reduced number of nodes in communication range due to the reduction in reaction time compared to that of all human reaction-based analysis. As mentioned, PATH and human reaction are identical and so will be treated as the same for the simulation; this can also be seen in Figure 13. The worst performing is the general guidance given by the highway code, and we can deem this to be because it is rather a guideline than an effective algorithm. It should also be noted that the human reactions are not due to the emerging situation but rather the reaction to the ADAS warnings provided by DSRC, whereas the ADAS reaction is a reaction based on automatic braking provided by DSRC. The figure also shows the losses scale by miles per hour with changes only occurring in incremental steps. This is a highly useful finding for the use of automatic gain control, as the diameter would be kept identical until a threshold to change to the next limit. As the number of nodes are now calculated for each speed, a simulation can be performed to find consecutive losses. The simulation has been conducted using MATLAB and is a representation of communication between DSRC nodes competing for channel  
Figure 13: Node density. access. The simulations have been performed with varying numbers of communicating nodes to represent the number of nodes in communication range for each traveling speed.