# Investigating and Modeling of Cooperative Vehicle-to-Vehicle Safety Stopping Distance
## 6 Simulation of Density Losses
### Density-Based Losses  
In this section, we use a simulation to monitor packet losses when considering multiple nodes in a 3-lane highway environment. We assume to eliminate the opposite flowing traffic with the use of location-based broadcast, which is the preferred method for Cooperative Collision Avoidance (CCA) [47]. Our initial calculation is to approximate the number of nodes within broadcast communication range. We choose to incorporate the use of Automatic Gain Control (AGC), which is used to alter the gain depending on the speed being traveled. Lower gains can be used at lower speeds to have a smaller communication range. The first step of this is to identify the communication range, which will be known as the safety distance. The safety distance is approximately the same as the reaction time for a human driver or DSRC/Advanced Driver Assistance Systems (ADAS) device, which, as we have mentioned, is approximately 1.5 s without the DSRC testbed and 2.92 ms with the testbed. For the consideration of safety distance, we do not use the separate measurement of braking distance. As we described previously, stopping distance is the combination of braking distance and reaction distance. In this scenario, reaction distance is essentially the safety distance, and we are calculating the minimum required gap between vehicles depending on the speed being traveled. When using a full ADAS system, an adequate approach must be made for the calculation of braking distance because, without this chain reaction, accidents would be prevalent. This is merely a simulation to represent an example for the safety distance with communication and the impacts of node density. It can be shown that the distance traveled in the reaction time (Safety Distance or \(D_{\text{s}}\)) is directly affected by: the time taken for a reaction to be made by the driver (\(T_{\text{R}}\)) and the acceleration of the vehicle being driven (\(a\)). This can be shown in Equation (6) as:  
\[D_{\text{s}}=a*T_{\text{R}}. \tag{6}\]  
In the case of the testbed reaction time, we must also consider a delay within the system due to the processing of the information and the mechanical delay of activatingthe brakes. We will assume this to be equal across all acceleration speeds and have set this value as 0.25 s, and it will be specified as Reaction Processing Time (\(T_{\text{RP}}\)). This is shown for human driver in Equation (7) and ADAS in Equation (8). \[D_{\text{s,h}}=a*T_{\text{R}}, \tag{7}\]  
\[D_{\text{s,a}}=a*(T_{\text{R}}+T_{\text{RP}}). \tag{8}\]  
The difference between the two safety distances according the traveling speed can be shown and in addition, we also show the results of various stopping distance algorithms. These algorithms will be the Mazda Algorithm [18], the Stop Distance Algorithm (SDA) [18], and a more recent variant, known as the PATH (Berkeley) Algorithm [18; 27; 48]. The PATH algorithm is a modified version of the Mazda algorithm and is used to show safety distance calculation or critical warning distance. In order to show the various algorithms, the deceleration of a vehicle is assumed to be at maximum for both following and leading vehicle. This is taken from a study conducted into various vehicles [48; 49], and, for our interpretation, the deceleration rate for a standard Petrol car is used. This can also be calculated using a deceleration formula and the initial calculated braking distance without the use of Reaction time. Deceleration (\(\dot{a}\)) can be calculated in two different methods: with \(S_{\text{f}}\) representing final speed, and \(S_{\text{i}}\) representing initial speed, \(t\) denotes time, and \(d\) is distance. \[\dot{a}=(\frac{S_{\text{f}}-S_{\text{i}}}{t}), \tag{9}\]  
\[\dot{a}=(\frac{S_{\text{f}}^{2}-S_{\text{i}}{}^{2}}{2d}). \tag{10}\]  
For this scenario, Equation (10) is used as the braking distance has already been calculated. The deceleration will then be modeled to represent the rate of deceleration (\(\dot{a}_{\text{R}}\)). This is taken from a work by [PERSON] et al.