# Autonomous Controller-Aware Scheduling of Intra-Platoon V2V Communications
## 6 Numerical Results  
The proposed heuristic approach has been evaluated in numerical simulations using MATLAB, as it allows us to abstract the communication layer and separate it from the platoon control model. These were performed according to the model described in Section 3. We assumed a platoon of six vehicles moving on a straight road section with an initial velocity of 20 m/s and a desired inter-vehicle spacing \(d_{d}\) of 3 m, with the leader changing its acceleration according to the disturbance process \(z(t)\). The acceleration disturbance \(z(t)\) has been modeled as a random process, where the disturbance is applied with an inter-arrival time being an exponentially distributed random variable, and the amplitude of \(z(t)\) being a uniformly distributed random variable in an interval \([z_{min},z_{max}]\). Figure 5 shows an example of the changes of a leader's acceleration over a single simulation run duration. Each platoon vehicle broadcasted its motion parameters (position, velocity, and acceleration) periodically, with the interval being selected according to one of the following two transmission policies:  
* Fixed periodic transmission--each vehicle broadcasts messages with the same pre-selected interval for the whole simulation duration. * Adaptive transmission period--the time interval between subsequent transmissions is selected dynamically according to the heuristic algorithm, with hysteresis assuming a memory size of \(r\). The main simulation parameters are summarized in Table 1.  
The different configurations of intra-platoon messaging have been compared in terms of the total use of resources, being understood as the average number of intra-platoon transmissions per simulation run, as well as in terms of the fraction of emergency braking distance violations observed on average per simulation run (as defined on the left-hand side of the inequality (8)). Figure 5: Example of leader acceleration changes (based on \(z_{3}\) random variable) in a simulation run. Figures 6 and 7 present the average use of resources (number of transmissions) and the fraction of emergency braking distance violations per simulation run, respectively, vs. different average inter-arrivals of the acceleration disturbance \(z(t)\). We have compared the proposed heuristic adaptive approach with the different memory depth used in hysteresis (\(r=\{0,200,500,1000\}\) ms), and the conventional approach using fixed messaging interval, with the period ranging from 200 ms to 1 s, representing different resources consumption scenarios. As expected, the best performance in terms of the avoidance of emergency braking activation is achieved with very frequent transmissions, assuming fixed intervals of 200 or 300 ms. However, these scenarios represent a greedy approach on the resources, where over 10,000 transmissions are performed per simulation run. On the other hand, transmission with a fixed low periodicity that is close to 1 s results in frequent emergency braking activation (up to over 15% of simulation time), simply meaning that the controller fails to achieve safe platoon operation. However, when applying an adaptive approach following the proposed heuristic approach, a performance that is similar to frequent fixed interval transmission can be achieved in terms of the avoidance of emergency braking, while using far fewer resources. For the adaptive configuration without hysteresis (\(r=0\) ms) hardly any emergency braking is observed, while the use of resources is comparable with fixed interval transmission using a 600 ms period. When applying the hysteresis approach, that which is intended to provide even higher robustness, one can notice the actual fraction of emergency braking activation slightly increases compared with the approach without memory, indicating that a conservative approach, relying on selecting rather more frequent transmissions, results in a lower stability of platoon control.