# Empirical Performance Models of MAC Protocols for Cooperative Platooning Applications
## 4 Empirical Models
### Discussion  
The results shown in the previous sections show that, as the selected parameters are changed, different but consistent behaviours of the target metrics may occur. The main takeaways are:  
* **Homogeneous platoon sizes can lead to degradation:** Situations of similar slot duration and small phase differences between rounds of disparate platoons can lead to a high collision rate and decrease of the known neighbourhood, specifically for protocols without round adaptation.
* **Sets of large platoons experience more collisions:** Increasing the platoon size in a convoy of platoons increases the number of messages in each round, and thus leads to more collisions and a busy time ratio. No new nodes are discovered if neighbours can be found up to the communication range.
* **High power can contribute to collision reduction:** Increasing the transmit power of followers increases spatial coverage, thus causing more neighbours to become known and more collisions up to a tipping point, after which we observed a reduction in the rate of collisions due to the inferior occurrences of uncoordinated medium accesses. This effect was also verified with the leader messages when varying the followers transmit power.
* **More lanes introduce new neighbours only up to a point:** Rearranging the platoons over more parallel lanes brings an immediate increase in the number of neighbours by spatially deploying new platoons side-by-side to existing ones. Our results reveal that this effect wears out as the number of lanes increases.
* **Protocol performance:** In all the experimented scenarios, RA-TDMAp consistently showed a smoother behaviour and no susceptibility to conditions of high coherence, leading to better fitting, with significantly lower MSE than the other protocols. Between CSMA/CA and PLEXE-slotted, the latter had, generally, lower MSE thus better fittings. The exception is the variation of the transmit power, in which case, the fitting for CSMA/CA was better (Table 3).  
In order to explore the existence of a universal model of the rate of collisions and busy time ratio with respect to the number of RF neighbours, we consolidated the data from all scenarios in Figure 12a,b, respectively. In the first case, we observe that the data points relating to varying number of lanes and varying transmit power do present an alignment along a bell-shaped curve. This alignment indicates that both factors influence the number of RF neighbours and the rate of collisions in the same way, and may indicate a universal relationship between the average rate of collisions and the number of RF neighbours. For this reason, we aggregated the data sets relating to a varying number of lanes and transmit power, and fitted a single curve to produce a common and generic model (bell-shaped curves in Figure 12a).  
The platoon size presents a different effect than that of the number of lanes and transmit power: The rate at which the number of RF neighbours increases is inferior, and yet collisions also grow as there are considerably more packets in the air (due to the smaller slot duration). Being different phenomena, the collision curve due to increasing platoon sizes does not fit the trend that occurs when increasing number of lanes and transmit power. We hypothesize that the bell-shaped curve of the rate of collisions drawn for the number of lanes and transmit power can be parameterized to the platoon size as an offset (e.g., \(C(N)=C+g(N)\)).  
The busy time ratio shows a very clear logarithmic and almost linear relationship with the number of RF neighbours. Again, the points concerning the platoon size scenario deviate from those of the number of lanes and transmit power scenarios, as different phenomena are involved. However, the deviation is, in this case, small, supporting a universal model to estimate the busy time ratio as a function of the number of RF neighbours, only.