# Empirical Performance Models of MAC Protocols for Cooperative Platooning Applications
## 4 Empirical Models
### Platoon Size and Homogeneity, and Coherence between Rounds of Platoons  
We start by observing the relationship between the platoon size and homogeneity of platoon sizes on the number of RF neighbours (Figure 6). If platoon sizes are set to be heterogeneous (Figure 6a), we see a monotonically increasing relationship between the number of neighbours and platoon size. For the homogeneous platoon size (Figure 6b), this relationship shows two different behaviours for the CSMA/CA and PLEXE-slotted: We register an increase in the number of neighbours as the platoon size increases until seven vehicles/platoon, while for larger platoons, the reported number of neighbours decreases.  
\begin{table}
\begin{tabular}{l r} \hline \hline
**Parameter** & **Values** \\ \hline (Avg.) Platoon size & 2 to 10 cars/platoon \\ Number of platoons & 16 \\ Number of lanes & 1,2,3,4, 5 \\ Inter-vehicle gap & 5 m \\ Inter-platoon gap & \(\simeq\)28 m \\ Controller & CACC \\ Car length & 4 m \\ Speed & 100 km/h \\ \hline \hline \end{tabular}
\end{table}
Table 1: Scenario configurations.  
\begin{table}
\begin{tabular}{l r} \hline \hline
**Parameter** & **Values** \\ \hline PHY/MAC model & IEEE 802.11p/1609.4 only (CCH) \\ Path loss model & Free space (\(\alpha\) = 2.0) \\ Channel & 5.89 GHz \\ Bitrate & 6 Mbit/s \\ MSDU size & 200 B \\ Access category & \((AC\_VI)\) \\ Leader’s Tx power & 20 dBm \\ Follower’s Tx power & \([-10,\,-6.9,\,-3,\underline{0},\,3,\,4.7,\,6,\,7]\) dBm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical layer (PHY) and MAC parameters.  
We attribute this effect to the differences in the slot duration \(T_{\text{xwin}}\) between nearby platoons. In a scenario where all platoons have the same size, slot duration (in other words, frequency of transmission by platoon elements) is equal, and despite the random operation delays assigned to each platoon at the start of the simulations, some overlap of transmissions of different platoons may occur. As CSMA/CA and PLEXE-slotted are not able to adjust round duration, this overlap persists and is not resolved except partially by the CSMA/CA backoff mechanism. Thus we fall into a _critical instant_, or a period during which there is a susceptibility for many platoon pairs to experience small or null phase differences among their rounds simultaneously. We refer to this state of generalized and small-phase (or even null) coherence as _high coherence_ conditions. Critical instants (and high coherence) are typically transient and eventually wear out; however, in this particular case, they become persistent. Accordingly, we identify the existence of two system conditions in Figure 5(b) with respect to the platoon size: one of **high coherence** (platoon sizes larger than 7) and a second of **non-high coherence** (platoon sizes up to 7). If the neighbouring platoons have different sizes, as in the case of heterogeneous platoon sizes (Figure 5(a)), slot duration is also different and the likelihood of overlapping periodic transmissions decreases. RA-TDMAp, in turn, is capable of handling both scenarios equally well, not exhibiting the effects of high round coherence, given its capacity to slide the relative phases of the platoons transmissions to avoid/reduce mutual interference. In this case, the homogeneous scenario is even more favourable (i.e., reaches more neighbours for the same number of vehicles/platoon), since the phase adjustment is more effective when all slot have similar width.  
These results show that the number of RF neighbours, in the absence of high coherence conditions, also reveals the impact of both platoon size and its homogeneity.