# Evolutionary Game for Content Cache in a mm-Wave-Based Vehicular Fog
## 5 Experiments  
Based on the channel, antenna and road segmentation models for V2V communications discussed in Section 3, we evaluate networking performance of the vehicular fog in terms of connectivity between a transmitter and receiver vehicle (both are apart by 20 m). Simulation parameters are shown in Table 3. All vehicles are assumed to use 60 GHz frequency and 2 GHz bandwidth, and constant transmission power, 12 dBm. Free-space pathloss is applied with exponents for LOS and NLOS cases, 2 and 4, respectively. The maximum number of lanes is 20 for each left and right-side from an origin vehicle. For a directional antenna, we use the rectangular sectoral radiation model (elevation \(\pi/2\) and \(\gamma=0.2\)). Figure 6 shows connectivity with varying SINR required for target modulation and coding scheme (MCS) levels. The connectivity decreases exponentially as the required SINR increases like in a typical BER (bit error ratio)-SNR curve. According to vehicle density, the connectivity is different due to the degree of interference from neighbor vehicles. For example, as the density increases from \(\lambda=2\times 10^{-4}\) to \(9\times 10^{-4}\), connectivity decreases more than 20% as shown in Figure 5(a)-c. For the proportion of cached sectors \(k/S\), the connectivity is improved as the \(k/S\) increases regardless of the node density. Thus, we can conclude that content caches contribute to diversifying beam directions and reduces interference. However, the improvement becomes less as the proportion becomes higher from 0.2 to 0.7. The connectivity decreases almost exponentially by increasing vehicle density, especially when the \(k/S\) is small, 0.2 versus 0.5 or 0.7 as shown in Figure 7. Compared to the SINR threshold, the vehicle density is more critical to networking performance because of increasing interference. With more sectorization using narrow beam-width, inter-beam interference can be reduced. For example, six sectors in Figure 6(a) lead to around 55% connectivity while 12 sectors achieve 85% in Figure 6(c) when caching probability is \(k/S=0.5\) and vehicle density is \(\lambda=6\times 10^{-4}\). The degree of sectorization can enhance vehicle connectivity by increasing spatial diversity. In Figure 8, the connectivity increases as vehicles have a higher probability to avoid inter-beam interference with more sectors. In addition, more antenna gain can be acquired from narrow beam-width. For \(|k/S|=0.2\), the connectivity of two and four sectors are similar because both have only one cached sector and beam-forming gain is comparable. This connectivity gain from sectorization is notable especially with higher vehicle density as shown in Figure 7(a),c. However, the connectivity increment becomes saturated. For example of Figure 7(a), the connectivity increases almost 8% from 4 to 6 sectors, but only 2% from 6 to 8 sectors in case of \(k/S=0.5\). In other words, there is a limitation to increase diversity gain from sectorization at a given vehicle density. As we observed from the above experiments, the number of cached sectors affects the connectivity. Figure 9 shows connectivity with a varying number of cached sectors, \(k\) of total 12 sectors. The connectivity increases drastically especially in small \(k\), but slightly after a certain \(k\) value. For example, increment after \(k=4\) is negligible in case of SINR threshold \(T=4\) dB. For a higher SINR threshold, more cached sectors are useful for enhancing connectivity. Figure 6: Connectivity (\(P_{c}\)) versus signal-to-interference-plus-noise ratio (SINR) threshold (T) with S = 12 sectors. \(|\,\mathrm{k/S}\,|\,\) is a proportion of cached sectors over total sectors.