# Evolutionary Game for Content Cache in a mm-Wave-Based Vehicular Fog
## 1 Introduction  
A fleet of the self-driving vehicles will form vehicular cloud or fog at a road in the near future, where they cooperate for safe driving and infotainment by sharing the limited computing resources. Autonomous driving requires rich sensor data not only collected from own equipped sensors such as LiDAR, near-medium range radar, long-range radar (LRR) and dash-cams, but also from other vehicles nearby through vehicle-to-everything (V2X) communication. The rich sensor data like high-resolution video (e.g., UHD 4K) from dash-cams or LiDAR can enhance control precision; road curvature can be recognized from 30 m advance if using a 2 MP (Mega Pixel) image while 50 m with a 0.3 MP image [1]. To deliver various and large data in the vehicular fog, the legacy V2X communication based on dedicated short-range communication (DSRC) and IEEE 802.11p is not suitable because of low data rate with insufficient bandwidth, up to 6-27 Mbps for safety and infotainment. Therefore, 5G community is now developing V2X communication using mm-Wave frequency bands, and are rushing to standardize in global standardization organizations such as ITU, 3 GPP, etc. The 3 GPP already studied and released a channel model of a side link for V2X communication in the release 15 [2], which includes sub-6 GHz band (FR1) and mm-Waves (FR2) together with features for Non-Line-of-Sight (NLOS) state. This mm-Wave V2X communication can increase data rate using a LOS link between vehicles and offload networks. Unfortunately, the mm-Wave link has low diffraction, poor penetration and high pathloss due to its frequency characteristics, which leads vehicles to adopt a directional antenna for beam-forming gain. Previous studies on the mm-Wave V2X communication have mainly focused on modeling the characteristics of V2X channels and aligning mm-Wave beams between moving vehicles. In dense vehicular fog, however, inter-beam interference is critical due to uncoordinated beams. [PERSON] et al. (2018) showed that interference from the adjacent lanes significantly degrade performance especially when highly directional antennas are used. For this, [PERSON] et al. (2018) proposed a multi-channel assignment for mm-Wave beams to reduce the inter-beam interference in the dense vehicular fog. [PERSON] et al. (2018) introduced deep learning-based beam management to reduce interference between beams. In this paper, we propose a content distribution technique to reduce the inter-beam interference in the vehicular fog. Within the vehicular fog, data contents are queried and delivered using information centric networking (ICN) technology ([PERSON] and [PERSON], 2018). Conventional host-centric networking can suffer from excessive routing procedures to recover connectivity from frequent disconnections caused by high vehicle mobility. The ICN allows vehicles to broadcast interest messages for contents nearby and to receive them using an intermittent mm-Wave link. For this, the ICN encourages vehicles to cache popular content in local storage in order to diversify content locations and reduce delivery latency. This cache distribution leads to diversification of V2V communication paths in the vehicular fog. Otherwise, \(n\) network flows for a certain content have to share for a same route and its links. Therefore, the cache distribution can reduce required link capacity from \(O(\sqrt{n})\) to \(O(1)\). Furthermore, the spatial division of the mm-Wave beams is increased as vehicles form beams toward different directions. As shown in Figure 1, the inter-beam interference can be avoided as two caches on vehicle C and D diversify beams from vehicle A and B for the same video content. To improve the efficiency of content cache, contents can be encoded by source coding techniques such as LT ([PERSON], 2018), Raptor (2018), etc and stored evenly in multiple vehicle caches, which can remove duplication and complexity of transmission schedule.