## 3 System Model
### ADP Weighted MV-MOS Model  
In summary, the multiple bitrate video distribution strategy is that if the video requested by the vehicle user has been pre-cached in the MECS, the video file with the highest bitrate within the MECS will be sent to the vehicle user directly. Otherwise, VUs request the lowest bitrate replicas of videos via the MBS. The intelligent caching in IoV problem aims to maximize vehicle users' QoE. The MV-MOS is a mobile video experience metric at the device level, it has been widely used in the QoE evaluation of mobile video, e.g., [33; 34; 38]), so it is expressed as  
\[f_{MOS}\left(\ell_{j},\mathcal{R}_{\ell_{j}}\right)=Mv\Big{(}\ell_{j};\mathcal{ R}_{\ell_{j}}\Big{)}. \tag{26}\]  
where \(Mv\Big{(}\ell_{j},\mathcal{R}_{\ell_{j}}\Big{)}\) is required data transmission rate, \(\ell_{j}\) is the video definition level, and \(\mathcal{R}_{\ell_{j}}\) is the minimum bitrate requirement corresponding to the video definition level \(\ell_{j}\). Then mobile video mean opinion score for the vehicle user to obtain the video from the MECS at the time \(t_{y,z}^{x}\) is calculated as  
\[Q_{MEC}\left(t_{y,z}^{x}\right)=\sum_{i\in I}\sum_{j\in L}x_{f_{j},\ell_{j}} \left(t_{y}^{x}\right)P_{F}^{x}(f_{i})f_{MOS}\left(\ell_{j},\mathcal{R}_{MEC} \left(t_{y,z}^{x}\right)\right). \tag{27}\]Hence, mobile video mean opinion score for the vehicle user to obtain a video from MBS at time slot \(t_{y,z}^{x}\) can be expressed as  
\[Q_{BH}\Big{(}t_{y,z}^{x}\Big{)}=\sum_{i\in F}\Bigl{(}1-\chi_{f_{i}}\left(t_{y}^{x} \right)\Bigr{)}P_{\mathcal{F}}^{x}(f_{i})\max_{j\in L}f_{MOS}\left(\ell_{j}, \mathcal{R}_{BH}\left(t_{y,z}^{x}\right)\right). \tag{28}\]  
When the number of users in the service coverage area at time slot \(t_{y,z}^{x}\) is \(U\left(t_{y,z}^{x}\right)\), and the number of VUs downloading videos through MBS is \(N\left(t_{y,z}^{x}\right)\), all are obtained from the MECS, mobile video mean opinion score for the vehicle user is expressed as  
\[Q_{M}\Big{(}U\left(t_{y,z}^{x}\right),N\left(t_{y,z}^{x}\right)\Big{)}=\left(U \left(t_{y,z}^{x}\right)-N\left(t_{y,z}^{x}\right)\right)P_{Ar}\left(U\left(t_ {y,z}^{x}\right),N\left(t_{y,z}^{x}\right)\right)Q_{MEC}\left(t_{y,z}^{x}\right). \tag{29}\]  
The mobile video mean opinion score for the \(N\left(t_{y,z}^{x}\right)\) VUs who obtain videos from MBS through the backhaul network at the time slot \(t_{y,z}^{x}\) is expressed as  
\[Q_{B}\Big{(}U\left(t_{y,z}^{x}\right),N\left(t_{y,z}^{x}\right)\Big{)}=P_{Ar} \left(U\left(t_{y,z}^{x}\right),N\left(t_{y,z}^{x}\right)\right)N\left(t_{y,z} ^{x}\right)Q_{BH}\left(t_{y,z}^{x}\right). \tag{30}\]  
When the number of vehicle users via the RSU service at the time slot \(t_{y,z}^{x}\) is \(U\left(t_{y,z}^{x}\right)\), and the number of vehicle users downloading videos through MBS is \(N\left(t_{y,z}^{x}\right)\), then the average mobile video mean opinion score at the time slot \(t_{y,z}^{x}\) is expressed as  
\[\overline{Q}_{AV}\Big{(}U\left(t_{y,z}^{x}\right),N\left(t_{y,z}^{x}\right) \Big{)}=\frac{Q_{M}\left(U\left(t_{y,z}^{x}\right),N\left(t_{y,z}^{x}\right) \right)+Q_{B}\left(U\left(t_{y,z}^{x}\right),N\left(t_{y,z}^{x}\right)\right) }{U\left(t_{y,z}^{x}\right)}. \tag{31}\]  
Hence, the average mobile video mean opinion score at time slot \(t_{y,z}^{x}\) is expressed as  
\[Q_{Aver}\Big{(}t_{y,z}^{x}\Big{)}=\sum_{N\left(t_{y,z}^{x}\right)=0}^{\mathbb{ E}\left[U\left(t_{y,z}^{x}\right)\right]}\overline{Q}_{AV}\Big{(}\mathbb{E} \left[U\left(t_{y,z}^{x}\right)\right],N\left(t_{y,z}^{x}\right)\Big{)}. \tag{32}\]  
Therefore, the average MV-MOS of vehicle users for one period \(\triangle t_{y}^{x}\) is expressed as  
\[Q_{MOS}\Big{(}t_{y}^{x}\Big{)}=\frac{\sum\limits_{z\in K_{SN}}Q_{Aver}\left( t_{y,z}^{x}\right)}{K_{SN}}. \tag{33}\]  
The multiple bitrate level of mobile video not only affects the resolution of the video, but is also related to the size of the video file.