## 2 Methodology, System Description, and Problem Formulation
### System Description
#### 2.2.3 Fairness-Oriented Transmission and Computing Resource Allocation  
In the proposed 360\({}^{\circ}\) VR video service system, to ensure fair service for users based on real-time and dynamic network resources, the resources for the transmissions from the MEC server-connected BS to the users, for the transmissions from the cloud server to the users, as well as the computing resources of the MEC server, should all be reasonably allocated. * Equal-Rate Transmission Resource Allocation: Let \(\mathbf{x}=(x_{1},x_{2},\ldots,x_{l})\) represent the user access indicator vector, where \(x_{i}=1\) indicates that user \(i\) is allowed to be admitted or accessed, and \(x_{i}=0\) indicates the opposite. Although we aim to ensure fairness in the service provided to each accessed user, when the system adopts different user access combinations \(\mathbf{x}\), the transmission rate received by an accessed user will change. Let \(R_{1}(t)\) represent the instantaneous transmission rate from the cloud server to the MEC server at time \(t\); \(R_{2,\mathbf{x}}(t)\) and \(R_{3,\mathbf{x}}(t)\) represent the instantaneous transmission rates from the MEC server to any accessed user, and from the cloud server to any accessed user at time \(t\), respectively, under equal-rate resource allocation and user access combination \(\mathbf{x}\). The transmission rate of the wired network can be estimated based on the transmission bandwidth; the transmission rate of the wireless network can be assessed based on the BS's spectrum resources, transmission power, and channel information between the users and the BS. The channel information between any user and the BS can be obtained through user-reported measurements and reference signal strength. Without loss of generality, to model the impact of the network dynamics on the video packet transmissions, similar to [19], we assume that, when video packets are transmitted along each of the three paths, i.e., from the cloud server to the MEC server, from the MEC server to the user, and from the cloud server to the user, the  
Figure 4: The video encoding and FoV prediction model at the cloud server. inter-arrival times of video packets follow a given but arbitrary distribution, with mean \(1/\lambda_{1}\)= \(\mathrm{E}[s/R_{1}(t)]\) and \(1/\lambda_{p,\mathbf{x}}=\mathrm{E}[s/R_{p,\mathbf{x}}(t)]\), and variance \(V_{1}=\mathrm{Var}[s/R_{1}(t)]\) and \(V_{p,\mathbf{x}}=\mathrm{Var}[s/R_{p,\mathbf{x}}(t)]\), where \(p\) = 2, 3; \(s\) represents the video packet size; \(\mathrm{E}(\cdot)\) denotes the expectation; and \(\mathrm{Var}(\cdot)\) denotes the variance. Because we do not impose constraints on the packet inter-arrival time distribution, except for the measurable mean and variance, which can be re-estimated with time if the network dynamics are time-varying, network dynamic characteristics are considered in our model. Proportional Computing Resource Allocation: In the computation stage of the MEC server, the MEC server needs to allocate computing resources to different users to complete the task of offloading cached data. In general, the computing resource allocation strategy at the MEC server can be designed from either a user or a tile perspective. From the user's perspective, computing resources are exclusively allocated to each user, making fewer chances to reuse computing resources among users due to the neglect of common hit tiles of different users. As such, in this work, we adopt the tile-based strategy design. Specifically, we allocate computing resources to tiles in a proportional way according to the number of users hit each tile, which is beneficial to improve user fairness specifically when the computing resources are insufficient. Specifically, let \(H(n,\,m)\) represent the number of users that hit the tile at coordinate \((n,\,m)\) cached by the MEC server.