## 3 Algorithm Design
### Performance Analysis
#### 3.1.1 Delay Analysis
Transmission Sub-stage from the MEC Server to User \(i\)  
Similarly, by applying the diffusion process analysis method proposed in [13], the probability density function of the transmission sub-stage delay \(D_{3,l}^{(i)}\) from the MEC server to user \(i\) can be expressed as:  
\[p_{D_{3,l}^{(i)}}(D_{3,l}^{(i)}=t_{2}\bigl{|}\mathbf{A}_{\text{c},l},\mathbf{ A}_{\text{r},l})=\frac{b_{2,l}^{(i)}}{\sqrt{2\pi\beta_{2,\mathbf{x}}x_{2}^{3}}} \exp\left\{-\frac{\left(b_{2,l}^{(i)}-\alpha_{2,\mathbf{x}}t_{2}\right)^{2}} {2\beta_{2,\mathbf{x}}t_{2}}\right\} \tag{9}\]  
where \(\alpha_{2,\mathbf{x}}\) and \(\beta_{2,\mathbf{x}}\) are the drift coefficient and diffusion coefficient, respectively, for the transmission from the MEC server to any accessed user given the equal-rate resource allocation strategy implemented at the BS and the user access indicator vector \(\mathbf{x}\), satisfying \(\alpha_{2,\mathbf{x}}=\lambda_{2,\mathbf{x}}\) and \(\beta_{2,\mathbf{x}}=\alpha_{2,\mathbf{x}}^{3}V_{2,\mathbf{x}}\)[13]; \(b_{2,l}^{(i)}=\left\lceil\Gamma_{1,l}^{(i)}h_{\text{C}_{\text{r}}}/s\right\rceil\) represents the number of data packets after computing offloading by the MEC server for user \(i\), with \(\Gamma_{1,l}^{(i)}=Q_{l}^{(i)}D_{1}fB\) denoting the amount of data cached by the MEC server and hit by user \(i\), \(Q_{l}^{(i)}\) being the number of tiles hit by user \(i\), and \(h\) representing the data size ratio between the computation output and input at the MEC server. 4. Transmission Sub-stage from the Cloud Server to User \(i\)  
The data size of the tile that the cloud server needs to retransmit to user \(i\) is equal to:  
\[\Gamma_{2,l}^{(i)}=D_{1}fB(E_{l}^{(i)}-Q_{l}^{(i)}) \tag{10}\]  
where \(E_{l}^{(i)}\) represents the number of tiles in the actual FoV of user \(i\) during the \(l\)-th period. Similar to Equation (9), the conditional probability density function of the transmission sub-stage delay \(D_{4,l}^{(i)}\) from the cloud server to user \(i\) can be calculated as:  
\[p_{D_{4,l}^{(i)}}(D_{4,l}^{(i)}=t_{3}\bigl{|}\mathbf{A}_{\text{c},l},\mathbf{ A}_{\text{r},l})=\frac{b_{3,l}^{(i)}}{\sqrt{2\pi\beta_{3,\mathbf{x}}x_{3}^{3}}} \exp\left\{-\frac{\left(b_{3,l}^{(i)}-\alpha_{3,\mathbf{x}}t_{3}\right)^{2} }{2\beta_{3,\mathbf{x}}t_{3}}\right\} \tag{11}\]  
where \(b_{3,l}^{(i)}=\left\lceil\Gamma_{2,l}^{(i)}C_{\text{r}}/s\right\rceil\) represents the total number of data packets that the cloud server needs to retransmit to user \(i\); \(\alpha_{3,\mathbf{x}}\) and \(\beta_{3,\mathbf{x}}\) are the drift coefficient and diffusion coefficient, respectively, for the transmission from the cloud server to any accessed user under equal-rate resource allocation and the user access indicator vector \(\mathbf{x}\), satisfying \(\alpha_{3,\mathbf{x}}=\lambda_{3,\mathbf{x}}\) and \(\beta_{3,\mathbf{x}}=\alpha_{3,\mathbf{x}}^{3}V_{3,\mathbf{x}}\)[13]. 5. Computation Sub-stage of User \(i\)After user \(i\) receives the data retransmitted by the cloud server, it still needs to complete the decoding and rendering tasks for these data. The data size that needs to be processed is \(\Gamma_{2,l}^{(i)}\), so the conditional probability mass function of the computation sub-stage delay \(D_{5,l}^{(i)}\) for user \(i\) can be expressed as:  
\[P(D_{5,l}^{(i)}=\frac{\Gamma_{2,l}^{(i)}}{W_{\text{U}}^{(i)}}|\mathbf{A}_{c,l},\mathbf{A}_{r,l})=1 \tag{12}\]  
where \(W_{\text{U}}^{(i)}\) represents the computation capacity of user \(i\), in bit/second.