## 4 System Model  
In this section, we introduce our system model which is adopted in this paper. As shown in Figure 2, we consider a set of \(\mathbb{N}\) VR game devices in which each device have a set of \(\mathbb{M}\) independent computation tasks that needed to be completed. In addition, these devices are connected with a single base station via a wireless channel which is equipped with a mobile edge computing server as well as connected with a centralized cloud computing via core network. We denote the set of VR devices and their computation tasks as \(\mathbb{N}=\{1,2,\ldots,N\}\) and \(\mathbb{M}=\{1,2,\ldots,M\}\) where the computation tasks can be executed locally on the device itself or will be offloaded and processed remotely on the edge server or cloud server.  
In the following subsections, communication and computation models are presented with more detail, followed by the formulation of the optimization problem for our model.  
The notations used in this study are summarized in Table 1.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline \(\mathcal{N}\) & Set of VR devices. \\ \(\mathcal{M}\) & Set of Computation Tasks. \\ \(i\) & Refer to the \(i^{th}\) VR device. \\ \(j\) & Refer to the \(j^{th}\) computation task. \\ \(a_{i,j}\) & Input data size for computation task \(j\) of VR device \(i\). \\ \(b_{i,j}\) & Output data size for computation task \(j\) of VR device \(i\). \\ \(c_{i,j}\) & CPU cycles to accomplish the computation task \(j\) of VR device \(i\). \\ \(\tau_{i,j}\) & Completion deadline for computation task \(j\) of VR device \(i\). \\ \(\alpha_{i,j,k}\) & Offloading decision of computation task \(j\) of VR device \(i\). \\ \(r_{i}^{l}\) & Uplink data rate. \\ \(r_{i}^{l}\) & Downlink data rate. \\ \(B^{U}\) & Uplink channel Bandwidth \\ \(B^{D}\) & Downlink channel Bandwidth \\ \(p_{i}^{T}\) & Transmission power of VR device \(i\) \\ \(p_{i}^{R}\) & Reception power of VR device \(i\) \\ \(G_{0}\) & Channel gain of Base Station \\ \(\omega_{0}\) & Density of noise power of channel \\ \(\zeta_{i}\) & Energy consumed per CPU cycle \\ \(\xi\) & Propagation delay between base station and Cloud \\ \(f_{i}^{L}\) & Computational capability of VR device \(i\) \\ \(f_{i}^{E}\) & CPU resource of Base Station assigned to VR device \(i\) \\ \(f_{i}^{C}\) & CPU resource of Cloud assigned to VR device \(i\) \\ \(\tilde{p}\) & Energy consumption for VR device being idle \\ \(T_{i}^{L}\) & Local time for executing task \(j\) of VR device \(i\). \\ \(E_{i,j}^{L}\) & Local energy for executing task \(j\) of VR device \(i\) \\ \(T_{i,j}^{off}\) & Offloading time for task \(j\) of VR device \(i\). \\ \(T_{i,j}^{town}\) & Downloading time for task \(j\) of VR device \(i\). \\ \(T_{i,j,rec}^{t,rec}\) & Execution time for computation task \(j\) of VR device \(i\) at Base Station. \\ \(T_{i,j}^{t,rec}\) & Execution time for computation task \(j\) of VR device \(i\) at Cloud server. \\ \(E_{i,j}^{E}\) & Energy consumption for executing task \(j\) of VR device \(i\) at base station. \\ \(E_{i,j}^{c}\) & Energy consumption for executing task \(j\) of VR device \(i\) at Cloud server. \\ \(w_{i,j^{\prime}}^{t}\) & Local computational time and energy weight of computation task \(j\) of VR device \(i\). \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations.  
Figure 2: System model.