## 5 Simulation Results and Prototype Implementation  
### Simulation Results and Discussion  
In our simulation settings, a Python-based simulator is used, in which the computer is equipped with Intel (r) Core(TM) i7-4770 CPU with 3.4 GHz frequency and 8 GB RAM capacity running Windows 10 Professional 64-bit platform. We consider a multi-player multi-task edge-cloud computing system with single cloud server, single small base station, \(N=20\) VR devices and each device has \(M=5\) independent computation tasks that can be executed locally or offloaded and processed remotely at the available base station or cloud server. Each computation task has an input data size which is uniformly distributed within the range \((5,15)\) MB while the output data size is assumed to be 20% of the input data size. In addition, the total number of CPU cycles required to complete each task is assigned to 1500 cycles/bit. The CPU computational capability of each VR device is uniformly distributed within range \(\{0.5,0.6,\dots,1.0\}\) GHz, while the CPU computational capability of edge server and cloud are set to 20 and 50 GHz, respectively. The local computing energy consumption per cycle follows a uniform distribution in the range \((0.20\times 10^{-11})\) J/cycle. The other simulation settings employed in the simulations are summarized in Table 2. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Number of VR Devices N & 20 \\ Number of Computation tasks M & 5 \\ Uplink Bandwidth \(B^{U}\) & 20 MHz \\ Downlink Bandwidth \(B^{D}\) & 40 MHz \\ Transmission and Reception Power \(p_{i}^{T}\) and \(p_{i}^{R}\) & 100 mWatts \\ Background Noise \(\omega_{0}\) & \(-100\) dBm \\ Input Data Size \(a_{i,j}\) & \((5,15)\) MB Unif-Dist \\ Output Data Size \(b_{i,j}\) & \(0.2a_{i,j}\) \\ Number of CPU cycles per bit \(c_{i,j}\) & 1500 Cycles/bit \\ Computation Capability of each VR device \(f_{i}^{L}\) & \(\{0.5,0.6,\dots,1.0\}\) GHz \\ Energy Consumption per CPU Cycle \(\zeta_{i}\) & \((0,20\) x \(10^{-11})\) J/cycle \\ Weights \(w_{i,j}^{t}\), \(w_{i,j}^{t}\) & 0.5 \\ Computation Capability of Edge Server \(F\) & 20 GHz \\ Computation Capability of Cloud Server \(F\) & 50 GHz \\ Cloud propagation delay & 15 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 4 shows the energy consumption of executing the computation tasks for the three different scenarios versus different values of edge server computation capabilities. It is observed from the figure that the energy consumption for our proposed system can achieve the lowest result. Specifically, the edge server scenario is decreasing as the edge server computation capability is increasing and becoming lesser than the cloud execution scenario. This is due to the energy consumption becoming shorter as the VR device is allocated more resources, whereas the cloud execution and local execution scenarios do not affect because they do not depend on the edge server resources. In addition, our proposed system gets the best execution place (i.e., local, edge and cloud). Figure 5 presents the processing time of executing the computation tasks for different edge server's capability. It is seen in this figure that the cloud execution and local execution policies are not affected by the edge server capability, whereas the time execution of our proposed system and edge server policies gradually decreases as edge server capability increasing. This is because of the shorter latency as the VR devices are allocated more resources. Figure 4: Energy consumption comparison under different values of edge server capability. Figure 5: Latency comparison under different values of edge server capability. The processing time and energy consumption of executing the computation tasks over different values of input data size (Input data size is uniformly distributed within the range (0,i) MB where i is the value of x-axis) are shown in Figures 6 and 7, respectively.