# Optimal Mobility-Aware Wireless Edge Cloud Support for the Metaverse
## 3 System Model
### Latency, Energy Consumption and Quality of Perception Experience
The OptimNT scheme could be regarded as a natural extension of our previous work [16]. Two other baseline schemes sharing same caching decisions as the proposed Optim scheme were also implemented for comparis  
\[\frac{Q}{Q_{max}}\geq Q_{bound} \tag{32}\]7 A typical tree-like designed network topology. selection scheme (RandS) and the closest EC first scheme (CEC) [38]. The RandS scheme operates a random EC selection while the other two both select the closest EC to the user's initial location. The CEC scheme also accepts the second closest EC as a back up choice [38]. According to Figure 5, the service delay for each request of the proposed schemes decreases, as expected, with an increasing weight \(\mu\). With a larger weight, the proposed schemes tend to select a larger data rate and direct the service to more powerful ECs, which naturally leads to a smaller overall delay. Compared to the OptimNT scheme, for example, the gain in delay of the OptimT scheme ranges from 1.9% to 10.4%. When seeking the best energy efficiency (\(\mu=0\)), since the CPU resources at the terminals are also shared by other functionalities, the OptimT scheme also tries to avoid the occupation of terminals. Hence, in this case, these two schemes share similar solutions and approaches. Noticing that the proposed schemes do not care about latency cost, they could choose a further away and busy EC, which even causes the OptimNT scheme to perform worse than the CEC scheme. Afterwards, as the weight \(\mu\) increases and the emphasis is placed on latency rather than energy, the OptimT scheme allocates some foreground interactions to terminals and becomes better than OptimNT. Since the baseline schemes neglect energy consumption, service decomposition and mobility, their gaps in relation to the proposed scheme become \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of available ECs & 6 \\ \hline Number of available VMs per EC (EC capacity) & 14 \\ \hline Number of requests & 30 \\ \hline Number of available models per user & 4 \\ \hline AR object size & \((0,10]\) MByte \\ \hline Total moving probability & \([0,1]\) \\ \hline Cell radius & 250 m \\ \hline Remained cache capacity per EC & \([100,400]\) MByte \\ \hline EC CPU frequency & [4,8] GHz \\ \hline EC CPU cores & [4,8] \\ \hline EC CPU core portion per VM & 0.25–0.5 \\ \hline Remained cache capacity per terminal & \([0,100]\) MByte \\ \hline Terminal CPU frequency & 1 GHz \\ \hline Terminal CPU cores & 4 \\ \hline CPU architecture coefficient & \(10^{-18}\) \\ \hline Foreground-interaction computational load & 4 cycles/bit \\ \hline Background-content-checking computational load & 10 cycles/bit \\ \hline Carrier frequency & 2 GHz \\ \hline Transmission power & 20 dBm \\ \hline Path loss exponent & 4 \\ \hline Noise power & \(10^{-11}\) W \\ \hline Number of resource blocks & 100 \\ \hline Frame resolution & \(1280\times 720\) \\ \hline Average latency per hop & 2 ms \\ \hline Cache miss penalty & 25 ms \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. larger with increasing weight. However, such a gain in delay comes with an extra cost in energy consumption. As shown in Figure 6, the energy consumption per request of the proposed scheme increases with a larger weight. Compared to the OptimNT scheme, the OptimT scheme consumes 2.9% to 23.0% more energy under different weights. Thus, it might not always be worth enduring lots of energy consumption for narrow gains in delay. By selecting a suitable weight, a balance could be achieved with the OptimT scheme between delay and energy consumption. Through the utilization of terminals, the OptimT scheme becomes the most sensitive to energy consumption and there could be instances in which it might consume more energy than the RandS scheme. Figure 5: Overall delay with weight \(\mu\) (6 EC, 30 requests, EC capacity is 14 and total mobility probability is 1). Figure 6: Average energy consumption with weight \(\mu\).