# Utility-Centric Service Provisioning in Multi-Access Edge Computing
## 4 Proposed Nested-Genetic Algorithm
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Population size of service placement individuals (Outer-GA), \(popSizeX\) & 60 \\ Population size of request scheduling individuals (Inner-GA), \(popSizeY\) & 100 \\ Number of the elite for the Outer-GA, \(eliteSizeX\) & 10\% \(\ast popSizeX\) \\ Number of the elite for the Inner-GA, \(eliteSizeY\) & 10\% \(\ast popSizeY\) \\ Tournament size of the Outer-GA, \(tourSizeX\) & 3 \\ Tournament size of the Inner-GA, \(tourSizeY\) & 5 \\ Mutation probability of the Outer-GA, \(p_{xm}\) & 0.1 \\ Mutation probability of the Inner-GA, \(p_{ym}\) & 0.2 \\ Maximum number of iterations for Outer-GA, \(outerMaxIter\) & 100 \\ Maximum number of iterations for Inner-GA, \(innerMaxIter\) & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nested-GA parameters. ### Simulation Results

First, we investigate the convergence of the proposed Nested-GA. Figure 6a displays the convergence of the Inner-GA of the Nested-GA. We observe that the total utility keeps increasing for about 62 iterations and becomes constant for the rest of the iterations. Meanwhile, Figure 6b plots the convergence of the Outer-GA of the Nested-GA. We observe that the Outer-GA even has a faster convergence rate than the Inner-GA and converges within 34 iterations due to smaller search space. These results show that our proposal can converge in a reasonable time. Next, we compare the performance of the proposed Nested-GA with the other algorithms in terms of the total utility of all users when varying different input parameters, one at a time. In Figure 7, we show the impact of increasing the storage capacity of MEC \(R_{n},\forall n\in\mathcal{N}\) on the total utility, cloud load (i.e., percentage of users scheduled to the core cloud) and percentage of dissatisfied users (i.e., \(W_{u}<0\)). In general, when \(R_{n}\) increases, the total utility achieved by all algorithms (except Top-R Nearest) increases (Figure 7a). Meanwhile, the cloud load of all algorithms and the percentage of dissatisfied users of all algorithms (except Top-R Nearest) decrease as shown in Figure 7b and Figure 7c, respectively. It is because when \(R_{n}\) becomes larger, more services can be placed at the MEC nodes, and more users can be served by the MEC nodes with low network latency, resulting in the improvement of user experience. However, at the same time, due to the computing resource limitation of MEC, the more users scheduled to the MEC nodes, the less the amount of computing resource assigned to each user. Hence, the processing latency of users becomes larger and affects the user experience. It can be observed from Figure 7a that when \(R_{n}\) increases, the total utility of all algorithms increases dramatically at first but then slows down. Among the algorithms, Top-R Nearest, which always schedules each user to the nearest MEC node hosting the corresponding service, performs the worst in all cases of storage capacity. As \(R_{n}\) increases, Top-R Nearest tends to only use the MEC computing resource to serve users (i.e., the cloud load gradually decreases to 0). Hence, when the storage capacity exceeds 700 GB, due to the computing resource bottleneck of the MEC nodes, the total utility of Top-R Nearest even decreases slightly and the percentage of dissatisfied users increases from 3% to 6% (Figure 7c). Compared to Top-R Nearest, Top-R Genetic better uses the cloud and MEC computing resources by scheduling the users to appropriate computing nodes (a MEC or the core cloud) based on Algorithm 2. Hence, the total utility of Top-R Genetic becomes much better than that of Top-R Nearest as \(R_{n}\) increases. Meanwhile, our proposed Nested-GA considerably outperforms the above algorithms by optimizing both the service placement and request scheduling decisions.