## 5 Performance Evaluation
### Simulation Setup  
To evaluate the performance of the proposed method, we conduct simulations based on real-world measured data. \(\hat{\lambda}_{i}(t)\) is determined by the number of users and the amount of workload they generate. In a wireless mobile communication network, the number of users connected to a BS during a time slot varies due to user movement. To account for such variation patterns, we utilize the geographical cellular traffic (GCT) dataset, which contains approximately 30 million user traffic records measured from 21 road sections in the Hsinchu area of Taiwan [37]. We assume that there is one BS at each road section. Then, we divide the 21 BSs into seven non-overlapping groups and assign one MECS to each group (i.e., \(|\mathcal{M}|=7\)). We construct the BS groups so that the MECSs have uniform computational capacities. In other words, we cluster BSs to ensure that the aggregate capacity of each BS group is approximately equal. To configure the capacity of a BS \(b\), we first calculate the workload offloaded through \(b\) during each timeslot over the entire simulation period. Subsequently, we set the capacity of \(b\) as 70% of the maximum observed workload. The capacity of a BS group \(i\) is the sum of the capacities of the BSs in \(B_{i}\). Thus, we divide BSs into groups so that the capacity of each BS group is balanced by considering both the geographic distribution of BSs and their capacities. We depict the resulting simulation topology in Figure 5.  
The GCT dataset includes the GPS coordinates where the cellular traffic is originated and the time the traffic is generated. We consider each cellular traffic as a user. By assuming that a cellular traffic is connected to the nearest BS from where it is generated, we form the set of users connected to each BS \(b\) during each time slot, which we denote by \(U_{b}(t)\). To obtain the amount of workload newly imposed on each BS during each time slot, we \begin{table}
\begin{tabular}{c l} \hline \hline
**Acronym** & **Meaning** \\ \hline \(ES_{R}\) & Exhaustive Search when \(\bar{\lambda}(t)\) is used \\ \hline \(ES_{p}\) & Exhaustive Search when \(\bar{\lambda}(t)\) is used \\ \hline \(GA_{T}\) & Genetic Algorithm whose search time is the same as our method \\ \hline \(GA_{A}\) & Genetic Algorithm configured to find valid solutions for all inputs \\ \hline \(d_{b}(t)\) & Hamming distance between \(\eta(t)\) of \(ES_{R}\) and that decided by other method \\ \hline \(d_{\lambda}(t)\) & Euclidean distance between \(\bar{\lambda}(t)\) and \(\bar{\lambda}(t)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Acronyms and notations used in Section 5.  
use the Alibaba cluster dataset [38]. The dataset contains a mix of training and inference jobs running machine learning algorithms. It was gathered from a large-scale production cluster in the Alibaba platform for AI, consisting of over 6500 GPUs across approximately 1800 machines during July and August of 2020. To extract \(\tilde{\lambda}_{i}(t)\) by combining the GCT dataset and the Alibaba dataset, we randomly select 21 machines from the latter and treat each machine as a BS in the former. The trace data, which include task arrival times and workload demands, enable us to construct the task set assigned to machine \(m\) at time slot \(t\) denoted by \(Y_{m}(t)\). If we denote the workload imposed by a task \(v\in Y_{m}(t)\) by \(w_{m,v}\), the average workload imposed on a machine \(m\) by the tasks in \(Y_{m}(t)\) becomes \(\bar{w}_{m}(t)=\sum_{v\in Y_{m}(t)}w_{m,v}/|Y_{m}(t)|\). We assume that the average workload imposed by the users connected to the same BS during the same time slot is similar. Then, since we consider a machine as a BS, we configure the workload newly sent to a BS \(b\) that belongs to a MECS \(i\) during a time slot \(t\) as \(x_{i,b}(t)=\bar{w}_{b}(t)|U_{b}(t)|\). Accordingly, \(\tilde{\lambda}_{i}(t)\) is set to \(\sum_{b\in B_{i}}x_{i,b}(t)\). For the simulation study, we configure the parameters as follows.