## 4 Performance Evaluation
In NR and LR, some MECSs are highly loaded; thus, if a task is offloaded to a highly loaded MECS, the task is likely to be blocked. Since the two lines representing RR and LMLBR look similar in Figure 4, we show and scrutinize the average blocking rate obtained by these two methods for \(\lambda=0.5,0.7,0.9\), separately, in Table 3. In our method, an overloaded MECS \(i\) considers the loads of other MECSs when it selects a MECS \(j\) to which it redirects its tasks. In addition, our method determines the amount of tasks to redirect to each \(j\) according to the load difference between \(i\) and \(j\). On the contrary, in RR, an overloaded MECS redirects its tasks to one randomly selected MECS until it becomes underloaded, regardless of the load of the selected MECS. Therefore, two adverse cases can happen when RR is used. Firstly, an overloaded MECS may redirect its tasks to another overloaded MECS. Secondly, an overloaded MECS may redirect an excessive amount of tasks to the selected MECS, which results in overloading the selected MECS. Thirdly, multiple overloaded MECSs may select the same MECS \(i\) to which they redirect their tasks. In this case, it is very likely that the selected MECS \(i\) becomes overloaded even though it was underloaded before accommodating the redirected tasks. If the load imposed on a MEC system is not so high, the number of MECSs overloaded by the tasks offloaded from devices is small. Accordingly, the adverse cases occur rarely. Therefore, we can observe in Table 3 that the average blocking rate obtained by RR is smaller than that achieved by LMLBR when \(\lambda\leq 0.7\). However, as the traffic offload rate increases, the two adverse cases by RR occur more frequently, which increases the average task blocking rate. Since our method avoids the two adverse cases, it can achieve a lower task blocking rate than RR when \(\lambda=0.9\). To further compare RR and LMLBR in terms of the blocking rate, we show not only the average blocking rate, but also the standard deviation of the blocking rate obtained by RR and our method in Figure 5. When we investigated the standard deviation of the blocking rate (denoted by \(\sigma_{b}\)) in Figure 5, our method achieved smaller  
Figure 2: Load per time slot of four methods. \(\sigma_{b}\) than RR for all \(\lambda>0.1\). This is attributed to the behavior of the proposed method. Unlike RR, our method redirects tasks from highly loaded MECSs to lightly loaded MECSs by considering the load difference between MECSs. Therefore, compared with RR, the proposed method achieves smaller load difference between the load of the MECS whose load is the highest and that of the MECS whose load is the smallest. Figure 3: Load per server for a given time slot (i.e., \(\rho_{i}(t),\forall i\in N\)). The rate of tasks completed within their delay constraints is affected by the total delay from the beginning of the task offloading process to the end of task computing. The total delay is composed of three parts. The first component is the transmission delay between a device and the MECS to which the device offloads a task. The second part is the queuing and service delay experienced by a task in the MECS that serves the task. The third component is a redirection delay that is included in the total delay only when a task is redirected from one MECS to another MECS. According to [PERSON]'s law, the queuing  
Figure 4: Average task blocking rate for various task offload rates. Figure 5: Comparison of RR and LMLBR in terms of the average task blocking rate. Each bar represents the average blocking rate at a given task offload rate. If we denote the average blocking rate as \(b\) and the standard deviation of the blocking rate as \(\sigma_{b}\), each line in each bar indicates the range of blocking rates from \(b-\sigma_{b}\) to \(b+\sigma_{b}\).