## 5 Performance Evaluation
### Performance Comparisons
To further examine this phenomenon, we show the changes in \(\alpha_{i}(t)\)s over time in Figure 4.  
Figure 3: Comparison of \(Q_{i}(t)\) for three classes. (**a**) \(Q_{1}(t)\) over time, (**b**) \(Q_{2}(t)\) over time, and (**c**) \(Q_{3}(t)\) over time. When the workload arriving at each queue is small and the length of each queue is small, all methods maintain \(Q_{i}(t)<\delta_{i}\) (\(\forall i\in N\)). However, when the workload fed to a queue \(i\) is small and the workload arriving at another queue \(j\) is high, the MES must decrease \(\alpha_{i}(t)\) and increase \(\alpha_{j}(t)\) to avoid the temporal overload of queue \(j\). However, EVEN and TPRA statically assign \(\alpha_{i}(t)\)s without considering the input workload dynamics and states of the queues. Because they cannot adjust the amount of CPU resources allocated to each queue, they cannot prevent the temporal overload of the queue. By contrast, our method dynamically adjusts \(\alpha_{i}(t)\)s according to \(Q_{i}(t)\)s, \(w_{i}(t)\)s, and \(\delta_{i}\). Because our method can increase \(\alpha_{j}(t)\) more than that allocated by TPRA and decrease \(\alpha_{i}(t)\) less than that allocated by TPRA, it can maintain the queue length below its target threshold. In Figure 5, we compare \(e_{i}(t)\)s over time. We observe that the energy consumed by a MES is high when static methods (EVEN and TPRA) are used. The results are attributed to the manner in which each method determines \(\alpha_{i}(t)\)s. We observe in Figure 4 that the static methods assign more service time to each queue than the dynamic methods (our method and WoPred) during times when the queues are not temporarily overloaded. That is, static methods make a MES in an active state unnecessarily longer than dynamic methods. A MES in an active state consumes energy, even when a queue is empty. According to [42], the idle energy consumed by a MES corresponds to 50\(\sim\)70% of the peak power consumption when a MES is fully used. In contrast, our method and WoPred dynamically determine \(\alpha_{i}(t)\)s at the start of each time slot by considering \(Q_{i}(t)\)s, reflecting the historical resource allocations. Therefore, a MES can be turned into a low-power mode for \((1-\sum_{i\in N}\alpha_{i}(t))\tau\). Thus, they consume less energy than the static methods. Because WoPred does not consider a workload arrival process (i.e., \(\hat{w}_{i}(t)\)), it determines \(\alpha_{i}(t)\)s in a reactive manner. Thus, when we examine the \(\alpha_{i}(t)\)s obtained by WoPred, the \(\alpha_{i}(t)\)s lag because WoPred reacts only to the previous situation reflected in \(Q_{i}(t)\)s. That  
Figure 5: Comparison of \(e_{i}(t)\) for three classes. (**a**) \(e_{1}(t)\) over time, (**b**) \(e_{2}(t)\) over time, and (**c**) \(e_{3}(t)\) over time. is, WoPred allocates the \(\alpha_{i}(t)\)s using only \(Q_{i}(t)\)s without considering \(\hat{w}_{i}(t)\)s. Thus, the \(\alpha_{i}(t)\)s determined by WoPred may be larger or smaller than the \(\alpha_{i}(t)\)s required to maintain \(Q_{i}(t+1)\leq\delta_{i}\). Note that \(Q_{i}(t+1)\) is affected by \(w_{i}(t)\). Because WoPred considers \(w_{i}(t)\) when it determines \(\alpha_{i}(t+1)\) using \(Q_{i}(t+1)\), WoPred reacts to \(w_{i}(t)\). In contrast, our method predicts \(w_{i}(t)\) at the beginning of a time slot \(t\) and considers \(\hat{w}_{i}(t)\) when it determines \(\alpha_{i}(t)\). Thus, by considering \(Q_{i}(t)\) and \(\hat{w}_{i}(t)\) at the start of time slot \(t\), our method can determine \(\alpha_{i}(t)\)s more optimally than WoPred, which results in smaller \(Q_{i}(t)\)s and \(e_{i}(t)\)s than WoPred.