# Modeling and Evaluation of Power-Aware Software Rejuvenation in Cloud Systems
## 6 Performance Evaluation
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Description** & **Value/Range** & **Unit** \\ \hline \(\lambda_{hf}\) & VMM failure rate & 0.00139 & VMM/h \\ \(\lambda_{hrj}\) & VMM rejuvenation rate & 30 & VMM/h \\ \(\lambda_{hrp}\) & VMM repair rate & 2 & VMM/h \\ \(\lambda_{pw}\) & PM wakeup rate & 1440 & PM/h \\ \(\lambda_{ua}\) & VM requests arrival rate & [5 \(\dots\) 20] & VM/h \\ \(\lambda_{vt}\) & VM switch off rate & 0.5 & VM/h \\ \(\lambda_{vmg}\) & VM migration rate & 1200 & VM/h \\ \(\lambda_{vl}\) & VM initiation rate & 120 & VM/h \\ \(P_{vmf}\) & Probability of VM migration failure & 0.01 & - \\ \(N\) & Number of PMs & 3 & - \\ \(M\) & Number of VMs per PM & 3 & - \\ \(Q_{c}\) & Size of input queue & 5 & - \\ \(Q_{m}\) & Size of migration queue & 6 & - \\ \(\rho_{b}\) & Power consumption of a PM running a VMM & 100 & W \\ \(\rho_{v}\) & Power consumption of a VM & 10 & W \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Configuration of the cloud system under study. identified and rejuvenated before age-induced failures occur. Thus, the forced rejuvenation of mode 2 decreases the probability of VMM failure compared to mode 1. The power saving scheme switches off idle VMMs, which in turn restarts the age of those VMMs, and result in even lower probability of VMM failure when combined with pure rejuvenation in mode 3. As shown in Figure 3b, simultaneous modeling of power saving and rejuvenation schemes in mode 3 improves the availability-related measure RSA of the cloud system. Such implementation of power-aware rejuvenation involves the migration of VMs between VMMs, so the number of tokens in place \(P_{Mig}\) increases and the denominator of the fraction in Equation (1) increases. However, as shown in Figure 3a, pure rejuvenation decreases the average probability of VMM failure, and thereby increases the mean number of active VMMs, increasing the average number of VMs that can be served at a given time. Since \(P_{CurrentVM_{S_{i}}}\) increases more than \(P_{Mig}\), power-aware rejuvenation causes a significant improvement in the ratio of serving VMs to accepted requests. Figure 3c represents the effect of applying rejuvenation and power-awareness schemes to cloud systems on the mean number of failed VMs. The greater the average probability of VMM failure, the greater the number of failed VMs. Consequently, for the same VMM failure probability results shown in Figure 3a, mode 3 performed the best and mode 1 the worst. Figure 3: Results obtained by solving the proposed SAN model representing (**a**) probability of VMM failure, (**b**) ratio of serving VMs to accepted VMs, (**c**) mean number of failed VMs and (**d**) total power consumption. In Figure 3d, the impact of software rejuvenation and power-awareness on power consumption of cloud system is considered. As indicated in Equation (4), the power consumption is directly related to the number of switched-on PMs and active VMs in a data center. In the pure rejuvenation mode, mode 2, all PMs are always on and therefore the power consumption in this mode is the greatest compared to the power consumed in modes 1 and 3, which are power-aware. In mode 3, newly rejuvenated VMMs are free of running VMs. Thus, they are more likely to be switched off by the power saving mode. Therefore, the total power consumption of mode 3 is less than that of mode 1. Figure 3d acknowledges the fact that by applying rejuvenation and power saving simultaneously, the number of active PMs decreases compared to the situation where rejuvenation is not applied.