## 4 Solution for MCRC Problem
### VM Placement
As can be seen from Figure 12, in terms of reducing the SLAV of CPU and memory, ARP-TSCP has obvious improvement over all baseline methods. We can argue that based on the workload prediction method and eliminating potential overloaded states in advance is a feasible approach. In addition, the memory SLAV caused by performing ARP-TSCP is much smaller than that of other methods. This is because the baseline methods are essentially designed based only on CPU resource. The baseline host overload detection strategies only consider the CPU overloading situation, and the premise of the PABFD algorithm assumes that the host can provide unlimited memory resources for VMs. In the actual production environment, the competition between VMs for host memory resources is very fierce, resulting in a high frequency of memory SLAV. Most of the VMs in the Alibaba VM workload dataset are not disk IO intensive and require more CPU and memory resources [49]. In addition, the NIC throughput rate of 1 GB/s can meet the business needs of many users most of the time. Therefore, in terms of both disk and network, the related SLAV caused by all methods is less than that of CPU and memory. Figure 11: Comparing the total energy consumption hosts by all methods. Figure 10: Comparing the energy consumption of hosts by all methods in every time segment. As shown in Equations (22)-(25), in the SLAV calculation formula, the entire life cycle of the host is involved, so we do not show the SLAV generated in each time period. In Figure 13, we compare the total cost of the SLAV penalty for all methods over a full day. It can be seen that in the case of \(pun_{cpu}=pun_{mem}=pun_{disk}=pun_{net}\), the SLAV penalty cost caused by ARP-TSCP is about 38% lower than that of LR-MMT (the best result of all baseline methods) and is about 52% lower than that of MAD-RS (the worst result of all baseline methods). Due to the importance of CPU and memory in actual use as well as their larger proportion of power consumption of the host, if the values of \(pun_{cpu}\) and \(pun_{mem}\) are greater than the values of \(pun_{disk}\) and \(pun_{net}\), then ARP-TSCP will have a lower SLAV penalty cost. The advantage will be more obvious. Figure 14 demonstrates the comparison of the number of VM migrations triggered by all methods in 288 consecutive periods in CDC. Figure 15 demonstrates the comparison of the total number of VM migrations caused by using these ten methods to consolidate servers throughout the day. As can be seen from Figure 14, in different periods, the number of VM migrations induced by ARP-TSCP is sometimes higher than that induced by the baseline methods, and it is sometimes lower than that induced by them. Therefore, as shown in Figure 15, the total amount of VM migrations induced by ARP-TSCP does not

Figure 12: Comparing the SLAV by all methods regarding four resources. Figure 13: Comparing the total SLAV penalty cost by all methods. have much advantage over that of induced by the baseline methods throughout the day, and the two are very close. In each period, ARP-TSCP and the baseline methods trigger VM migration for different reasons, respectively. ARP-TSCP actively considers the situation of overloaded hosts and SLAV occurrence in the next period and initiates VM migrations to deal with it in advance. The baseline methods passively respond to the host overloaded phenomenon generated in the current period. The total numbers of VM migrations are very close, but the mechanisms of triggering migration are different. Such differences are reflected in the final result, which is that the amount of SLAV occurrences caused by ARP-TSCP is much smaller than that caused by LR-MMT, as shown in Figure 13.

Compared with the baseline methods, our proposed ARP-TSCP has better improvements in host energy consumption, SLAV occurrence, and VM migration cost. Therefore, in the final total cost comparison, ARP-TSCP outperforms the other methods.