## 4 Solution for MCRC Problem
### VM Placement
As shown in Figure 16, compared to LR-MMT (the best result of all baseline methods), ARP-TSCP reduces the CDC operating cost by about 26.1%, and compared to MAD-RS (the worst result of all baseline methods), ARP-TSCP reduces the CDC operating cost by about 39.3%. This is because the comprehensive performance of ARP-TSCP is better than that of the baseline methods in all aspects. Figure 14: Comparing the number of VM migrations triggered by all methods in every time segment. Figure 15: Comparing the total number of VM migrations triggered by all methods. ## 6 Conclusions

In this paper, we focus on reducing CDC operating costs while ensuring user SLA requirements. We first established a cost model based on multiple computing resources in the CDC, taking into account the host energy cost, VM migration cost, and SLAV penalty cost. Based on this model, we define the MCRC problem in server consolidation. We devised the following step-by-step solution to deal with this problem. We employ a convolutional autoencoder-based filter to preprocess the workload of VMs and to reduce noise in the sampling record. Subsequently, an attention-based RNN method is used to predict the usage of computing resources by VMs in the future period, allowing us to trigger VM migration before the host enters the overloaded state to reduce the occurrence of SLAV. We design a heuristic algorithm based on the complementary use of multiple resources in space and time, ARP-TSCP, to solve the VM placement problem. Finally, simulations driven by real VM workload traces verify the effectiveness of our proposed method. Compared with the existing server consolidation methods, ARP-TSCP can reduce host energy consumption from 18.5% to 30.3%, SLAV cost by 38% to 52%, and total cost by 26.1% to 39.3%. In the future, we will first consider a more comprehensive cost model, such as taking into account multi-core CPU, the network topology of CDC, use of network equipment, and cooling system. We will also design a forecasting method that can predict the resource usage of equipment over multiple time periods in the future, thereby further reducing the generation of SLAV. Conceptualization, H.L., Y.X. and Y.S. ; methodology, H.L., Y.X. ; software, H.L. ; validation, H.L. and Y.S. ; formal analysis, H.L. ; investigation, H.L. and H.X. ; resources, H.L. and H.X. ; data curation, H.L. and H.X. ; writing--original draft preparation, H.L. ; writing--review and editing, Y.X. and Y.S. ; visualization, H.L. ; supervision, Y.X. ; project administration, Y.S. ; funding acquisition, H.L., Y.X., H.X. and Y.S. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No.62002067), the Guangzhou Youth Talent Program (QT20220101174), the Department of Education of Guangdong Province (No.2020 KTSCX039), the SRP of Guangdong Education Dept (2019 KZDZX1031), and the Natural Science Foundation of Education of Guizhou Province (No.KY[2017]351). **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. Figure 16: Comparing the total cost by all methods. ## References

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