EWM: An entropy‐based framework for estimating energy consumption of edge servers

In mobile edge computing (MEC), accurately predicting and monitoring the energy consumption of edge servers is a key challenge in achieving green computing. The importance of solving this problem is that it can help optimize the energy usage in data centers and thus reduce the carbon emission of MEC. To this end, we propose an innovative entropy‐based power modeling framework called entropy weighted model (EWM). The EWM framework weights and combines classical prediction models by analyzing the major components of a server and selecting appropriate parameters. We validate the performance of EWM using real server power and performance counter data and compare it with other classical prediction models by Friedman test. The results show that EWM outperforms other classical prediction models in all test datasets. This result validates the significant advantages of our EWM framework in solving the critical problem of edge server power prediction, and provides an effective tool for achieving data center energy optimization and promoting green computing, resulting in a highly general and accurate prediction model.

3][4] Therefore, this study's primary motivation and question is: How to accurately estimate the energy consumption of servers to improve the energy efficiency of data centers and reduce operating costs?
To address this question, the main contribution of this research is to propose a new performance counter and entropy-based energy consumption estimation framework.This framework can accurately estimate the energy consumption of servers based on their workloads and other relevant parameters, thus providing an effective tool for energy management in data centers.
Beyond prior art, our performance counter and entropy-based energy estimation framework combine the accuracy of performance counters with the complexity of entropy concepts.Our approach can provide higher accuracy and stronger robustness than existing estimation methods based only on statistics or performance counters.
Overall, this study aims to contribute to advancing energy management in data centers by investigating and developing a new performance counter and entropy-based energy estimation framework, which can help solve the critical energy consumption problem in data centers.

RELATED WORK
The study of server power estimation has been the subject of many researchers who have proposed solutions.Roy et al 5 suggest representing the power model as the sum of CPU and memory power.The shortcoming of the model is that too few components are taken into account.
Tudor and Teo 6 consider more components of the server and propose that server power can instead function as a combination of CPU, memory, and I/O device power.The disadvantage of this model is that it is difficult to measure the actual energy consumption of individual server components and is not suitable for modeling data center energy consumption.
Song et al 7 consider more ground components and represent the server power model as the sum of CPU, memory, disk, and network card power.This model provides a detailed way for data centers to manage and understand server power consumption more accurately.However, some aspects could be improved with this approach.Measuring the power of individual components of each server can be a complex and costly task.It may require specific hardware to be installed on each server to monitor the power of each component in real-time during operation.This may be impractical for large data centers with many servers.
Alan et al 8 further construct a new server power model considering the different resource utilization utilities of the various components of the server.The main shortcoming of the model is the low prediction accuracy.
Tian et al 9 have proposed an alternative energy consumption model.The main shortcoming of the model is that it is challenging to measure each server's specific energy consumption, the calculation granularity is too large, and the accuracy of the energy consumption prediction for the data center is low.
Mills et al 10 created a different model from the previous ones.The main disadvantage of this model is that it only considers the CPU components' energy consumption and does not consider the energy consumption of other members.
2][13][14] The results show that server energy utilization is greatly improved.][17] Zhou et al 18 introduce a power regression model with the limitation of assuming that the power model consists of a single mathematical model, leading to low accuracy.
Zhang et al 19 propose a cubic polynomial power model but suffers from low prediction accuracy.
Bertran et al 20 show that power models based on performance monitoring counters (PMCs) maintain good performance, with an average error below 3%.
Park and Mun 21 present a power prediction method where server power is dependent on the base and active power rather than the actual power.Hardware determines the base power, while active power calculations involve cloud monitoring.However, this method demonstrates low prediction accuracy.
Liu et al 22 introduce an abstract power model for estimating power in cloud data centers but cannot estimate power for specific servers.
Yu et al 23 proposed a CMP power model, which has the main drawback of utilizing too few selected parameters.Foo et al [24][25][26] developed a power model based on evolutionary neural networks, but the main drawback is its high training complexity.
Liang et al 27 proposed a model based on feature selection and deep learning, but the main shortcoming is its tendency to overfit.
Shaqudianhid et al 28 conducted a comparative study on power modeling techniques using PMCs on modern multicore CPUs.The experimental results showed that the platform-level linear regression model had 5.09 times and 4.37 times higher prediction accuracies than the random forest and neural network models, respectively.They also proposed a viewpoint based on the theory of power calculation that any power estimation model using only linear models needs to be more accurate.
As a summary of the current work, there are two main problems with the past work.
1.The majority of models are primarily suited for specific scenarios, demonstrating somewhat limited generalization capabilities.2. Many studies traditionally lean toward utilizing a single type of model, whether they are straightforward linear models or intricate machine learning algorithms, to conduct their analyses.While these approaches have their merits, they might not fully leverage the diverse and complex aspects inherent in the data, potentially limiting opportunities to enhance predictive accuracy and broaden the model's applicability.
For these problems, this paper proposes a framework that combines linear regression, random forest, and other models of EWM.
In current research, we identified an emerging and forward-looking research area combining meta-heuristic algorithms with machine learning/deep learning to address the challenges in cloud computing and data center energy estimation.
Meta-heuristic algorithms such as Genetic Algorithms and Particle Swarm Optimization have shown remarkable results in many optimization problems with their global search advantages.However, these methods may encounter problems such as high computational resource demand and a tendency to fall into local optimization when dealing with complex energy estimation problems.
On the other hand, machine learning and deep learning models, especially neural networks, have demonstrated excellent performance in many fields, such as image recognition and natural language processing.However, these models may encounter challenges, such as the need for large amounts of labeled data and difficulty interpreting the model training process when applied to energy estimation.
Combining meta-heuristics with machine learning/deep learning approaches that combine the advantages of global optimization search and fine-grained local tuning by leveraging the robust adaptability of deep learning offers new possibilities for solving complex energy estimation problems in cloud computing environments. 30For example, meta-heuristic algorithms can be used to search for optimal server configurations globally.In contrast, deep learning models can finely tune parameters locally for more accurate energy consumption estimation.
This hybrid approach opens a new research path in energy consumption estimation in cloud computing and data centers, which promises to effectively address the challenges posed by the dynamism, uncertainty, and large scale of cloud computing environments.We look forward to seeing more innovations and research results in this area.

Energy consumption modeling process
The energy consumption modeling process consists of the following steps: parameter selection, data acquisition, model construction, construction of entropy-weighted models, construction of the EWM framework, conducting experiments, and evaluating the results.Figure 1 represents this process.

Parameter selection
With upwards of 2000 performance counter parameters, it is critical to select effective performance counters as parameters.The power consumption of edge servers in edge computing comes mainly from CPU, Memory, Disk, and Network Device components.The server power model is represented in Equation ( 1), 18 P server = P cpu + P memory + P disk + P net +  ( where P server , P cpu , P memory , P disk , and P net represent the total power of the server, the power of the processor component, the power of the memory component, the power of the storage component, and the power of the network, respectively. represents the power of the other component devices.According to the above energy consumption model, each component is discussed and analyzed separately in the following classification.The next is a breakdown of each component. The energy consumption model of CPU is shown in Equation (2), 18 where Based on the above model, we select %Committed Bytes in Use, %Page Faults/sec, %Page Write/sec, and %Page Reads/sec as the main parameters of the Memory component.
The energy consumption of a disk is mainly due to the read and write operations of the disk, Therefore, the energy consumption model is shown in Equation ( 4), The parameters P read , P write , and P idle represent the power consumption in the disk state, write state and idle state, respectively.Based on the above model, we select %Disk Read Time, %Disk Write Time, %Disk Time, and %Idle Time as the main parameters of the Disk component.
Net device energy consumption mainly comes from the network interface card.The power consumption model of the NIC is shown in Equation ( 5), 29 The parameters D s and D r indicate the amount of data sent and received by the NIC respectively in a fixed period of time, respectively, and C 0 , C 1 , and C 2 are constant parameters.Based on the above model, we select Sent Packets/sec, Received Packets/sec, Bytes Received/sec, and Bytes Sent/sec as the main parameters of the Net device component.
In summary, we selected 16 performance counters as parameters.They will be used to build power consumption models.

Data acquisition
This paper uses a power meter to collect server energy consumption and performance monitor software to obtain performance counter data.The power supply is monitored by connecting the power meter between the edge server and the power supply.Then the data is sampled by collecting the performance counter indicator data and the power meter data from the recorded server through dual devices such as laptops.The sampling process is shown in Figure 2 below.

The entropy method
Rudolf Clausius first proposed entropy, then Claudy Shannon introduced entropy into information theory, solving the problem of measuring information and quantifying uncertainty concretely to achieve quantitative analysis.The entropy method is a method of quantifying and synthesizing multiple indicators for decision-making.The specific steps for applying the entropy method to calculate weights follow as outlined below.
1. Construct a combined decision evaluation matrix A with n evaluation objects and k attribute evaluation indicators.As shown in Equation ( 6) 2. The data x ij in the multi-attribute evaluation matrix A were standardized using the outlier standardization method.As shown in Equation ( 7) 3. Calculate the weight of the ith data group in the jth attribute p ij .As shown in Equation ( 8) 4. Calculate the entropy value e j for the jth attribute.As shown in Equation ( 9) 5. Calculate the coefficient of variation g j for the jth attribute.As shown in Equation ( 10) 6. Calculate the weighting factor ω j for the jth attribute.As shown in Equation ( 11)

Entropy-based power model
The Entropy-method power prediction model follows below.As shown in Equation (12).
where F is a vector of existing model prediction values, W is a vector of weights obtained by using the entropy weighting method, in the entropy weighting method, n evaluation objects are equivalent to n sets of data, k attributes are identical to k model energy consumption estimates, through the entropy weighting method for different prediction models and then find the expectation of a more accurate energy consumption estimate.

Evaluation methodology
We use root mean square error (RMSE) as an evaluation method for the experimental model.Its expression is shown in Equation (13).
where n denotes the number of samples, y i and ŷi represent the sample's actual energy consumption and the model predicted energy consumption.

Experimentation environment
The experiments conducted in this study were performed on a computer system detailed in Table 1, which illustrates the following specifications: This environment provides a balanced and high-performance platform for conducting the experiments and evaluating the algorithms.The system is built around an eight-core AMD Ryzen 95900HX processor, ensuring adequate computational resources.It includes 32 GB of Micron DDR4 RAM, providing ample memory for running the tests.The primary hard drive is a 1 TB Samsung SSD, offering fast and efficient data storage and retrieval.The system uses a Realtek Gigabit Ethernet Controller for network connections.The operating system is the 64-bit version of Windows 11 Home Edition, which ensures compatibility and support for the latest software.The Windows' built-in tool, perfmon.exe, was used to gather performance counters, and the Deli DL333501 power meter was used to measure actual power consumption.All the experiments were carried out under this configuration to maintain consistency and reproducibility.For server simulation runs, the software utilized was Prime95 (64-bit), which aids in stress testing and ensuring the stability and performance of the system.

Results
We used eight of the models for comparison with the EWM model.These predictive models include linear regression (Linearregression_), cubic model (cubic_), support vector machine (SVM_), Lasso regression (Lasso_), decision tree regression (DecisionTreeRegressor_), random forest regression (RandomForestRegressor_), AdaBoost regression (AdaBoostRegressor_), and CMP model (CMP_).Figure 3 illustrates the predicted values derived from the various models.In this boxplot, the horizontal axis represents different models, including linear regression, SVM, Lasso, and so on, while the vertical axis displays the predicted value

Hypothesis testing
The Friedman test 31 is a nonparametric statistical method to detect differences between two or more related samples.This method is designed to address situations where the sample data does not satisfy the assumptions of normal distribution or chi-squareness of variances; in this study, our data is the ranking of nine predictive models on three datasets, so we chose to use the Friedman test.
In conducting the Friedman test, our null hypothesis is that all predictive models have the same predictive performance, that is, no significant difference in their rankings on the three datasets exists.On the other hand, our alternative hypothesis is that at least two predictive models with different predictive performances exist.Table 2 shows the RMSEs derived by each model on the three datasets.Clearly, the EWM model yields the lowest RMSEs across these datasets, indicating superior predictive accuracy.However, the cubic and SVM models display higher RMSEs in these datasets, suggesting lesser accuracy compared to others.
Table 3 shows the average Friedman rankings calculated on the three datasets.As can be seen from the table, the EWM model has achieved the best average Friedman rankings, indicating it possesses the best performance across these three datasets.
We performed the Friedman test and obtained a statistic value of 17.5111 and a p-value of 0.0252.Since the p-value is less than the commonly used significance level of 0.05, we rejected the null hypothesis that all predictive models have the same predictive performance.Specifically, our results show that the EWM model has the lowest average ranking across all datasets (average ranking of 1.33), indicating that the EWM model has the best predictive performance among these nine models.

CONCLUSIONS AND FUTURE RESEARCH DIRECTIONS
This paper proposes an entropy-based energy consumption prediction framework through natural data experiments.Compared with other energy consumption prediction models, our model demonstrates significant superiority.Specifically, our proposed EWM framework achieves the best prediction performance on all tested datasets, statistically validated by the Friedman test.
In addition, the scalability of the EWM framework enables it to incorporate more advanced energy models.As a result, it can be widely used for energy consumption prediction of edge servers, providing reliable data support for energy-aware optimization.
However, despite these advantages of our framework, some aspects still require further research.First, we must investigate how to predict energy consumption in environments facing variable and mixed workloads.Second, we will consider combining our prediction framework with real-time AI machine learning methods (e.g., reinforcement learning) to improve prediction accuracy and efficiency.
In theory, our model still has some limitations.For example, it has yet to be fully validated in multiple workload environments.Indeed, edge servers typically need to handle various types and volumes of requests, which requires our model to be more adaptable.In addition, the performance of our model relies heavily on the accuracy and quality of real-time data, which can be challenging in real-world applications.Therefore, our future work will address these issues to improve our model's generalization and usefulness.

F I G U R E 1
Energy consumption modeling flow chart.

F I G U R E 3
Predicted and true values for each model.F I G U R E 4 Root mean square errors from each model.range from 20 to 55.The predicted results of each model are represented by a box, facilitating a quick comparison of the prediction accuracy of different models.

Figure 4
shows the RMSEs derived from each model.This figure illustrates the RMSEs of each model through a bar graph.The horizontal axis lists the different models, while the vertical axis shows the RMSE values of each model.As can be seen from the figure, the EWM model has the lowest RMSE, indicating that it has higher prediction accuracy compared to other models.
23u indicates CPU utilization and C 0 and C 1 are constant parameters.Based on the above model, we select Processor Time, %Idle Time, %User Time, and % Privilege Time as the main parameters of the CPU component.The memory energy consumption model is shown in Equation (3),23E memory = ∫The parameters P pre , P read , P write , P ac , and P ref indicate the power in the pre-charge, read, write, act, and new states, respectively.
TA B L E 1 RMSEs derived from nine different predictive models on three datasets.Mean Friedman ranks.
TA B L E 2 TA B L E 3Abbreviation: EWM, entropy weighted model.