Electrical Power Optimization of Cloud Data Centers Using Federated Learning Server Workload Allocation

Abstract

Cloud Data Centers (CDCs) are the foundation of the digital economy, enabling data storage, processing, and connectivity for different academia/industry/commerce activities and digital services worldwide. As a result, their consistent power supply and reliable performance are critical factors; however, few works have considered power consumption optimization based on intelligent workload allocation. To this end, the proposed paper presents a Federated Learning (FL)-based server workload allocation model for optimal power optimization. In this strategy, the servers are modeled based on their Central Processing Unit (CPU), memory, storage, and network usage. A global server is considered as the global model responsible for final workload allocation decisions. Each server acts as a client in the federated learning framework, sharing its derived parameters with the global model securely and federatedly. Finally, after ten epochs of the system running, the model could optimize the system, decrease the overall power consumption, and reduce the workload pressure in each server by distributing it to other servers. The model is evaluated using different Key Performance Indicators (KPIs), and an appendix is provided, including the full performance results, workload shifting logs, and server resource status. Overall, the suggested FL allocator model shows promise in significantly lowering power consumption and alleviating server workload efficiently.

1. Introduction

Cloud Data Centers (CDCs) are considered fundamental infrastructure globally, with reliable performance being the top priority, relying on their role in the digital economy [1,2,3,4,5,6,7], as well as the Artificial Intelligence (AI) applications [8,9,10,11,12,13,14]. Based on a report by Goldman Sachs, a banking investment corporation, about $\$1$ trillion will be invested in AI, chips, and a CDC power supply [15]. Given their significance, CDCs consume considerable electricity, highlighting the necessity for more efficient, clean, and sustainable power sources, making them ideal candidates for power-efficient designs [16]. To this end, several works have been conducted to pave the way for developing efficient and clean CDC power optimization [17]. Chidolue et al. [18] introduced the concept of green CDCs. These centers concentrate on power-efficient hardware, as well as renewable power utilization, advanced cooling, and resource optimization with sustainability. Despite their higher upfront costs and technical complexity, these technologies promise lower operational costs and less environmental impact. The rise of server workload analytics can significantly affect CDC power consumption and resource utilization. The dynamics of server operations, including task scheduling and resource allocation, directly impact different parts, such as cooling systems [19]. Optimizing workloads through intelligent management strategies, such as load balancing, spatio-temporal flexibility [20,21,22,23], and virtualization, can reduce power demands and improve sustainability in CDC operations. For instance, GreenGLB, an online algorithm, is presented in [24] utilizing a greedy approach for distributing interactive, indivisible workloads across geo-distributed CDCs. Indivisible workloads, sequential tasks assigned to a single CDC, are allocated based on current electricity prices, renewable energy availability, and predefined constraints. Following this concept, a game theory-based workload management framework was designed, in [25], to minimize cloud operating costs through intelligent scheduling. The framework accounts for data transfer costs, CDC queueing delays, and factors such as heterogeneous compute capabilities, cooling power, task co-location interference, time-of-use electricity pricing, renewable energy, net metering, peak demand pricing, and network pricing. Additionally, the work [26] presented a hierarchical workload management approach for geographically distributed CDCs, considering two algorithms for workload assignment and migration. These algorithms calculate a cost function to determine the optimal site for running workloads across CDCs, requiring minimal state information exchange while preserving CDC autonomy and enabling integrated management of heterogeneous platforms. Moreover, a review of optimization-based workload distribution strategies is conducted by [27], for geographically distributed CDCs, focusing on recent research. It examined optimization factors, including workload type, load balancer, renewable energy availability, energy storage, and server specifications.

The study [28] proposed an energy and workload management framework for sustainable CDCs, using stochastic optimization to adapt to variable renewable energy availability, cooling efficiency, Information Technology (IT) workload shifts, and energy price fluctuations while meeting long-term quality-of-service requirements.

Additionally, The review conducted in [29] highlighted the importance of energy efficiency in CDCs in reducing operational costs, minimizing carbon footprints, and promoting sustainable growth. Over 25 energy efficiency metrics and 250 literature references were considered, analyzing various energy-consuming components and configurations in CDCs. Through real-world case studies, the review evaluated how corporations implement these metrics, while also considering their challenges and limitations.

In addition to the significance of power consumption, the model designed to optimize power is also important. Accordingly, a FL-based workload allocation model is presented in this paper. Besides other previously published models, the proposed strategy models the CDC servers by their Central Processing Unit (CPU), network, memory, and storage devices. Next, it considers a global server as the global model and the other servers as the clients. Each client is analyzed using the local 3rd-degree polynomial regressor model, and the results are then federatively transferred to the global server to make the final evaluation and decision. Then, the proposed model is evaluated against several Key Performance Indicators (KPIs), and shifting results are derived. Moreover, the contributions of the proposed model are summarized as follows:

• a FL-based intelligent model is developed to allocate the workload quickly, efficiently, and securely with the least errors;
• the distribution process is conducted in just 10 intervals, tending Mean Square Error (MSE) to zero;
• an appendix is provided, including the workload shift logs, full global/local KPIs, and server status, demonstrating the low error rates in the presented KPIs.

The paper is structured as follows: the proposed system and the FL strategy are presented in Section 2. The results and conclusion are drawn in Section 3 and Section 4, respectively. Finally, the details of log shifts, server status, and KPIs are available in Appendix A.

2. Proposed Workload Shifting Strategy

2.1. Preliminary Statement

The workload shift, in this paper, is conducted on CDC servers. In each server (Figure 1), the power consumption is mainly from the CPU, memory, storage, and network devices.

In a CDC server, the CPU is among the main components responsible for executing instructions and performing calculations, directly impacting the server’s processing power and power consumption [30]. The memory, including Random Accessible Memory (RAM), stores data that is actively used by the CPU, with higher memory usage leading [31] to increased power consumption due to the need for faster data retrieval/processing. Storage devices, typically consisting of Hard-Disk Drive (HDD) or Solid-State Drive (SSD), store large volumes of data and increase power consumption, particularly during read/write operations [32]. Finally, network devices, such as the Network Interface Card (NIC) [33] and switches [34], handle data communication between servers, often influencing power use as network traffic increases, particularly in high-throughput or low-latency environments.

2.2. Intelligent Shifting Strategy

Federated Learning (FL), firstly introduced in [35], is a decentralized approach to Machine Learning (ML), where multiple devices or data sources work together to train a global model, all while keeping their data private and secure [36]. In a typical FL setup, data resides on distributed devices, such as smartphones, Internet-of-Things (IoT) sensors, or edge servers, where each device locally processes its data to generate model updates. Instead of transmitting raw data, these updates are sent to a central server, where they are aggregated to improve the global model. This process is repeated, with the central server sending the updated model back to the devices for further training. It also solves issues related to data access by allowing data from different devices or locations to contribute to training without needing to store it all in one place. Additionally, FL reduces communication overhead compared to traditional distributed learning, as only model parameters or gradients are transferred, not entire datasets of each server. To this end, the overall structure of the developed FL model for the server’s workload allocation is shown in Figure 2.

The proposed FL-based model optimizes power consumption across a distributed system of 100 servers, each acting as a client. Each server trains a local $3\mathrm{rd}$-degree polynomial regression model to predict power consumption based on workload characteristics, specifically CPU, memory, storage, and network usage.

These models are aggregated into a global model to guide dynamic workload redistribution, minimizing total power consumption while considering server capacity constraints and a power threshold. The proposed strategy is conceptualized in Figure 3 and presented in Algorithm 1 and Figure 4.

Algorithm 1 Proposed strategy.

1: Initialize: Set $N\leftarrow 100$ servers. For each server $S_i$, define:   2:      Capacity vector ${\mathbf{C}}_i\leftarrow [C_i^{\mathrm{CPU}},C_i^{\mathrm{Mem}},C_i^{\mathrm{Stor}},C_i^{\mathrm{Net}}]\in {\mathbb{R}}_{\ge 0}^4$.   3:      Dynamic state vector at time t, ${\mathbf{X}}_i(t)\leftarrow [X_i^{\mathrm{CPU}}(t),X_i^{\mathrm{Mem}}(t),X_i^{\mathrm{Stor}}(t),X_i^{\mathrm{Net}}(t)]\in {\mathbb{R}}_{\ge 0}^4$.   4: Function UpdateUsage($S_i,t$):   5:      Sample metrics from uniform distributions:   6:          $X_i^{\mathrm{CPU}}(t)\sim \mathcal{U}(10,90)$, $X_i^{\mathrm{Mem}}(t)\sim \mathcal{U}(0.1,C_i^{\mathrm{Mem}})$,   7:          $X_i^{\mathrm{Stor}}(t)\sim \mathcal{U}(0.1,C_i^{\mathrm{Stor}})$, $X_i^{\mathrm{Net}}(t)\sim \mathcal{U}(0.1,C_i^{\mathrm{Net}})$.   8:      Compute power consumption:   9:          $P_i(t)\leftarrow 50+200{\left({\displaystyle \frac{X_i^{\mathrm{CPU}}(t)}{100}}\right)}^{1.5}+0.5X_i^{\mathrm{Mem}}(t)+3{(X_i^{\mathrm{Net}}(t))}^{1.2}+0.1X_i^{\mathrm{Stor}}(t)+\mathcal{N}(0,0.3)$. 10: Function TrainLocalModel(${\mathcal{D}}_i$): 11:      Let ${\mathcal{D}}_i\leftarrow {\{({\mathbf{x}}_{i,j},y_{i,j})\}}_{j=1}^{m_i}$, where ${\mathbf{x}}_{i,j}\in {\mathbb{R}}^4$ (CPU, Mem, Net, Stor usage), $y_{i,j}\in \mathbb{R}$ (power). 12:      Standardize features: ${\mathbf{x}}_{i,j}\leftarrow {\displaystyle \frac{{\mathbf{x}}_{i,j}-{\mu }_i}{{\sigma }_i+{10}^{-10}}}$, where ${\mu }_i,{\sigma }_i$ are mean and std of ${\mathcal{D}}_i$. 13:      Scale outputs: $y_{i,j}\leftarrow {\displaystyle \frac{y_{i,j}}{\max (y_{i,1},\dots ,y_{i,m_i})}}$. 14:      Split data: ${\mathcal{D}}_i^{\mathrm{train}}\leftarrow 80\%$, ${\mathcal{D}}_i^{\mathrm{val}}\leftarrow 20\%$. 15:      Train 3rd-degree polynomial regression: ${\widehat{y}}_{i,j}\leftarrow f({\mathbf{x}}_{i,j};{\theta }_i)$, minimizing: 16:          $J({\theta }_i)\leftarrow {\displaystyle \frac{1}{|{\mathcal{D}}_i^{\mathrm{train}}|}}{\sum }_{j\in {\mathcal{D}}_i^{\mathrm{train}}}{(y_{i,j}-{\widehat{y}}_{i,j})}^2$. 17:      Evaluate on ${\mathcal{D}}_i^{\mathrm{val}}$: Compute KPIs {MSE, RMSE, MAE, MAPE, MaxErr} using EvaluateModel. 18:      Return model $M_i$, KPIs, ${\mu }_i$, ${\sigma }_i$, $y_{\max ,i}$. 19: Function AggregateModels(${\{M_i\}}_{i=1}^N,{\{{\mathcal{D}}_i\}}_{i=1}^N$): 20:      Pool data: ${\mathcal{D}}_{\mathrm{pool}}\leftarrow {\bigcup }_{i=1}^N{\mathcal{D}}_i$, where ${\mathcal{D}}_{\mathrm{pool}}\leftarrow {\{({\mathbf{x}}_j,y_j)\}}_{j=1}^m$. 21:      Standardize features: ${\mathbf{x}}_j\leftarrow {\displaystyle \frac{{\mathbf{x}}_j-{\mu }_{\mathrm{pool}}}{{\sigma }_{\mathrm{pool}}+{10}^{-10}}}$, where ${\mu }_{\mathrm{pool}},{\sigma }_{\mathrm{pool}}$ are mean and std of ${\mathcal{D}}_{\mathrm{pool}}$. 22:      Scale outputs: $y_j\leftarrow {\displaystyle \frac{y_j}{\max (y_1,\dots ,y_m)}}$. 23:      Train global 3rd-degree polynomial regression: ${\widehat{y}}_j\leftarrow f({\mathbf{x}}_j;{\theta }_{\mathrm{g}})$, minimizing: 24:          $J({\theta }_{\mathrm{g}})\leftarrow {\displaystyle \frac{1}{m}}{\sum }_{j=1}^m{(y_j-{\widehat{y}}_j)}^2$. 25:      Return global model $M_{\mathrm{g}}$, ${\mu }_{\mathrm{pool}}$, ${\sigma }_{\mathrm{pool}}$, $y_{\max }$. 26: Function EvaluateModel($\mathbf{y},\widehat{\mathbf{y}}$): 27:      For true values $\mathbf{y}\leftarrow [y_1,\dots ,y_m]$, predictions $\widehat{\mathbf{y}}\leftarrow [{\widehat{y}}_1,\dots ,{\widehat{y}}_m]$, compute: 28:          $\mathrm{MSE}\leftarrow {\displaystyle \frac{1}{m}}{\sum }_{j=1}^m{(y_j-{\widehat{y}}_j)}^2$, 29:          $\mathrm{RMSE}\leftarrow \sqrt{\mathrm{MSE}}$, 30:          $\mathrm{MAE}\leftarrow {\displaystyle \frac{1}{m}}{\sum }_{j=1}^m|y_j-{\widehat{y}}_j|$, 31:          $\mathrm{MAPE}\leftarrow {\displaystyle \frac{100}{m}}{\sum }_{j=1}^m\left|{\displaystyle \frac{y_j-{\widehat{y}}_j}{\max (y_j,{10}^{-10})}}\right|$, 32:          $\mathrm{MaxErr}\leftarrow {\max }_j|y_j-{\widehat{y}}_j|$. 33:      Return {MSE, RMSE, MAE, MAPE, MaxErr}. 34: Function ShiftWorkload(${\{S_i\}}_{i=1}^N,M_{\mathrm{g}},{\mu }_{\mathrm{pool}},{\sigma }_{\mathrm{pool}},y_{\max }$): 35:      Identify high-power servers: $\mathcal{H}\leftarrow \{S_i\mid P_i(t)>150\}$. 36:      For each $S_i\in \mathcal{H}$: 37:          Define workload to shift: $\Delta {\mathbf{X}}_i\leftarrow [X_i^{\mathrm{CPU}}(t)/2,X_i^{\mathrm{Mem}}(t)/2,X_i^{\mathrm{Net}}(t)/2,X_i^{\mathrm{Stor}}(t)/2]$. 38:          For each candidate server $S_k\ne S_i$: 39:              If $S_k$ satisfies: $X_k^{\mathrm{CPU}}(t)+\Delta X_i^{\mathrm{CPU}}\le 90$, $X_k^{\mathrm{Mem}}(t)+\Delta X_i^{\mathrm{Mem}}\le 0.8C_k^{\mathrm{Mem}}$, $X_k^{\mathrm{Net}}(t)+\Delta X_i^{\mathrm{Net}}\le 0.8C_k^{\mathrm{Net}}$, $X_k^{\mathrm{Stor}}(t)+\Delta X_i^{\mathrm{Stor}}\le 0.8C_k^{\mathrm{Stor}}$: 40:                    Predict power: $P_i^{\mathrm{old}}\leftarrow M_{\mathrm{g}}({\mathbf{X}}_i(t);{\mu }_{\mathrm{pool}},{\sigma }_{\mathrm{pool}},y_{\max })$, $P_k^{\mathrm{old}}\leftarrow M_{\mathrm{g}}({\mathbf{X}}_k(t);{\mu }_{\mathrm{pool}},{\sigma }_{\mathrm{pool}},y_{\max })$. 41:                  Predict new power: $P_i^{\mathrm{new}}\leftarrow M_{\mathrm{g}}({\mathbf{X}}_i(t)-\Delta {\mathbf{X}}_i;{\mu }_{\mathrm{pool}},{\sigma }_{\mathrm{pool}},y_{\max })$, $P_k^{\mathrm{new}}\leftarrow M_{\mathrm{g}}({\mathbf{X}}_k(t)+\Delta {\mathbf{X}}_i;{\mu }_{\mathrm{pool}},{\sigma }_{\mathrm{pool}},y_{\max })$. 42:                  Compute savings: $\Delta P\leftarrow (P_i^{\mathrm{new}}+P_k^{\mathrm{new}})-(P_i^{\mathrm{old}}+P_k^{\mathrm{old}})$. 43:              Select $S_k$ with maximum savings $-\Delta P>0$. 44:          If valid $S_k$ found, update: ${\mathbf{X}}_i(t)\leftarrow {\mathbf{X}}_i(t)-\Delta {\mathbf{X}}_i$, ${\mathbf{X}}_k(t)\leftarrow {\mathbf{X}}_k(t)+\Delta {\mathbf{X}}_i$, recompute $P_i(t),P_k(t)$. 45:          Log shift.

The process, as outlined in Figure 4 and Algorithm 1, manages a system of 100 servers to optimize resource usage and minimize power consumption through a FL-driven approach. Each server $S_i$ is initialized with a capacity vector (${\mathbf{C}}_i$):

$${\mathbf{C}}_i=[C_i^{\mathrm{CPU}},C_i^{\mathrm{Mem}},C_i^{\mathrm{Stor}},C_i^{\mathrm{Net}}]\in {\mathbb{R}}_{\ge 0}^4$$

(1)

representing its CPU ($C_i^{\mathrm{CPU}}$), memory ($C_i^{\mathrm{Mem}}$), storage ($C_i^{\mathrm{Stor}}$), and network (($C_i^{\mathrm{Net}}$)) capabilities. Then, a dynamic state vector (${\mathbf{X}}_i(t)$) is considered as

$${\mathbf{X}}_i(t)=[X_i^{\mathrm{CPU}}(t),X_i^{\mathrm{Mem}}(t),X_i^{\mathrm{Stor}}(t),X_i^{\mathrm{Net}}(t)]\in {\mathbb{R}}_{\ge 0}^4$$

(2)

capturing real-time resource usage ($X_i^{\mathrm{CPU}}(t),X_i^{\mathrm{Mem}}(t),X_i^{\mathrm{Stor}}(t),X_i^{\mathrm{Net}}(t)$, for CPU, memory, storage, and the network) at time t.

The strategy proceeds by updating each server’s usage metrics through sampling from uniform distributions: $X_i^{\mathrm{CPU}}(t)\sim \mathcal{U}(10,90)$, $X_i^{\mathrm{Mem}}(t)\sim \mathcal{U}(0.1,C_i^{\mathrm{Mem}})$, $X_i^{\mathrm{Stor}}(t)\sim \mathcal{U}(0.1,C_i^{\mathrm{Stor}})$, and $X_i^{\mathrm{Net}}(t)\sim \mathcal{U}(0.1,C_i^{\mathrm{Net}})$. Power consumption is calculated based on

$$P_i(t)=50+200{\left({\displaystyle \frac{X_i^{\mathrm{CPU}}(t)}{100}}\right)}^{1.5}+0.5X_i^{\mathrm{Mem}}(t)+3{(X_i^{\mathrm{Net}}(t))}^{1.2}+0.1X_i^{\mathrm{Stor}}(t)+\mathcal{N}(0,0.3)$$

(3)

incorporating contributions from all resources with an additional noise, which is Gaussian.

Next, each server trains a local $3\mathrm{rd}$-degree polynomial regression model on its dataset by

$${\mathcal{D}}_i={\{({\mathbf{x}}_{i,j},y_{i,j})\}}_{j=1}^{m_i}$$

(4)

where ${\mathbf{x}}_{i,j}\in {\mathbb{R}}^4$ represents resource usage, and $y_{i,j}\in \mathbb{R}$ is the power consumption. Features are standardized using

$${\mathbf{x}}_{i,j}\leftarrow {\displaystyle \frac{{\mathbf{x}}_{i,j}-{\mu }_i}{{\sigma }_i+{10}^{-10}}}$$

(5)

In Equation (5), ${\mathbf{x}}_{i,j}\in {\mathbb{R}}^4$ is the $j\mathrm{th}$ workload feature vector for server i, containing a CPU, memory, network, and storage usage. The symbol ${\mu }_i\in {\mathbb{R}}^4$ denotes the mean of the feature vectors in the local dataset ${\mathcal{D}}_i$ of server i. Additionally, ${\sigma }_i\in {\mathbb{R}}^4$ is considered as the standard deviation of the feature vectors in ${\mathcal{D}}_i$. A small constant ${10}^{-10}$ is added to ${\sigma }_i$ to prevent division by zero.

Then, the outputs are scaled: $y_{i,j}\leftarrow {\displaystyle \frac{y_{i,j}}{\max (y_{i,1},\dots ,y_{i,m_i})}}$. The data is split into 80% training and 20% validation sets, and the model minimizes the MSE ($J({\theta }_i)$):

$$J({\theta }_i)={\displaystyle \frac{1}{|{\mathcal{D}}_i^{\mathrm{train}}|}}\sum _{j\in {\mathcal{D}}_i^{\mathrm{train}}}{(y_{i,j}-{\widehat{y}}_{i,j})}^2$$

(6)

Performance is evaluated on the validation set using KPIs (MSE, Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Max Error).

Local models are aggregated by pooling all datasets as in

$${\mathcal{D}}_{\mathrm{pool}}=\bigcup _{i=1}^N{\mathcal{D}}_i$$

(7)

standardizing features and scaling outputs similarly, and training a global ($3\mathrm{rd}$)-degree polynomial regression model to minimize global MSE ($J({\theta }_{\mathrm{g}})$):

$$J({\theta }_{\mathrm{g}})={\displaystyle \frac{1}{m}}\sum _{j=1}^m{(y_j-{\widehat{y}}_j)}^2$$

(8)

The global model’s performance is assessed using the same KPIs.

Workload optimization identifies high-power servers ($P_i(t)>150$) in a set $\mathcal{H}$. For each $S_i\in \mathcal{H}$, a workload of Equation (9) is defined for transfer:

$$\Delta {\mathbf{X}}_i=[X_i^{\mathrm{CPU}}(t)/2,X_i^{\mathrm{Mem}}(t)/2,X_i^{\mathrm{Net}}(t)/2,X_i^{\mathrm{Stor}}(t)/2]$$

(9)

The proposed FL-driven strategy searches for a target server $S_k$ subject to the properties defined in

$$F(X_k,\Delta X_i,t)=\left\{\begin{array}{cc}1\hfill & \mathrm{if}\left\{\begin{array}{c}{X}_k^{\mathrm{CPU}}(t)+\Delta X_i^{\mathrm{CPU}}\le 90\hfill \\ X_k^{\mathrm{Mem}}(t)+\Delta X_i^{\mathrm{Mem}}\le 0.8C_k^{\mathrm{Mem}}\hfill \\ X_k^{\mathrm{Net}}(t)+\Delta X_i^{\mathrm{Net}}\le 0.8C_k^{\mathrm{Net}}\hfill \\ X_k^{\mathrm{Stor}}(t)+\Delta X_i^{\mathrm{Stor}}\le 0.8C_k^{\mathrm{Stor}}\hfill \end{array}\right.\hfill \\ 0\hfill & \mathrm{Otherwise}\hfill \end{array}\right.$$

(10)

The feasibility function for the system at time t, denoted $F(X_k,\Delta X_i,t)$, is defined as 1 if the presented conditions are satisfied. In this sequence, $\Delta X_i^{\mathrm{CPU}},\Delta X_i^{\mathrm{Mem}},\Delta X_i^{\mathrm{Net}},\Delta X_i^{\mathrm{Stor}}$ are the incremental resource demands, and $C_k^{\mathrm{Mem}},C_k^{\mathrm{Net}},C_k^{\mathrm{Stor}}$ are the capacity limits for Memory, Network, and Storage; otherwise, $F(X_k,\Delta X_i,t)=0$.

Power predictions from the global model are used to compute savings as

$$\Delta P=(P_i^{\mathrm{new}}+P_k^{\mathrm{new}})-(P_i^{\mathrm{old}}+P_k^{\mathrm{old}})$$

(11)

selecting the $S_k$ with maximum savings ($-\Delta P>0$). If a valid $S_k$ is found, workloads are updated, power is recomputed, and the shift is logged. If no valid target exists, the failure is logged.

Finally, the global model is finalized. Then, performance metrics and workload shift logs are logged, showing balancing resource usage and minimizing power consumption through FL-driven optimization.

As a result, each server will require fewer resources to handle the workload, leading to reduced power consumption while all dedicated workloads will be completed as intended.

Performance is evaluated using KPIs [37], such as MSE, MAE, MAPE, RMSE, and maximum error, summarized in

Table 1. Considered KPIs in this work.

Metric Name	Formulation	Best/Worst
MSE	${\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2$	0/$+\infty$
MAE	${\displaystyle \frac{1}{n}}{\sum }_{i=1}^n|y_i-{\widehat{y}}_i|$	0/$+\infty$
MAPE	${\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|{\displaystyle \frac{y_i-{\widehat{y}}_i}{y_i}}\right|\times 100$	0%/100%
RMSE	$\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(y_i-{\widehat{y}}_i)}^2}$	0/$+\infty$
Max. Error	${\max }_i\left|y_i-{\widehat{y}}_i\right|$	0/$+\infty$

where n, $y_i$, and ${\widehat{y}}_i$ are the total number of analyzed, real, and predicted values, respectively.

.

The Mean Square Error measures the average of the squared differences between predicted and actual values, emphasizing larger errors due to the squaring operation [37]. On the other side, the MAE quantifies the average magnitude of errors in a set of predictions, calculated as the average of the absolute differences between predicted and actual values [38]. Following this concept, the MAPE expresses the average absolute error as a percentage of the actual values, calculated by taking the absolute difference between predicted and actual values, dividing by the actual value, and averaging these percentages [39]. Additionally, the RMSE is considered a measure of the average magnitude of prediction errors in the same units as the original data [40,41]. Finally, maximum error represents the largest single deviation between a predicted and actual value in a dataset, capturing the worst-case scenario of a model’s predictions.

3. Results and Discussion

The proposed 100 servers are modeled in this section, and the FL strategy, with simultaneous training across all servers, is applied in the $GoogleColab$ platform. For the evaluation, the KPIs are calculated for the global model and each local model of servers. For the final phase, a log file is considered for the workload shift, including the initial and final servers. The results are shown in Figure 5, Figure 6, Figure 7 and Figure 8.

The proposed model reduced total power consumption across intervals, defined by workload distribution cycles, as shown in Figure 5. Power distribution became more consistent, demonstrating the model’s effectiveness in optimizing power efficiency and minimizing consumption disparities. Also, the term frequency, here means the repetitive number of servers over an identical power consumption. For example, there are about five servers that their final consumption is 150 W. As shown in Figure 6, the model balanced resource metrics, including CPU, memory, network, and storage, resulting in more uniform and optimized usage profiles. This highlights the model’s effectiveness in workload allocation, reducing bottlenecks and improving system performance.

The reduction in global model loss over successive epochs, shown in Figure 7, presents the learning convergence, confirming the effectiveness of the FL approach in adapting to server conditions and optimizing workload distribution. As depicted in Figure 6 the global model MSE decreases from approximately 2.5 to 1.0 across 10 epochs, demonstrating a steady improvement in model accuracy. This trend is complemented by the aggregated resource usage data in Figure 6 which manifests the stable average utilization of the CPU, memory, storage, and network resources over time intervals. The consistent resource usage, with the CPU and memory peaking around 40 units and storage and network remaining low, presents the efficient workload distribution and minimal overhead. Consequently, aggregated resource usage metrics remained stable over time, as shown in the results.

This observed stability, achieved through dynamic workload adjustments, underscores the robustness of the model in sustaining consistent performance even when server capacities fluctuate. Following implementation, server statuses were systematically categorized into four distinct power consumption levels—Low, Moderate, High, and Very High—as illustrated in Figure 8, providing a clear framework for monitoring and comparison. Notably, higher initial consumption levels were closely linked to increased memory and network activity, reflecting the greater strain placed on resources during peak demand. However, by intelligently redistributing workloads across servers, the system effectively alleviated these imbalances, mitigating excessive resource usage on heavily burdened nodes and narrowing disparities in utilization.

The proposed FL model reduced discrepancies in resource utilization by aligning workloads, ensuring balanced computational demands, and promoting equitable resource usage.

The model achieved the defined KPIs, with the least errors, as detailed in the Appendix A, demonstrating the precision and efficiency of the approach in optimizing workload allocation and enhancing system performance.

4. Conclusions

This study presented a novel FL-based intelligent workload allocation model designed to optimize server utilization. The approach treats each server as a client and utilizes a global model for dynamic workload distribution. Servers were categorized into five clusters, enabling targeted workload management. The FL model decentralized data processing, ensuring privacy and scalability. The global model aggregated local server data to dynamically balance workloads, minimizing bottlenecks and enhancing efficiency. The model’s effectiveness was assessed using KPIs, including resource utilization, load balancing, scalability, and power efficiency. Logs and detailed KPI analytics are provided in the appendix. By addressing critical demands for power-efficient and reliable CDCs, the proposed model presents a scalable solution to workload management. The challenges in this field involve ensuring secure and efficient communication between distributed servers acting as clients, handling heterogeneous server resources with varying CPU, memory, storage, and network capabilities. Additionally, managing the complexity of synchronizing model updates in a federated environment, addressing potential latency issues, safeguarding data privacy, and defending against cyber attacks during the FL process, such as model poisoning or data inference attacks, are critical concerns. Future work could focus on enhancing the scalability of the model to accommodate larger and more diverse CDC infrastructures, integrating adaptive learning mechanisms to respond to dynamic workload patterns in real time, exploring hybrid optimization approaches combining FL with other AI techniques, and implementing robust fault tolerance to ensure continuous operation despite server failures or communication disruptions. Moreover, extending the framework to consider renewable energy sources and considering environmental impacts, such as $C{O}_2$ footprint, could further optimize sustainability in CDC operations, while developing advanced security protocols to detect and mitigate cyber threats would strengthen the resilience of the system.