Spatio temporal attention mechanism for real time cellular traffic prediction

Data preprocessing

Preprocessing the data is an essential step to ensure that input features are reliable and consistent for model training. To preserve the temporal structure of the dataset, the original time intervals were retained. Any missing entries were handled using forward and backward fill techniques, maintaining continuity within the time series. Core traffic indicators such as SMS, call, and internet usage were normalized using Min-Max scaling, bringing all values into the [0, 1] range to support effective model learning. The dataset is then divided into training, validation, and testing subsets chronologically in 70%:15%:15% ratio respectively based on time, enabling a robust and temporally consistent evaluation of model performance. This research focuses on short-term forecasting, predicting the traffic load for the next 10-min interval using the previous 60 min of observations. Each model was trained on aggregated features including smsin, smsout, callin, callout, and internet usage to capture temporal dependencies in multi-service network behavior. This prediction window was chosen based on operational relevance in real-time network traffic optimization, enabling timely decisions for congestion control and resource allocation. The notations used throughout this article is summarized in Table 2.

Lightweight convolution module

In the proposed traffic prediction model, the LC module plays a crucial role in enhancing computational efficiency while maintaining high quality spatial feature extraction. In the proposed framework, the input data is represented in a structured spatio temporal format with dimensions $T_g\times D_g\times A_g$, where $T_g$ and $D_g$ correspond to the spatial width and height of the grid (e.g., $100\times 100$), and $A_g$ denotes the number of input channels typically normalized traffic features such as SMS, call volume, and internet usage.

To extract spatial features, a convolutional kernel of size $E\times E$ is applied, resulting in an output feature map of shape $T_o\times D_o\times A_o$. This operation is performed with stride 1, no padding, and zero bias, ensuring that spatial locality is preserved without increasing the input dimensions. To reduce computational overhead, we employ DSC instead of standard convolution. The total number of trainable parameters $R_a$ in a conventional convolution is given by Eq. (2).

(2) $$R_a=E\times E\times A_g\times A_o$$where $E\times E$ is the kernel size and $A_o$ is the number output channels. The corresponding computational cost $A_f$ is expressed by Eq. (3).

(3) $$A_{\mathrm{f}}=E\times E\times A_g\times D_o\times T_o\times A_o.$$

This can be computationally expensive for large spatial grids and deep networks. To address this, we use DSC, which breaks the process into two lightweight stages. First, a depthwise convolution applies one $E\times E$ filter per input channel without combining them, resulting in the parameter count $R_p$ given by Eq. (4).

(4) $$R_{\mathrm{p}}=E\times E\times A_g.$$

The corresponding computational cost $A_{\mathrm{p}}$ is given by Eq. (5).

(5) $$A_{\mathrm{p}}=E\times E\times A_g\times D_o\times T_o.$$

Subsequently, a pointwise convolution using $1\times 1$ kernels combines channel-wise information. This operation adjusts the channel dimension and has a parameter count $R_i$ expressed in given by Eq. (6).

(6) $$R_{\mathrm{i}}=1\times 1\times A_g\times A_o$$with its computational cost $A_{\mathrm{i}}$ defined in Eq. (7).

(7) $$A_{\mathrm{i}}=1\times 1\times D_o\times T_o\times A_g\times A_o.$$

Thus, the total number of parameters $R_s$ and overall computation $A_v$ for the DSC are then significantly reduced, as defined by Eqs. (8) and (9).

(8) $$R_{\mathrm{s}}=E\times E\times A_g+1\times 1\times A_g\times A_o$$

(9) $$A_{\mathrm{v}}=E\times E\times A_g\times D_o\times T_o+1\times 1\times D_o\times T_o\times A_g\times A_o.$$

For example, with a kernel size $E=3$, number of input channels $A_g=3$, and output channels $A_o=64$, the standard convolution requires.

$$3\times 3\times 3\times 64=1,728\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{s}.$$

In contrast, the DSC only needs.

$$3\times 3\times 3+1\times 1\times 3\times 64=27+192=219\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{s}.$$

This represents a significant reduction in parameter count and computational complexity.

Before feature extraction, the input is normalized using a Batch Normalization (BN) layer, and a Rectified Linear unit (ReLU) activation function is applied to introduce non-linearity, defined as in Eq. (10).

(10) $$\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}(x)=max\{0,x\}.$$

Additionally, a preliminary $1\times 1$ convolution is used to reduce the number of channels before the depthwise convolution, further minimizing parameter count. Together, these steps enable the LC module to efficiently extract spatial features from cellular traffic data while keeping the model lightweight and suitable for large-scale real-time applications.

Efficient hybrid attention module

To further enhance spatial and temporal feature representation while maintaining computational efficiency, the proposed model incorporates an EHA mechanism. This module focuses the model’s attention on the most informative features across both Channel Attention (CA) and Spatial Attention (SA), ensuring that important traffic patterns are effectively captured without introducing significant computational overhead. The process begins by taking the output $X_g^{(c,t)}$ from the LC layer, where $c$ and $t$ refer to the channel and time step, respectively. First, the input undergoes a normalization operation, followed by the application of the ReLU activation function to produce the feature map $X_i^{(c,t)}$. This process can be mathematically expressed as shown in Eq. (11).

(11) $$X_i^{(c,t)}=\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}\left(\mathrm{B}\mathrm{N}(X_g^{(c,t)})\right).$$

Next, the feature map $X_i^{(c,t)}$ is refined using the ECA mechanism. Global average pooling is first applied, followed by a 1D convolution and sigmoid activation to generate channel attention weights $D_f^{(c,t)}$. These weights are then multiplied element-wise with the input to obtain the output $X_f^{(c,t)}$, as shown in Eq. (12). This lightweight approach highlights important feature channels while keeping parameter count low.

(12) $$X_f^{(c,t)}=D_f^{(c,t)}\cdot X_i^{(c,t)}.$$

Following channel attention, a SA mechanism is applied to focus on the most informative regions in the spatial domain. Max pooling and average pooling operations are performed along the channel axis, and their results are concatenated and passed through a convolutional layer with a $7\times 7$ kernel. A sigmoid function is then used to generate the spatial attention weights $D_l^{(c,t)}$, which are multiplied element-wise with the input to produce the output feature map $X_s^{(c,t)}$, as defined in Eq. (13).

(13) $$X_s^{(c,t)}=D_l^{(c,t)}\cdot X_f^{(c,t)}.$$

To further refine the learned representation, the feature map $X_b^{(c,t)}$ is processed with another batch normalization and ReLU activation, yielding $X_v^{(c,t)}$ as shown in Eq. (14).

(14) $$X_v^{(c,t)}=\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}(\mathrm{B}\mathrm{N}(X_b^{(c,t)})).$$

Finally, a SE Block refines channel importance. Average pooling is applied, followed by two linear layers with ReLU and sigmoid activation’s to generate attention weights $D_o^{(c,t)}$. These are multiplied with the input $X_v^{(c,t)}$ to produce the final output $Q_s^{(c,t)}$, as defined in Eq. (15).

(15) $$Q_s^{(c,t)}=D_o^{(c,t)}\cdot X_v^{(c,t)}.$$

In summary, the EHA module combines lightweight channel and spatial attention mechanisms to selectively emphasize critical features in both domains. This results in improved model focus, higher prediction accuracy, and reduced computational burden making it particularly well suited for large-scale and real-time cellular traffic forecasting.

Spatio temporal model with attention mechanism

To enhance the precision of cellular traffic forecasting, the final stage of the proposed architecture introduces a spatio-temporal model with attention mechanism. This module is designed to capture complex interactions between spatial locations and their evolving temporal patterns. While the preceding LC and EHA layers focus on extracting spatial features and emphasizing salient channels or regions, the STAM module complements this by enabling the model to attend to significant time intervals and spatial regions dynamically. Let the input to the STAM be a feature map denoted as $B\in {\mathbb{R}}^{Q_g\times T_g\times D_g\times A_g}$, where, $Q_g$ is the number of time intervals (e.g., 144 for a full day), $T_g$ and $D_g$ represent the height and width of the spatial grid, $A_g$ denotes the number of feature channels (e.g., SMS, calls, internet).

To model temporal dependencies for each spatial location, we reshape the input tensor into $B^{\prime }\in {\mathbb{R}}^{Q_g\times (T_g\cdot D_g)\times A_g}$, treating each spatial location independently across time. A learnable attention matrix $A_{\mathrm{a}\mathrm{t}\mathrm{t}}\in {\mathbb{R}}^{A_g\times A}$ is used to project the features to a lower-dimensional space. The attention weights $\alpha$ are then computed by the Eq. (16).

(16) $$\alpha =\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}\left({(B^{\prime }\cdot A_{\mathrm{a}\mathrm{t}\mathrm{t}})}^{Q_g}\right).$$

These attention scores determine the importance of each time interval at every spatial location. The refined temporal representation $\gamma$ is calculated using Eq. (17).

(17) $$\gamma =\alpha \cdot B^{\prime }.$$

Feature fusion and output prediction is to retain both the original and temporally refined representations, we concatenate them along the feature axis by the Eq. (18).

(18) $$\overline{R}=B^{\prime }\oplus \gamma .$$

The concatenated features $\overline{R}$ are then passed through a fully connected layer with a weight matrix G, followed by a ReLU activation to produce the final prediction $\overline{P}$ by Eq. (19).

(19) $$\overline{P}=\mathrm{R}\mathrm{e}\mathrm{L}\mathrm{U}(\overline{R}\cdot G).$$

In practical terms, the STAM functions like a dynamic reviewer that learns to re-focus on the most informative time intervals and spatial locations in the data. This mirrors human reasoning, where recent spikes in traffic or historically congested zones are prioritized for decision-making. By attending to these patterns adaptively, the model generates more accurate and context-aware traffic predictions.

The novelty of STAM lies in its adaptive integration of LC and EHA for joint spatial-temporal learning. Unlike CNN-LSTM or ConvLSTM models that rely on deep, sequential layers, STAM captures essential spatial and temporal features simultaneously with minimal parameters. This design achieves superior efficiency, faster inference, and better interpretability, making it a practical and scalable solution for real-time cellular traffic prediction.

Environment setup

The experiments were conducted on a workstation equipped with an Intel Core i9-12900K CPU (3.2 GHz, 16 cores), 64 GB DDR5 RAM, and an NVIDIA RTX 3090 GPU (24 GB VRAM), Ubuntu 22.04 LTS. The models were implemented using Python 3.10 with PyTorch 2.0.1, PyTorch Lightning 1.7.7, and PyTorch Forecasting 0.10.3 frameworks. Supporting library includes NumPy 1.24.2, Pandas 1.5.3, Scikit-learn 1.2.2, and Matplotlib 3.7.1. To maintain experimental integrity each experiments were repeated three times and the mean values of RMSE, MAE, and SMAPE are reported for performance evaluation.

Evaluation indicators

The proposed model is evaluated through RMSE, MAE, and SMAPE metrics. The RMSE, is a commonly used statistic to evaluate the performance of regression models. It is employed to measure the difference between the observed actual values and the predicted values. RMSE can be used to evaluate a regression model’s performance in a continuous numerical prediction job, its expression is given below in Eq. (20).

(20) $$RMSE=\sqrt{\frac{1}{X\times Y}\sum _{x=1}^X\sum _{y=1}^Y{({\hat{P}}^{(x,y)}-P^{(x,y)})}^2}.$$

MAE is a commonly used metric to assess regression model’s efficiency. RMSE includes squaring operations, but MAE does not. Instead, it finds the mean of the absolute variances between the values that are actual and those that are expected. The average difference between expected and actual values can therefore be captured more precisely by MAE due to its improved adaptability and insensitivity to outliers. The MAE formula can be found in the following Eq. (21).

(21) $$MAE=\frac{1}{X\times Y}\sum _{x=1}^X\sum _{y=1}^Y|{\hat{P}}^{(x,y)}-P^{(x,y)}|$$where $P^{(x,y)}$ represents the model’s predicted value and $p^{(x,y)}$ the actual value.

SMAPE is used to evaluate how close the predicted values are to the actual. It calculates the error as a percentage, giving a fair measure of both overestimation and underestimation. Unlike traditional error metrics that depend on data scale, SMAPE adjusts the error by considering both the predicted and actual values, making it effective for comparing model accuracy across different data ranges. It’s mathematical expression is presented in Eq. (22).

(22) $$SMAPE=\frac{1}{N}\sum _{i=1}^N\frac{|{\hat{P}}_i-P_i|}{(|P_i|+|{\hat{P}}_i|)/2}.$$

A lower SMAPE value indicates a higher level of forecasting precision and model robustness. To assess the model’s performance, we analyze the error loss between predicted and actual values across multiple iterations to confirm convergence. The model is trained and tested on three traffic types SMS, calls, and internet usage.

The prediction ability of the models used in this research was assessed in terms of the coefficient of determination i.e., $R^2$ which is a popular regression measure that estimates the degree of similarity between the model’s predictions and the real observed values. The $R^2$ score shows how much a model captures the variance of the target variable. Its mathematical expression is presented in Eq. (23).

(23) $$R^2=1-\frac{{\sum }_{i=1}^n{(y_i-{\hat{y}}_i)}^2}{{\sum }_{i=1}^n{(y_i-\overline{y})}^2}$$where, $y_i$ is the actual value, ${\hat{y}}_i$ is the predicted values.

Accurate traffic prediction is critical for optimizing network efficiency in next-generation cellular systems. This study introduces a framework that integrates lightweight convolution, an efficient hybrid attention mechanism, and a temporal attention module. The proposed model is designed to enhance key performance indicators such as QoS, SE, and NU, with each metric mathematically defined to ensure robust performance in 5G environments.

Comparison with baseline models

In this section we have compared our proposed model with baseline models in terms of their RMSE, MAE, and SMAPE for SMS, call, and internet traffic data services. To ensure a fair comparison, all baseline models were implemented and tuned under consistent experimental conditions using the same training, validation, and testing data set splits. The hyperparameter tuning of the baseline models are presented in Table 3.

The comparison of model performance can be found from Table 4, it is observed that the traditional models like Historical Average (HA) and ARIMA were limited in capturing dynamic and spatial traffic patterns. Deep learning models such as RNN and LSTM improved temporal learning but lacked spatial awareness, reducing their effectiveness on regionally distributed data.

The proposed STAM model shows strong accuracy while staying lightweight and efficient. Unlike models like DCG-MAM, STMP, and TFT, which need heavy computation or extra data, STAM uses simple yet powerful layers to detect local trends, connect past and future patterns, and understand how traffic changes across time and locations. While previous models such as STEHA performed well, they were often slow or required high-end devices. STAM balances performance and efficiency, making it a better fit for real-time use, especially in future 6G networks and systems with limited resources.

Ablation study

To understand the importance of each module in the proposed framework, an ablation study was conducted. The complete model integrates LC, EHA, and STAM. For fair comparison, each module was removed individually while keeping the others intact. This allows us to isolate the contribution of each component and observe its effect on overall performance. The ablation analysis shows that each module contributes meaningfully to the overall framework presented in Table 6. From the ablation study it is evident that the proposed model is performing slightly better as compared to the model without LC or EHA or STAM.

Comparison with related work

From the results obtained from our experiment, it is observed that the traffic prediction is influenced by many factors such as LC, EHA, and STAM. Our proposed STAM model is compared with existing models like ARIMA, LSTM, DCG-MAM, STMP, and TFT. While these models have their own advantages, they often miss complex time and location-based traffic patterns. STAM handles these better, giving more accurate results with fewer errors across different types of network traffic. Followings are the observations drawn from this study.

• The proposed STAM model, which integrates LC, EHA, and STAM, shows significant improvements in traffic prediction accuracy.

• Compared to the classical ARIMA (Moayedi & Masnadi-Shirazi, 2008) model, STAM achieves nearly 99.8% reduction in error across all traffic types, proving that traditional linear models are less effective for complex network data.

• When compared with the LSTM (Graves & Graves, 2012) model, which is commonly used for time series prediction, STAM reduces both average and peak errors by over 99%, demonstrating the benefits of attention-based architectures over recurrent ones.

• Spatio Temporal Efficient Hybrid Attention (STEHA) (Su et al., 2024) models spatial and temporal features separately, while STAM outperforms it by up to 98% and unifies lightweight convolution with spatio temporal attention, enabling joint learning of local, temporal, and spatial patterns. This unified design yields lower prediction errors.

• In comparison with the TFT (Kougioumtzidis et al., 2025), a widely used attention-driven forecasting model, STAM outperforms it by up to 97%, showing its ability to offer accurate, lightweight, and efficient predictions across various Telecom datasets.

• Compared to STMP, STAM (Gong et al., 2025) provides more than 93% improvement, indicating better handling of both spatial and temporal dependencies.

• Against the hybrid DCG-MAM (Xiao et al., 2025) model, which uses graph-based learning and attention mechanisms, STAM still achieves up to 45% lower errors, highlighting its superior learning capacity and robustness.

Additionally, we conducted a comparative analysis to evaluate the effectiveness of our proposed model against the baseline models such as STEHA, TFT, STMP, DCG-MAM. Figures 8, 9, 10 illustrates the prediction results across three types of services such as SMS, call, and internet while comparing our proposed model with all the baselines. Where, $x$ axis represents time, while the $y$ axis shows the normalized traffic volume for each service. From the result it is evident that the predictions generated by our model align more closely with the actual values compared to those from the baseline model. This clearly demonstrates the proposed model’s capability to capture essential patterns in cellular networks.

Table 7 highlights the performance of the proposed STAM model across multiple datasets, including Telecom Italia, the Big Data Challenge, and cellular traffic data from the Milan area. Unlike previous methods that often showed inconsistent performance across different datasets and traffic types, STAM delivers consistently low error rates for Call, SMS, and Internet traffic across all benchmarks. The results clearly demonstrate the superior performance of the STAM model on the datasets, achieving remarkably low RMSE values of 0.018 for call, 0.010 for sms, and 0.012 for internet substantially outperforming earlier approaches and highlighting the model’s effectiveness in capturing spatio temporal patterns in cellular traffic data. This consistent accuracy across diverse datasets demonstrates the adaptability and generalization capability of the STAM model, making it highly effective for real-world cellular traffic prediction scenarios.

STAM stands out by combining three streamlined yet powerful methods lightweight convolutions for efficient local pattern detection, hybrid attention that intelligently maps past data to future predictions, and spatio temporal attention to model how usage shifts both across time and regions. Unlike earlier models, which either relied on computationally heavy architectures (like 2D-CNN or hybrid networks) or separated spatial and temporal processes, STAM handles everything in a unified and resource-efficient manner. This cohesive design enables STAM to reduce average and extreme forecasting errors measured through RMSE and MAE by over 99% across three different telecom datasets, significantly outperforming traditional solutions. Its success reflects recent findings in spatio temporal attention research that emphasize the benefits of integrating attention mechanisms with efficient convolutional structures.

Estimation of QoS, network utility, and spectrum efficiency

In addition to forecasting cellular traffic, the proposed lightweight deep learning model is extended to support the estimation of key performance indicators including QoS, NU, and SE. These indicators are vital for maintaining reliable, fair, and efficient network operations, especially in dense and dynamic urban cellular environments.

Estimation of quality of service

QoS evaluation has become a crucial field of research due to the growing need for dependable and reliable telecommunications services. QoS is a measure of a network’s performance as seen by its users, usually impacted by packet loss, latency, and throughput. A mathematical methodology for assessing QoS is presented in this research utilizing an actual dataset of telecommunications activities, such as voice calls, SMS, and internet usage. The suggested method computes an overall QoS score by normalizing these metrics, combining them into a single throughput measure, and correcting for the negative effects of packet loss and latency. The proposed traffic prediction model can improve QoS by guaranteeing dependable and consistent network performance. The model’s ability to predict traffic patterns accurately can assist minimize congestion, which lowers latency and improves service quality (Mazhar et al., 2023). QoS is commonly described by the metrics latency $L_P$, throughput $T_P$, and packet loss rate $P_L$, that can be expressed as per the following Eq. (24).

(24) $$QoS=\frac{T_P}{L_{norm}+P_{norm}}.$$

Throughput $(T_P)$ is computed by aggregating normalized and weighted components from SMS, call, and internet usage data. Equations (25) and (26) compute the weighted contributions of in and out SMS, and call volumes respectively, using their normalized values. Equation (27) accounts for normalized internet activity, also weighted accordingly. Finally, Eq. (28) combines these partial components to form the complete traffic input value $(T_P)$, capturing the composite activity across all modalities.

(25) $$T_{P1}=w_{\mathrm{s}\mathrm{m}\mathrm{s}\mathrm{\_}\mathrm{i}\mathrm{n}}\cdot \frac{{\mathrm{S}\mathrm{M}\mathrm{S}}_{\mathrm{i}\mathrm{n}}}{{\mathrm{S}\mathrm{M}\mathrm{S}}_{\mathrm{i}\mathrm{n},\mathrm{m}\mathrm{a}\mathrm{x}}}+w_{\mathrm{s}\mathrm{m}\mathrm{s}\mathrm{\_}\mathrm{o}\mathrm{u}\mathrm{t}}\cdot \frac{{\mathrm{S}\mathrm{M}\mathrm{S}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{S}\mathrm{M}\mathrm{S}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{m}\mathrm{a}\mathrm{x}}}$$

(26) $$T_{P2}=w_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{\_}\mathrm{i}\mathrm{n}}\cdot \frac{{\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}}_{\mathrm{i}\mathrm{n}}}{{\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}}_{\mathrm{i}\mathrm{n},\mathrm{m}\mathrm{a}\mathrm{x}}}+w_{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{\_}\mathrm{o}\mathrm{u}\mathrm{t}}\cdot \frac{{\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{C}\mathrm{a}\mathrm{l}\mathrm{l}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{m}\mathrm{a}\mathrm{x}}}$$

(27) $$T_{P3}=w_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{t}}\cdot \frac{\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{t}}{{\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{t}}_{\mathrm{m}\mathrm{a}\mathrm{x}}}$$

(28) $$T_P=T_{P1}+T_{P2}+T_{P3}$$where w_{sms_in}, w_{sms_out}, w_{call_in}, w_{call_out}, represent the weights assigned to each metric based on its relative importance to network performance. The terms $\mathrm{S}\mathrm{M}{\mathrm{S}}_{\mathrm{i}\mathrm{n}}$, $\mathrm{S}\mathrm{M}{\mathrm{S}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$, $\mathrm{C}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{i}\mathrm{n}}$, $\mathrm{C}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$, $\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{e}\mathrm{t}$ denote the observed traffic values, while the terms $\mathrm{S}\mathrm{M}{\mathrm{S}}_{\mathrm{i}\mathrm{n},\mathrm{m}\mathrm{a}\mathrm{x}}$, $\mathrm{S}\mathrm{M}{\mathrm{S}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{m}\mathrm{a}\mathrm{x}}$, $\mathrm{C}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{i}\mathrm{n},\mathrm{m}\mathrm{a}\mathrm{x}}$, $\mathrm{C}\mathrm{a}\mathrm{l}{\mathrm{l}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{m}\mathrm{a}\mathrm{x}}$, and $\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{n}\mathrm{e}{\mathrm{t}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ denote the maximum values used to normalize the corresponding traffic features. Latency $L_P$ refers to the delay in data transmission over the network. In this framework, latency is normalized using the following Eq. (29).

(29) $$L_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}=\frac{L_P}{L_{\mathrm{m}\mathrm{a}\mathrm{x}}}$$where, $L_P$ represents the observed latency (in milliseconds). $L_{max}$ is the network’s maximum allowable latency threshold, such as 100 ms. Packet loss $P_L$ measures the percentage of data packets lost during transmission. It is normalized as expressed in the following Eq. (30).

(30) $$P_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}=\frac{P_L}{P_{\mathrm{m}\mathrm{a}\mathrm{x}}}.$$

Let $P_L$ represent the observed packet loss as a percentage, and let $P_{\mathrm{m}\mathrm{a}\mathrm{x}}$ denote the maximum acceptable packet loss threshold. The QoS score is calculated by combining the throughput with the effects of latency and packet loss. A penalty function is used to account for these impairments. The formula for QoS is in the Eq. (31).

(31) $$QoS=\frac{T_P}{L_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}+P_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}+\epsilon }\cdot 100.$$

Let $T_P$ denote the throughput, as previously defined. The normalized latency is represented as $L_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}$, while the normalized packet loss is denoted by $P_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}$. A small constant, ε, typically set to ${10}^{-5}$, is used to avoid division by zero. To ensure interpretability, the QoS score is expressed as a percentage and is limited to a maximum of $100\%$ the result shown in Fig. 11.

A crucial component of network performance, QoS indicates the network’s capacity to provide dependable and consistent services. For applications like virtual reality and driver less cars that need high bandwidth and low latency, QoS is crucial in the context of next generation cellular networks. Efficient resource allocation is made possible by accurate traffic prediction, which is essential to preserving QoS. The network can efficiently distribute bandwidth during peak hours by accurately predicting traffic loads. This reduces congestion and guarantees steady service quality, both of which are essential for improving user pleasure and experience.

Estimation of spectrum efficiency

To enhance resource utilization, the model leverages spatio temporal attention mechanisms. By accurately predicting traffic demand patterns, it enables more efficient spectrum allocation and ensures optimal use of available bandwidth. This capability is particularly crucial for cellular networks, where the growing number of connected devices demands effective management of limited spectrum resources. The throughput $(T{P}_t)$ at time t is calculated as the average of the actual throughput $(A{T}_t)$ and the predicted throughput $(P{T}_t)$ represents in Eq. (32).

(32) $$T{P}_t=\frac{A{T}_t+P{T}_t}{2}$$where $A{T}_t$ denotes the actual throughput at time $t$ (in bits per second), $P{T}_t$ represents the predicted throughput at the same time, and $T{P}_t$ is the average observed throughput at time $t$, also measured in bits per second.

Spectrum efficiency is calculated as the ratio of throughput to the total bandwidth (BW). The spectrum efficiency $(S{E}_t)$ at time $(t)$ is expressed in Eq. (33).

(33) $$S{E}_t=\frac{T{P}_t}{BW}.$$

The total bandwidth (in Hz) is represented by BW. Here, $BW=20\mathrm{M}\mathrm{H}\mathrm{z}=20\times {10}^6\mathrm{H}\mathrm{z}$, and $S{E}_t$ represents the spectrum efficiency at time $t$ (in bps/Hz). The sum of the throughputs for each observation is the total throughput $T{P}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ for all time periods represents in Eq. (34).

(34) $$T{P}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\sum _{t=1}^{T}T{P}_t$$where $(T)$ the sum of all time periods. Throughput at time $(t)$ is represented by $(T{P}_t)$. The overall spectrum efficiency $S{E}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$, is calculated by dividing the entire throughput by the bandwidth in Eq. (35).

(35) $$S{E}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=\frac{T{P}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}{BW}$$where total throughput (measured in bits per second) is represented by $T{P}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$. Bandwidth (measured in hertz) represented by bandwidth (BW). $S{E}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ the overall spectrum efficiency, expressed in bits per second. Total throughput, expressed in bits per second and represented by the symbol $T{P}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$, is the cumulative data rate over all time periods. Usually expressed in hertz (Hz), BW is the range of frequencies that can be employed for transmission. Bits per second/hertz (bps/Hz) is the unit of measurement for overall spectrum efficiency, $S{E}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$,which is determined by dividing the entire throughput by the bandwidth. This measure offers an evaluation of how well data is being transmitted using the available bandwidth. The result shown in the Fig. 12.

This value reflects the total amount of data transmitted during the observed time period. However, its magnitude alone does not provide insight into the model’s effectiveness unless it is evaluated in the context of available bandwidth and network traffic demands. The overall spectrum efficiency achieved is 2.1188 bps/Hz, which serves as a key measure of how efficiently the bandwidth is utilized for data transmission. It represents the ratio of throughput to the bandwidth in use. To enhance spectrum efficiency and enable the network to manage fluctuating traffic loads while minimizing congestion (Hu & Qian, 2014), the proposed model employs advanced techniques. Achieving higher spectrum efficiency is vital for the optimal utilization of limited frequency resources, especially in next generation cellular systems. This strategy not only improves the quality of service but also reduces operational costs, ultimately boosting the performance and economic viability of the network infrastructure.

Estimation of network utility

The model improves network utility by accurately predicting traffic, enabling proactive resource allocation and reducing congestion risks. Its use of temporal attention and lightweight convolution ensures efficient, adaptive management of network loads. This leads to more stable performance and supports high demand applications like autonomous systems and smart cities.

Network utility is a key performance indicator used to assess the overall quality of a network. It provides a quantitative measure of how well the network performs by considering multiple factors such as throughput, latency, and resource allocation. A higher network utility score generally suggests better performance, with more efficient resource usage and optimized network conditions. The calculation of NU integrates three fundamental components efficiency, penalty, and QoS. Traffic Demand (TD) is calculated as the sum of incoming and outgoing calls and SMS denoted by $T{D}_t$ in the Eq. (36).

(36) $$T{D}_t={\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{i}\mathrm{n}}_t+{\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{t}}_t+{\mathrm{s}\mathrm{m}\mathrm{s}\mathrm{i}\mathrm{n}}_t+{\mathrm{s}\mathrm{m}\mathrm{s}\mathrm{o}\mathrm{u}\mathrm{t}}_t.$$

Allocated Resources (AR) where $A{R}_t$ denotes the time index in the below Eq. (37).

(37) $$A{R}_t=1.1\times T{D}_t.$$

Throughput $T{P}_t$ is defined as the average of the actual throughput and the predicted throughput, as shown in Eq. (38).

(38) $$T{P}_t=\frac{{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{\_}\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{p}\mathrm{u}\mathrm{t}}_{\mathit{t}}+{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{\_}\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{o}\mathrm{u}\mathrm{g}\mathrm{h}\mathrm{p}\mathrm{u}\mathrm{t}}_{\mathit{t}}}{2}.$$

Efficiency $E_t$ quantifies how effectively the allocated resources meet the traffic demand, as defined in Eq. (39).

(39) $$E_t=min\left(\frac{A{R}_t}{T{D}_t},1\right).$$

Congestion Penalty $P_t$ is applied when traffic demand exceeds allocated resources in Eq. (40).

(40) $$P_t=\{\begin{array}{cc}k\times {(T{D}_t-A{R}_t)}^2\hfill & \mathrm{i}\mathrm{f}T{D}_t>A{R}_t,\hfill \\ 0\hfill & \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}.\hfill \end{array}$$

$Qo{S}_t$ is calculated as a weighted combination of throughput and latency in Eq. (41).

(41) $$Qo{S}_t=\alpha \times T{P}_t-\beta \times {\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{y}}_t$$where ( $\alpha$) is the weight for throughput. ( $\beta$) is the weight for latency. NU is the summation of utility scores over all time intervals in Eq. (42).

(42) $$NU=\sum _{t=1}^T\left(E_t-P_t+Qo{S}_t\right)$$where $E_t$ is the efficiency, and $P_t$ is the congestion penalty. $(Qo{s}_t)$ is the quality of service, $(T)$ is the total number of time intervals. Network utility quantifies the performance by assessing how well resource allocation meets traffic demands. NU Efficiency captures the alignment between allocated resources and user needs, while penalties account for congestion when demand exceeds capacity. To reflect user experience, the metric integrates QoS parameters higher throughput and lower latency increase utility. This combined approach offers a holistic measure for optimizing resource allocation under varying network conditions.

The model shows different learning behaviors for SMS, call, and internet data. SMS data converges quickly and stabilizes early, while call data takes longer, indicating higher complexity. Internet data shows minor fluctuations before rapid convergence. Figure 13 illustrates these trends, helping assess learning speed, stability, and overfitting. This analysis supports early detection of training issues and guides parameter tuning. Model convergence is verified by comparing predicted and actual errors across iterations using each data type.

Limitations and future scope

• The proposed framework focuses on short-term forecasting. Hence, its performance over longer horizons may require further validations.

• A grate computational effort is required when adopting the proposed framework on large scale datasets while performing long-term traffic forecasting.

• The work reported in this study can be suitably extended for resource allocation and optimization in 5G and beyond cellular networks.