3.1. Model Framework

The attention layer, encoder layer, and prediction layer are the three primary layers that comprise the MASTGCNet model framework. The traffic data are initially converted using a tanh activation function for stability, starting with the flow input. A feature embedding block is then used to capture complicated patterns. After that, the traffic data are analyzed through several spatiotemporal attention (ST-Attention) layers to identify geographical and temporal correlations. The encoded data are sent to the encoder layer, which manages temporal patterns and dynamic traffic variations using multiscale temporal unit (MUST) modules and Dynamic Graph Generation Networks (DGGNs). After the traffic flows are adjusted, they enter the prediction layer, where a GCN is used to capture spatial dependencies, and a sequence of ResUnits further develop deep representations. Ultimately, the prediction output is generated by a fully connected (FC) layer, which uses the processed data to represent the expected traffic flows.

3.2. Modeling Dynamic Generation Graph Network Module

Consider a graph denoted by its adjacency matrix A ∈ R^N×N and the associated degree matrix D. Additionally, let θ ∈ R^C×F and b ∈ R^F symbolize the learning weights and biases, respectively. Here, X denotes the input, while Z denotes the output derived from the GCN layer. In the context of isolating a single node i for analysis, the operation performed by the GCN can be construed as effecting a transformation of the features of the node from an initial state, represented as Xⁱ ∈ R^1×C, to a result in the state denoted as Zⁱ ∈ R^1×F. Note that G_Conv represents the graph convolution operation, T₁(L) denotes the first-order Chebyshev polynomial applied to the graph Laplacian matrix L, and X represents the input feature matrix. In contrast, ⊖ denotes the learnable weight parameters.

Given an individual node, denoted as i, the procedure involves extracting parameters ⊖_i, unique to the i node, with a widely shared reservoir weight W_n, while exploiting the inherent node embeddings $$. Conceptually, this process can be seen as a mechanism for acquiring node-specific patterns by identifying specific patterns inherent in a broader collection of prospective patterns derived from all the traffic sequences.

3.3. Modeling Dynamic Multiscale Spatiotemporal Feature Unit

3.4. Modeling Attention-Based Spatiotemporal Module

To ensure robustness, we use a residual connection W^′ = W + Z during training phase. The resulting output of every node is denoted as Y^′ = U + W^′, and this process ultimately leads to the parallelization of outputs across all nodes, yielding $$.

To extend the scope of time series forecasting for extended prediction horizons, we intelligently capture bidirectional temporal dependencies over an extended period. This is accomplished within the structure of a sliding window, operating at each discrete temporal instance. The hierarchical architecture of the TT effectively captures complex dependencies across multiple layers, thereby enabling the prediction of long sequences without sacrificing computational efficiency by increasing the parameter T. In contrast, RNN-based methods face vanishing gradients, while models based on convolutional methods require an explicit specification of an expanding convolutional layer concerning the parameter T.

3.5. Multiscale Feature Extraction Unit

4.1. Efficient Cloud-Based Traffic Flow Analysis

In the context of edge-cloud computing, the prediction model performance is optimized in large part by the energy-efficient resource allocation. Through the distribution of computational activities between edge servers and the cloud, the edge-cloud architecture guarantees low latency and energy-efficient processing. By prioritizing tasks using the attention mechanism, the resource allocation technique enables the system to distribute computational resources and reduce energy usage dynamically. This method guarantees timely and effective traffic projections, particularly in smart city settings. This dual focus is reflected in the title, highlighting energy efficiency and traffic prediction, ensuring that both are well represented in the final solution.

We leverage the Azure platform as a service (PaaS) for our system, ensuring efficient resource allocation and task assignment, particularly when processing the vast amounts of data generated by IoV systems. Table 2 offers a comprehensive breakdown of the Azure resources utilized in our setup, meticulously optimizing for both performance and cost-effectiveness. In forecasting crowd flows for the near future, we prioritize energy-efficient resource allocation by employing a VM known as the A2 standard in Azure. With its 2 cores and 3.5 GB memory, this VM strikes a balance between computational power and energy consumption. To efficiently handle potential heavy traffic from numerous users, especially the data influx from IoV systems, we employ an energy-efficient task assignment strategy by hosting both the website and web service on an App Service. Furthermore, to minimize energy consumption while ensuring data accessibility, historical data are stored on local servers, while a 6-GB Redis cache efficiently caches real-time trajectories from the past half-hour, crowd flow data, extracted features from the past 2 days, and inferred results.

4.2. Local GPU Servers

While many tasks can be performed on the cloud, GPU services are unavailable in certain regions such as China. Implementing energy-efficient resource allocation and task assignment strategies is essential in optimizing cloud-based operations. Additionally, there are expenses associated with other edge computing services, such as storage and I/O bandwidth. Therefore, cost-saving measures are crucial for a research prototype. Moreover, transferring large volumes of data from local servers to the cloud is time-consuming due to limited network bandwidth. Energy-efficient data transfer protocols and task prioritization algorithms can help mitigate delays caused by data migration. For example, historical trajectories can span hundreds of gigabytes or even terabytes, resulting in significant delays when copying data from local servers to the cloud. Efficient compression algorithms and prioritization mechanisms can be employed to streamline the transfer process and minimize energy consumption.

4.3. Training Process

Algorithm 1 describes the training procedure of MASTGCNet. Backpropagation is used randomly to initialize and optimize the trainable parameters based on MASTGCNet. Backpropagation minimizes the loss function of our proposed model using the stochastic gradient method. We implement the dropout strategy approach to increase the overall effectiveness of our method. Algorithm 2 aims to optimize resource allocation for energy-efficient traffic flow prediction. During training, it iteratively adjusts the allocation of computational resources based on the processing time, prediction accuracy, and energy consumption. The optimization process involves fine-tuning the model and resource distribution to meet the constraints of maximum allowable processing time; minimum required prediction accuracy, and maximum available resources, ensuring that the model achieves high accuracy with minimal energy usage.

5.1. Experiment Setup and Datasets

We use a Linux server with numerous software, as defined later in Section 5.3, and hardware described in Table 3.

5.2. Compared Methods

To measure the overall performance of our approach, we conducted a comprehensive comparative assessment by comparing the MASTGCNet to prominent, well-known models and state-of-the-art methods in the field, including the following:

5.3. Implementation Details and Evaluation Metrics

5.4. Experiment Results and Analysis

Using the setup and settings mentioned above, we compared how well our MASTGCNet model performed against other competing methods on two real-world datasets: BikeNYC and TaxiBJ. The results are shown in Figures 5 and 6, respectively. The MASTGCNet stands out by achieving the lowest MAPE and RMSE values among all methods, demonstrating its superior performance. Specifically, for BikeNYC, the RMSE is about 4.02, and the MAPE is 18.75%. Similarly, for TaxiBJ, the MAPE is about 14.09 and the RMSE is about 12.43%, respectively. This indicates that our added attention and multiscale feature framework effectively improve the performance of the proposed model. We also use standard deviation, which serves as a valuable metric to assess the consistency and stability of traffic patterns, aiding in anomaly detection, model evaluation, and informed traffic management decisions.

We compared the average results of our method with other methods on two datasets, TaxiBJ and BikeNYC. The results are shown in Table 6. We calculated the average performance for each model by running it 10 times. Table 6 clearly shows that our proposed MASTGCNet model outperforms the other models regarding effectiveness and prediction accuracy. These results highlight the value of our model in understanding the spatiotemporal relationships in predicting traffic flows.

Our MASTGCNet method significantly reduces prediction errors during model training when combined with the spatiotemporal GCN. This demonstrates the adaptability of our method for urban traffic flow prediction. The efficiency of the MASTGCNet model exhibits consistent enhancement, particularly within the domain of long-term traffic flow prediction. In particular, traditional methods, such as ARIMA and HA, struggle to produce highly accurate forecasts, highlighting the limitations of approaches that ignore dynamic spatiotemporal dependencies and focus solely on historical statistical relationships. ARIMA focuses on modeling univariate time series and does not incorporate spatiotemporal correlations between different regions. This limitation prevents the model from exploiting important network structure and road system insights. Incorporating spatial correlations improves regression models such as FC-LSTM and GRU-ED, but they can still not capture the complex dynamic nonlinear spatial and temporal dependencies. The FC-LSTM cannot typically explicitly capture the spatial dependencies in traffic data, which can be crucial for accurate traffic flow prediction in scenarios where road networks play a significant role. Furthermore, our model outperforms the ST-ResNet and MST3D models. The ST-ResNet residual structure is limited in capturing the highly nonlinear relationships in complex traffic dynamics. Similarly, the MS3TD model has a higher number of hyperparameters that require thorough tuning to achieve optimal performance. Insufficient tuning can lead to suboptimal results.

The current methods struggle to predict traffic flow prediction in a given area accurately. Existing approaches such as CNN, RNN, and LSTM manually extract information from images, which reduces prediction accuracy. We need updated methods that automatically gather information using techniques such as the GCN and attention modules. These approaches dynamically gather information from models, improving prediction accuracy while saving time and resources. If we look at the figures (Figures 5 and 6) and compare them with existing methods, it is clear that existing models do not perform as well as our proposed model. Our proposed model achieves better accuracy regarding time, cost, and reliability. It is more reliable and adaptable because it dynamically processes information instead of manually manipulating images. We also combined our model with spatiotemporal techniques to improve training and reduce prediction errors. This combination also speeds up the training time, showing that our model can work well in different situations.

Our model combines the spatiotemporal GCN network to make training more accurate and reduce prediction errors. We tested our model against existing long-term traffic flow prediction methods and found that it performed much better. The existing models used CNN, LSTM, or RNN separately with manual data extraction, which made training longer instead of more efficient. To improve prediction accuracy, we need to extract features from the traffic flow data dynamically. Our model, which uses neural networks such as GCN and RNN with an attention mechanism, allows us to easily estimate traffic flow in a city, including the number of people entering and leaving. This allows us to reduce training time, make predictions more accurate, and save time and cost.

In addition, Figure 7 illustrates the prediction performance of various models across different horizons on the TaxiBJ dataset. Our proposed model consistently performs best across all prediction horizons and evaluation metrics, demonstrating its superior ability to capture heterogeneous spatiotemporal dependencies. While STDN shows comparable performance to our model in the first three horizons, its accuracy declines as the prediction horizon increases. This indicates that our model is robust to changes in prediction horizons and underscores the effectiveness of the temporal dependence extraction units in MASTGCNet.

5.5. Results of Different MASTGCNet Variants

To validate the effectiveness of the MASTGCNet method, we conducted a thorough empirical assessment, examining different variants while maintaining consistent experimental setups. Our evaluation focused on three key aspects: (i) assessing the impact of model depth, (ii) analyzing the effects of varying kernel and filter numbers, and (iii) investigating computational complexities, including prediction and training times. The subsequent sections delve into a detailed discussion of these findings, shedding light on our proposed algorithm’s performance and computational considerations.

5.5.1. Impact of Depth Model

We conducted an extensive empirical experiment with nine different variations of the MASTGCNet model, each characterized by different depths. We aim to achieve deeper insights into the effectiveness of different depths within the MASTGCNet model. The experimental results are shown in Figure 8. Focusing specifically on the TaxiBJ dataset, Figure 8 provides a detailed visualization of the impact of model depth. Our results show a compelling relationship between the number of residual units representing network depth and the RMSE metric. As we progressively increase the depth of the network by increasing the number of residual units, we observe an initial increase in RMSE, followed by a subsequent increase in RMSE. This trend indicates that deeper networks yield better results. Nevertheless, it is crucial to note that as the number of residual units exceeds a certain threshold, such as ≥ 12, the training process becomes more complex, and the risk of overfitting increases.

5.5.2. Impact of Filter Numbers and Filter Sizes

We have extensively explored different dataset training configurations to optimize filter size selection. Achieving precise prediction accuracy depends on the careful selection of filter size. As shown in Figure 9(b), we observed the profound impact of filter size on the performance of the MASTGCNet methodology. To carefully observe and illustrate the effects of filter size, we systematically adjusted the filter dimensions, ranging from 2 × 2 to 5 × 5. Figure 9(b) shows a noteworthy trend: an increase in kernel size corresponds to a decrease in the RMSE metric. In addition, as shown in Figure 9(a), the use of larger filter sizes consistently yields significantly better results than the use of smaller filter sizes. This pattern is consistent with our observations regarding filter size and number of filters.

5.6. The Convergence of MASTGCNet Model

Figure 10 illustrates the loss curve of the MASTGCNet model on two real datasets, depicting the training and validation RMSE during the experiment. In Figure 10(a), on the BikeNYC dataset, the RMSE for both the training and validation sets gradually decreases with increased training iterations. Around Iteration 65, the RMSE for both sets stabilizes. In Figure 10(b), for the TaxiBJ dataset, the RMSE for both the training and validation sets also decreases with increasing iterations, reaching stability around Iteration 128.

Figure 11 illustrates that the traffic state matrix varies across different time segments. Initially, the feature matrix before training appears random and unstructured. However, after training, the feature matrix displays distinct temporal patterns similar to the traffic state matrix. This demonstrates that the model successfully learns and abstracts temporal features for prediction.

5.7. Model Efficiency

Subsequently, we conduct a thorough investigation of the performance of our proposed model works both in predicting outcomes and in the training phase, taking into account the response time. We have summarized the results in Table 7. One thing that immediately stands out is that our MASTGCNet model performs better than the STDN and MST3D models in both the training and prediction phases. It is worth noting that the STDN method takes the longest time for both training and prediction. This is because STDN uses certain computations called local CNNs to make predictions, and it also has to go through the entire region using a sliding window. For example, if we work with a dataset like BikeNYC, predicting values for the entire region requires performing a certain computation 16 × 8 times. On the BikeNYC dataset, our MASTGCNet model significantly outperforms the ST-ResNet approach. This happens mainly because our MASTGCNet method combines two techniques, GCN and GRU, based on GCNs. We see a similar trend on the TaxiBJ dataset. Our MASTGCNet model outperforms both the MST3D and STDN baselines in terms of both prediction speed and training speed. These results demonstrate the advantages of our model.

The time and space complexities of Algorithm 1 are closely related to key parameters, mainly the amount of available historical information and the number of features. In particular, the complexities depend on two crucial factors: the training time, denoted by m, which is the time required to form the dataset D, and the learning time, denoted by n, which characterizes the time required to acquire knowledge within the model while keeping the computational overhead for θ constant. It is important to understand that the algorithm’s performance shows different behaviors under different circumstances. In the best-case scenario, the algorithm exhibits a time complexity denoted by ω(m + n). In this case, the computational cost escalates linearly with both training and learning times. This scenario represents an optimal match of algorithm efficiency with available computational resources, culminating in a favorable performance profile. Conversely, the worst-case scenario reveals a potentially significant time complexity that can rise to O((mn)(m + n)) and further simplifies to O(m²n + n²m). This particular scenario depends on the number of observations and the dimensionality of the features. This worst-case behavior serves as a stark reminder of the paramount importance of carefully considering resource constraints and dataset characteristics when implementing Algorithm 1.

6.1. Traffic Flow Prediction

In the field of traffic prediction, the incorporation of predictive spatial information is emerging as a key factor. Modern methods using convolution neural networks (CNNs) [27, 28] for traffic flow mapping often rely on grid-based map segmentation. However, the inherent regularity of grid-based data limits their ability to represent complex spatial information effectively. Reference [29] proposed a unique multitask spatiotemporal network for highway traffic flow prediction (MT-STNet) that combines multitask learning, generative inference system, and encoder–decoder structure. References [30, 31] (DCRNN) innovatively presented a diffusion convolution RNN based on distance graphs. Their approach incorporates bidirectional random walks on the graph to capture spatial dependencies.

However, the establishment of spatial topology in these methods through predefined adjacency matrices remains static and limited in nature, with inherent limitations in encapsulating the complex characteristics of complex road networks. Existing methods based on predefined graph structures face significant challenges. First, predefined graph constructs struggle with sparsity issues. Sparsity, which is particularly evident in large graphs, manifests itself in the adjacency matrix, leading to computationally inefficient operations and may fail to encapsulate the totality of spatial dependencies comprehensively. This, in turn, can potentially undermine the accuracy of the model [32]. A secondary concern revolves around the inflexible nature of predefined adjacency matrices, which makes them ill-suited for accommodating dynamic graphs or graphs characterized by recurrent structural changes [33].

In conjunction with the previous discourse on the construction of spatial topology, the strategic modeling of spatial and temporal dependencies emerges as a key factor in traffic prediction. Capturing temporal dependencies requires recourse to rRNNs and their diversification, which are expertly tailored to sequential data with intrinsic capabilities to capture temporal correlations of a temporal nature [34, 35]. The recurrent nature of RNN operations provides increased model flexibility. In Ref. [36], this paper proposes a unique deep learning approach to improve traffic volume forecasting accuracy by addressing these shortcomings. In order to create synthetic data or synthetic traffic volume, a new spatiotemporal dependencies generative adversarial network are first proposed.

In contrast to the more complicated LSTM [37], GRU advocates a simpler and more trainable architecture. Gaining prominence for their effectiveness and versatility, attention mechanisms [38] have found widespread application in various domains. These mechanisms automatically focus on central information extracted from historical input data. Graph attention networks (GANs) [5] have made significant progress in traffic prediction by constructing spatial models. STSGCN [39] introduces a novel concept by devising a synchronized GCN model for spatial and temporal aspects. These modules adeptly capture correlations across space and time. In Ref. [40], to further improve the traffic flow forecasting outcomes, the researchers offer a unique spatial–temporal gated hybrid transformer network (STGHTN), which utilizes global features by transformer and local information from temporal gated convolution and spatial gated graph convolution, respectively. We advised the MASTGCNet model, which combines the GCN with the attention unit to collectively incorporate both the features of spatiotemporal traffic flow, drawing inspiration from previous research as discussed above.

6.2. Attention Mechanism

The attention mechanism has become an important tool in various tasks such as language translation and image recognition, helping to decide which parts are most important to focus on Ref. [41]. This mechanism uses a process where a question and a set of key-value pairs create an output. The output is a mixture of the values, with the importance of each value determined using a compatibility function between the question and its key. Attention mechanisms are generally used in conjunction with convolutional or recurrent networks. In Ref. [42], they present an attention-based spatiotemporal graph attention network (ASTGAT) model for network degradation and oversmoothing issues. In Ref. [43], the model relies on attention to see connections between input and output. Recently, attention mechanisms have also been used in graph neural networks. In Ref. [44], they introduced gated attention networks for graph learning. In Ref. [45], a brand-new GCN dubbed TFM-GCAM incorporates attention mechanisms to better capture nodes’ dynamic properties and spatial–temporal attributes.