With the rapid development of the Internet of Things (IoT) and urban computing, the massive deployment of sensors provides a reliable source of data for intelligent transportation systems [1, 2]. To alleviate the pressure of the growing population and vehicles in urbanization, research on data-driven traffic systems has become a hot topic in academia and industry. Traffic prediction, as a fundamental-level task of Intelligent Transportation System (ITS), supports a large number of upper-layer applications on the traffic scene, such as congestion warning, route planning and location services [3]. Traffic forecasting is achieved through the statistics, analysis and summary of historical traffic data to realize the judgment of future flow trends [4]. In traffic management and control systems, accurate traffic forecasting can help city managers perceive the health of the traffic road network in real-time, adopt timely solutions to optimize the traffic flow, and thus improve road traffic efficiency. In addition, online maps (e.g., Google Maps, Baidu Maps) can improve the quality of urban services by planning routes in advance for travelers and shortening travel time.

Traffic prediction exhibits typical spatial-temporal correlations. As shown in Fig. 1, traffic variation exhibits intricate and multifaceted patterns of spatial and temporal interdependence. In terms of time, traffic volumes (such as, flow, speed, and demand) are affected by the living routine of urban residents and show significant periodicity, e.g., weekdays morning and evening peaks and weekend/holiday aggregated traffic flow [5]. The traffic at an observation point is closely related to the traffic state in the periods before and after, showing certain closeness and trend. In addition to the temporal properties, the intuitive traffic volume changes are also reflected in the information transmission between nodes in the traffic network. Unlike temporal correlations, the potential spatial relationships are diverse [6, 7], as illustrated in Fig. 1a, where node 7 and node 10 are connected on the same road with essentially the same traffic patterns. Both node 7 and node 1 belong to the residential area and have significant semantic similarities despite their physical distance. Node 7 and node 4 have the same location function (Same POI, i.e., School, Bank), and even though they are not directly connected, they have the similar spatial pattern [8]. These complex and changing spatial-temporal properties make accurate traffic forecasting still challenging.

Extensive research has been devoted to address the challenge of modeling spatial-temporal data. The earliest statistical models (e.g., VAR [9], ARIMA [10]) are widely used for time series forecasting because of their simplicity and interpretability. However, these designs with restricted parameters are difficult to accomplish complex pattern recognition and the data cannot satisfy the assumption of stationary. Although machine learning methods (e.g., SVR [11], FNN [12]) are often good at non-linear representation, the performance of the models heavily depends on feature engineering and expert experience. Data-driven deep learning techniques, especially temporal convolution [13], recurrent neural network (and its variants LSTM [14], GRU [15]) and Transformer [16], have made breakthroughs in sequence tasks. However, they treat traffic data as independent signal streams [17], ignoring or barely exploiting the spatial dependence information.

One attempt is to divide the spatial region into same-size grids. ST-ResNet [18] implicitly represents the correlations between variables in fixed-size convolution kernels by using deep convolutional networks. However, due to the irregularity of roads, topological information inside the traffic network is inevitably missing grid modeling. Inspired by graph neural networks modeling topology graphs, STGCN [19] first proposed to stack gated temporal convolution with graph convolution into Spatial Temporal Blocks to achieve spatial-temporal prediction. This practice demonstrates that embedding prior knowledge of the traffic graph is beneficial to improve the model’s predictive performance greatly. In later model design, extensive research efforts have integrated graph neural networks into sequential models to jointly model the potential temporal and spatial dependencies of traffic data [20], and have achieved state-of-the-art performance. Some models such as DCRNN [21] integrates diffusion convolution into GRU to propose a multi-step prediction architecture that can capture bidirectional random walking graph signals. MTGNN [22] designed a structure that combines adaptive graph learning with dilation convolution to capture spatial-temporal correlation. GMAN [23] uses spatial-temporal attention fusion to expand the perceptual domain of information but reduce the loss of long-term prediction.

Over the years, although a considerable number of spatial-temporal graph neural network models have been proposed for traffic prediction, the existing literature lacks comprehensive surveys specifically focusing on graph learning and graph computing. While some studies [24, 25] attempt to comprehensively and meticulously organize all the datasets and methods for traffic tasks, they are too broad and fall short in providing precise insight into the core issues and methods of spatial-temporal prediction modeling. Unfortunately, the absence of a fair and standardized benchmark is a significant drawback in the field. Existing benchmarks such as [26, 27, 8] suffer from either irregular experimental settings and limited scalability or exhibit inconsistent results compared to the original papers. Furthermore, the evaluation of these diverse models remains confusing and lacks proper organization.

To address the above problems, a focused, well-understood, and inslightful survey will be of significance to the development of traffic prediction. In this paper, we highlight graph structure designs and graph computation methods used in spatial modeling, followed by a concrete survey of spatial-temporal graph neural networks. Then we propose a standardized and easily extensible benchmark to evaluate the performance of the different models. Lastly, we conclude with a prospective analysis of the difficulties and challenges in this study, and possible solutions to resolve them.

In summary, the main contributions of our paper are provided as follows:

• 1.

  Firstly, we provide a comprehensive overview of graph structure design and graph computation methods employed in spatial-temporal graph modeling. This aspect has received less attention in previous surveys, making our discussion particularly valuable.

• 2.

  Secondly, we conduct an in-depth survey of spatial-temporal graph neural networks used for traffic prediction. We categorize these methods into three groups based on their temporal characteristics: CNN-Based, RNN-Based, and Attention-Based. Furthermore, we analyze the technical details and limitations of each specific model.

• 3.

  Thirdly, we introduce a benchmark named STG4Traffic, which facilitates a comprehensive evaluation of approximately 18 models on traffic speed datasets (METR-LA, PEMS-BAY) and traffic flow datasets (PEMSD4, PEMSD8). Our benchmark yields results that closely align with those reported in the original papers. It not only offers a common data access interface but also provides a unified model training pipeline for future studies in model design.

• 4.

  Lastly, we outline the challenges encountered in traffic modeling from the perspective of data quality, research perspectives, and migration methods. We aim to provide feasible approaches to overcoming the difficulties faced in this field.

The traffic network can be abstracted as a graph $\mathcal{G}=(V,E,A)$. $V$ is the set of $N=|V|$ nodes, which represent different observation locations (e.g., traffic sensors, roadway monitoring stations) distributed in the road network. $E$ is the set of edges and $A\in\mathbb{R}^{N\times N}$ denotes the adjacency matrix depicting the relations between nodes, where each element represents the quantification of proximity from a certain insight, such as road connectivity, distance proximity, POI similarity, etc.

The traffic data observed on $\mathcal{G}$ at time $t$ is denoted as the graph signal $X_{t}\in\mathbb{R}^{N\times D}$, and the signal of the $i$-th node is denoted as $X_{t}^{(i)}\in\mathbb{R}^{D}$, where $D$ denotes the feature dimension of the node (e.g., traffic flow, speed, and density). Similarly, we can represent the signals of all nodes on $\mathcal{G}$ at time length $T$ as a 3D feature tensor $X\in\mathbb{R}^{T\times N\times D}$. Finally, the traffic prediction problem can be formalized as follows:

This formula indicates that given $P$ time lengths of historical observations and graph $\mathcal{G}$, predict future traffic status for $Q$ time lengths. The task aims to learn a non-linear function $f(\cdot)$ based on the gradient descent of the error. The mathematical form of $\mathcal{L}$ optimization objective is defined as follows:

where $\Theta$ is the parameters to be optimized in the function.

Although graph neural networks (GNNs) have the advantage of aggregating node neighborhood contexts to generate spatial representations [28], the performance of the task is closely related to the quality of the input graph structure and the computational method used for graph convolution. As shown in Fig. 1a, the spatial relationships among nodes in traffic networks are complex and diverse. The complex spatial dependencies behind the traffic system cannot be explored by a single graph design and simple equation [29]. Therefore, this section focuses on the following two issues:

• 1.

  Q1: How to design a reasonable graph structure? And how to mine underlying spatial relationships from the time-series data itself without prior knowledge?

• 2.

  Q2: How to perform efficient convolution computation on the existing graphs?

Spatial-temporal graph neural networks (STGNNs) have gained popularity as a deep learning approach that integrates graph convolutional layers into sequence models. This methodology effectively captures the spatial and temporal characteristics of traffic signals. By considering the entire road network and modeling spatial information, STGNNs surpass the limitations of analyzing independent data streams separately and the prediction accuracy of the model is significantly improved. Through the rapid development in the past five years, a large amount of work has been accumulated to apply spatial-temporal graphs to traffic prediction. According to the modeling strategy of the temporal axis, it can be divided into three categories, namely CNN-Based, RNN-Based, and Attention-Based. The representative STGNNs architectures are shown in Fig. 3. The CNN-Based methods (STGCN, Graph WaveNet, MTGNN, etc.) employ 1D CNNs (TCNs) in tandem with graph convolutional layers to construct ST-Blocks and then learn asynchronous spatial-temporal patterns through the cascading ST-Blocks. 1D CNNs capture more long-range temporal features by stacking convolutional layers or adding dilation factors, thus enjoying the advantages of good computational efficiency and gradient stabilization. However, the implicit temporal connections represented by fixed convolution kernels deprive them of some flexibility and, more importantly, fail to capture the synchronized information in spatial-temporal signals.

In contrast, Recurrent Neural Networks (RNNs, e.g., LSTM, GRU) are powerful in modeling sequence dependencies. Many RNN-Based methods (DCRNN, MRA-BGCN, AGCRN, etc.) extend the fully-connected operation in RNNs using GCNs so that they use graph convolution to capture local spatial dependencies at both input-to-state and state transitions. This design approach associates each time step with graph convolution, enabling the learning of spatial-temporal signals that undergo synchronous changes. However, it suffers from gradient instability and being very time-consuming in training and inference stage. Furthermore, the forgetten gate mechanism in RNNs has constrained their capability in capturing long-term temporal dependencies.

Theoretically, the attention mechanism and its variants possess a large global receptive field, which has led to their widespread use in capturing long-term temporal dependencies in sequence models. Attention-based methods (such as GMAN, ASTGCN, DSTAGNN, etc.) typically combine temporal attention with spatial attention, excelling at handling global contextual features and spatial-temporal correlations in the evolution of states. By dynamically computing attention scores, these methods enhance the model’s focus on critical information, effectively addressing the limitations of TCN and RNN approaches. However, the attention mechanism introduces additional parameters and complexity, making the model overly sensitive to noise or irrelevant information in the training data, which can impact its generalization capability. In addition to the aforementioned methods, there are various other widely-used time series processing techniques, including neural controlled differential equations, Fourier domain transformations, and time pattern decomposition, among others. These provide a diverse set of tools and techniques that can be employed for analyzing and modeling different types and characteristics of time series data.

In recent studies, “GRU-GCN” is one of the most used spatial-temporal graph modeling frameworks. To overcome the challenges of high run-time and error accumulation, several works have proposed “curriculum learning” to optimize the training phase of the model. Curriculum Learning [22, 8] argues that it is not necessary to calculate the error and backpropagation for all time steps early in the training but to gradually increase the prediction length of the model as the number of iterations increases, i.e., in a progressive convergence way. This strategy for the encoder-decoder architecture substantially reduces the training time consumption and alleviates the pressure in terms of efficiency and resource occupation.

Just like the No-Free-Lunch theorem [66] in machine learning, using STGNNs to model the spatial-temporal correlation of traffic scenes requires selecting appropriate components according to specific problems and conditions. Here we summarize some representative research works, as shown in Table 2. Some of these methods had reached the state-of-the-art in prediction tasks. STGCN [19] first combines gated temporal convolution with ChebNet operator for spatial-temporal prediction and achieves better performance than traditional time series models in all metrics. DCRNN [21] extends the diffusion graph convolution to a recurrent neural network of encoder-decoder to solve the directional problem of asymmetric traffic graph propagation. Graph WaveNet [45] innovatively proposes an adaptive graph dissipation of biases caused by human-defined spatial relations, and WaveNet based on causal convolution is used to learn temporal relations. Inspired by ST-ResNet [18], ASTGCN [56] proposes a set of temporal components called Clonesss, Period and Trend. Structurally, it utilizes a skip connection to connect the spatial-temporal attention layer to the convolutional layer to form model branchs, and finally fuses the three components together for prediction. These early studies of spatio-temporal graph neural networks significantly outperform traditional statistical methods and machine learning models in terms of predictive performance.

The complexity of traffic scenarios has also given rise to some novel research perspectives. STSGCN [33] argues that spatial-temporal dependence often affects traffic volumes not individually but synergistically. It proposes a unique local spatial-temporal graph for capturing spatial-temporal heterogeneity and models synchronous spatial-temporal relationships through multiple graph convolutional layers. GMAN [23] proposes gated spatial-temporal attention fusion to capture dynamic nonlinear spatial-temporal correlations and establish the temporal connections between historical and future time steps based on transforming attention. STFGNN [37] combines a novel fusion operation to learn hidden dependencies from spatial and temporal graphs, and handles long sequences by stacking fusion graphs and gated convolutional modules. However, the accuracy of these methods heavily relies on pre-defined graph designs, and the number of layers of graph convolution is superficial.

Adaptive graph convolutional recurrent network (AGCRN) [44] designs two types of adaptive modules based on parameter decomposition. Firstly, the node adaptation module decomposes the shared weights and biases to generate node-specific parameters to capture node-specific patterns. Secondly, the data-adaptive graph generation module automatically infers the interdependencies between different traffic series. STGNN [17] first combines the improved GAT and GRU, and then captures different scales of temporal patterns by concatenating a Transformer neural network architecture. This approach can effectively learn the dependencies among spatio-temporal data and provides a design framework that can be readily adapted. ASTGNN [59] adopts a Transformer-like spatio-temporal encoding-decoding architecture. It first extends the computation of query, key, and value matrices using temporal convolutions, proposes a trend-aware attention layer, and then replaces the feedforward network layer with GAT. The method has been proven effective on multiple traffic datasets, but the complex parameter training brings heavy system strain. DGCRN [8] found the fact that the connectivity of nodes is not immutable, but dynamically evolves with time periods. It proposes using a hyper-network to generate a dynamic adjacency matrix before each step of the RNN to accommodate the dynamic changes in the road network. Additionally, the generated dynamic matrix is merged with the original road network matrix to capture more spatial information. DMSTGCN [61] designs a dynamic graph constructor and dynamic graph convolution method to propagate node hidden states based on dynamic spatial relationships. It also provides a multi-aspect fusion module to merge auxiliary hidden states and primary hidden states in both time and space. They have made a lot of efforts in graph design and graph computing.

Spatio-Temporal Multi-Graph Convolution Network (ST-MGCN) [7] and Temporal Multi-Graph Convolutional Network (T-MGCN) [38] devise multiple attribute graphs to assist in enhanced spatial modeling and mine spatial information from multiple insights. But this means that more expert knowledge is required. STGODE [36] adopts ODE to handle multipe layer GCN over-smoothing problem by expressing residual-connected GCNs as continuous GCNs. Then it adopts the dual branching of TCN and CGCN to solve the spatial-temporal prediction problem. Similarly, STG-NCDE [64] employs neural control differential equations to tackle the knowledge of temporal and spatial dimensions separately. The neural differential equation restores the temporal continuity that is lost due to interval sampling. Unlike previous work, STEP [63] is motivated by unsupervised learning and proposes a time-series pre-training strategy to enhance the graph structural design of STGNNs with promising results.

According to our survey, the studies of spatial-temporal graphs focus on designing graph structures and combining spatial-temporal components. Meanwhile, other related pieces of techniques (unsupervised pre-training, generative adversarial networks, graph contrastive learning, reinforcement learning, etc.) are widely applied to traffic prediction, which greatly expand the technical basis of spatial-temporal data mining and achieve great performance gains.

In this section, we first provides an overview of the datasets and models, the experimental setup, and the evaluation results used in the benchmark. Then we analyze the performance and efficiency of some models through the visualization of charts. Finally, we provide a brief introduction to the benchmark interface and its extended usage.

Over the years, significant advancements have been achieved in traffic forecasting using STGNNs. However, there are still several challenges that require further attention and resolution. In this section, we highlight some future research directions for addressing the challenges.

Data Quality: Data collected from sensors often suffer from noise or contain a certain percentage of missing data (zero-value padding during preprocessing). While we address this issue carefully during test evaluation, the training process is highly susceptible to being influenced by these anomaly samples. Additionally, the narrow time frame of data sampling, represented by parameters $P=Q=12$, poses challenges in capturing the periodicity of long sequences on one hand, and makes learning similarity graphs of node pairs unreliable on the other [63]. Moreover, the datasets collected in the study are limited, lacking the introduction of enriched external information or metadata such as weather, events, dates, etc. [69] and the fusion of these heterogeneous data presents a persisting challenge. Some studies have explored effective approaches to addressing data quality concerns in traffic forecasting. For instance, graph contrastive learning methods [70, 71] have shown promise in combating training noise and capturing robust spatial-temporal features. Time Series Pre-training techniques [63] have also been found effective for long time series data with periodicity. In the ST-MetaNet model [57], meta-knowledge is leveraged to parameterize the model, while considering heterogeneous information in the road network to model spatial-temporal dependencies and achieve improved feedback. These studies provide valuable insights and serve as strong references for addressing concerns related to data quality.

Research Perspectives: Research on traffic forecasting mainly revolves around the modeling of temporal and spatial correlations. (1) Temporal Heterogeneity: Existing approaches that model temporal correlation for all nodes often adopt a shared parameter space, ignoring the temporal heterogeneity among different nodes. STID [20] argues that this difference in temporal patterns is due to spatial heterogeneity, and it identifies this indistinguishability in combination with multiple spatial-temporal embeddings. Spatial-Temporal Self-Supervised Learning (ST-SSL) [72] proposes a novel paradigm that enhances the representation of traffic patterns to capture both spatial and temporal heterogeneity by augmenting traffic-level and topology-level data. (2) Dynamic Graph: Although adaptive graphs can compensate for the knowledge bias caused by pre-defined graphs, they can only represent fixed node relations after training and cannot be dynamically adjusted with the data characteristics. Some work as DGCRN [8] and D²STGCN [73], among others, take into account the basic fact that the location dependence of a road network changes dynamically with time. They propose a time-driven dynamic connectivity graph that infers instantaneous connection patterns based on the current traffic state. Although some related work exists, the design of dynamic graphs remains a significant technical challenge. (3) Long-Range Dependence: Attention mechanisms are very flexible in global spatial-temporal modeling, especially in capturing long-range temporal dependencies with good performance, and time series models based on Transformer variants are widely used in various fields. Sequence pattern decomposition [74] is also a potential solution for the future. Long-term dependence information is inferred from three structural components of time series trends, periods and residuals to improve prediction performance. (4) GNN-Free Method: MLP-based spatial-temporal prediction models [20, 75] have become a new idea of spatial-temporal prediction with its advantage of balancing efficiency and performance. It does not advocate the use of complex STGNN modeling spatial-temporal dependence, but adopts diversified spatial-temporal information encoding, and combines the most simple MLP model to process spatial-temporal data. However, essentially, the MLP-Based approaches also draw on graph signal propagation or diffusion to represent neighborhood node correlation, and this viewpoint revisits the features behind spatial-temporal and pays more attention to the research and design of the Embedding layer.

Migration Methods: In the realm of STGNNs, the integration of various methods from different fields has shown the potential to enhance model performance. Generative adversarial networks [76, 77] combat training generators (STGNNs) and discriminators by comparing the proximity of the predicted information to make the predictions converge to the ground truth as much as possible. Knowledge graphs [78, 79, 80] have also emerged as a valuable tool, establishing relationships among different transportation entities and concepts. They enable the consolidation and sharing of knowledge from diverse fields, facilitating comprehensive analysis and prediction of the entire traffic system. Recent studies such as AutoSTG [81] and AutoCTS [82] propose the use of automated machine learning to streamline the construction and optimization of traffic prediction models. These approaches efficiently build STGNNs that meet performance requirements while emphasizing accuracy. Additionally, transfer learning [83, 80] has demonstrated its usefulness by leveraging models trained in other cities or regions with similar traffic patterns to initialize new models. This approach accelerates the training process and alleviates challenges arising from limited data availability. The advancement of these techniques has diversified the research approaches for traffic forecasting, providing greater potential for solving the problems in this domain. However, the transferred methods from other domains have not been well applied due to the differences in data distribution and domain knowledge, which poses challenges to their effective utilization.

In this paper, we first present a systematic survey of graph design and graph computation techniques for traffic prediction. Then we provide a detailed introduction to the key modeling components, technical details, and well-established methods of spatial-temporal graph neural networks. In order to establish a standardized benchmark, we introduce STG4Traffic, providing a thorough overview of the performance and efficiency of various methods within this framework. Finally, we conduct an analysis of the challenges encountered in this study and summarize potential solutions for future investigations. We hope that this research make a positive and impactful contribution to the field of spatial-temporal prediction.

Chunjiang Zhu is supported by UNCG Start-up Funds and Faculty First Award. Detian Zhang is partially supported by the Collaborative Innovation Center of Novel Software Technology and Industrialization, the Priority Academic Program Development of Jiangsu Higher Education Institutions.