Graph Neural Network for Trafﬁc Forecasting: The Research Progress

: Trafﬁc forecasting has been regarded as the basis for many intelligent transportation system (ITS) applications, including but not limited to trip planning, road trafﬁc control, and vehicle routing. Various forecasting methods have been proposed in the literature, including statistical models, shallow machine learning models, and deep learning models. Recently, graph neural networks (GNNs) have emerged as state-of-the-art trafﬁc forecasting solutions because they are well suited for trafﬁc systems with graph structures. This survey aims to introduce the research progress on graph neural networks for trafﬁc forecasting and the research trends observed from the most recent studies. Furthermore, this survey summarizes the latest open-source datasets and code resources for sharing with the research community. Finally, research challenges and opportunities are proposed to inspire follow-up research.


Introduction
Traffic forecasting is the foundation of modern transportation infrastructures and intelligent transportation systems (ITSs). It has a wide range of applications in trip planning, road traffic control, and vehicle routing [1][2][3][4][5][6]. Traffic forecasting has drawn a great amount of attention from both academia and industry in recent decades [7][8][9][10][11][12][13][14]. However, the traffic forecasting problem has not been fully resolved due to the complex spatiotemporal dependencies of traffic activities. Furthermore, developments in the Internet of things (IoT), the Internet of vehicles (IoV) and artificial intelligence (AI) techniques [15] have helped to measure and model more diverse traffic-related characteristics, allowing the design of autonomous and efficient data-driven traffic forecasting methods [16][17][18]. To gain a comprehensive understanding of the opportunities and challenges in traffic forecasting, we summarize here the recent research progress in this vibrant field to facilitate future research.
Depending on the data format used, traffic forecasting problems can be classified into different types, including time series data, grid data, and graph data. Among them, the earliest and most common problem formulation is time series forecasting, where historical data points are used as model input to predict future conditions [19][20][21]. Furthermore, time series forecasting problems can be divided into univariate problems and multivariate problems. For univariate time series problems, only one traffic variable is considered, such as traffic flow or traffic speed. For multivariate time series problems, multiple traffic variables are considered simultaneously. In addition to univariate and multivariate settings, time series forecasting can also be formulated as single-step forecasting and multiple-step forecasting. In single-step forecasting problems, only one data point needs to be predicted in the next step. In multiple-step forecasting problems, there is more than one value to predict. Some typical time series forecasting models include simple linear regression, autoregressive integrated moving average (ARIMA), and seasonal autoregressive integrated moving average (SARIMA). SARIMA outperforms ARIMA because it captures seasonal patterns. In the transportation domain, both daily and weekly patterns are observed and useful for forecasting. SARIMA was further improved using the Kalman filter in [19], and the improved model outperformed other time series models. Empirical mode decomposition (EMD) is often used together with time series models, where the time series is first decomposed into different components and each component is then modeled with a time series model. This combination has been shown to be effective for traffic forecasting [21].
Although time series data are the most commonly used data format in traffic-related studies, they are insufficient because they do not consider the spatial dependence of traffic activities. To overcome this problem, two data formats, grid data and graph data, are further used. For traffic forecasting with grid data, at each time step, the traffic data are aggregated by some regularly divided regions in the studied urban area. Each regularly divided region can be regarded as a grid. By aggregating the corresponding traffic variables in each grid, we obtain an intensity map that can be displayed in an image format, as shown in Figure 1. In single-step traffic forecasting problems with the grid-data format, the historical grid data in a predefined lookback window are formulated as image frames and used as the input feature. The frame in the next time step is used as the prediction target.
For traffic forecasting problems in graph format, traffic data are aggregated by specific locations or stations, which are regarded as nodes in a traffic graph. Node features are collected traffic variables such as traffic flow or speed. Edges can model road topological connections or spatial distances between different nodes. In single-step traffic forecasting problems with the graph format, the historical graph data in a predefined lookback window are used as the input feature. The graph in the next time step is used as the prediction target, as shown in Figure 2.
Existing traffic forecasting methods can also be divided into different categories according to the models used, including statistical models, shallow machine learning models, and deep learning models. Each has its own scope of applicable scenarios and can be adapted to different situations [26]. Statistical models are mainly linear models such as ARIMA and SARIMA. These models are advantageous due to their low computational cost and good interpretability. However, their predictive performance is inferior to that of machine learning and deep learning models, which are better at capturing nonlinear relationships. Shallow machine learning models are represented by tree-based models such as decision trees and random forests [27]. They were the first choice for early research until recently with the adoption of more intelligent and accurate deep learning models represented by modern neural networks such as convolutional neural networks (CNNs) [28] and recurrent neural networks (RNNs) [29].
These deep learning models have been proven effective for a variety of forecasting problems in the finance, energy and communications sectors [30][31][32][33][34][35][36][37][38][39][40]. Among various deep learning models, graph neural networks (GNNs) have become state-of-the-art solutions to various forecasting problems. In the financial field, a comprehensive survey of deep learning models for stock market forecasting showed that emerging GNN models received the most attention [30]. In the economic field, deep learning models have been proven effective for retail forecasting [37] and market demand forecasting [39], which are the basis of supply chain management. In the energy field, it has also been confirmed that deep learning models are becoming the main solution [31,33,34]. It is worth mentioning that external factors such as temperature and weather information have a great impact on the forecasting performance [32,38]. This observation is insightful for traffic forecasting problems, as transportation systems are also highly influenced by weather information, e.g., road traffic decreases during bad weather. For communication networks, various deep learning models have been proven to be more effective than statistical and machine learning models, such as the InceptionTime model adopted in [35] based on the time series data format and the convolutional LSTM model adopted in [36] based on the grid-data format. It is also observed that GNNs are gaining popularity in cellular traffic prediction [40]. GNNs utilize graph structures, which are common in transportation infrastructure, such as road networks and subway systems. GNNs can effectively capture interactions between nearby traffic sensors or stations, thereby improving prediction performance.
The research topic of this survey focuses on GNN-based solutions, and there are still many recent publications introducing CNN-based or decision-tree-based solutions [28,[41][42][43]. As discussed in previous relevant studies [44,45], compared to CNN-based or decision-treebased solutions, GNN-based solutions have a wide range of applicable scenarios and achieve state-of-the-art performance. GNN-based solutions can be applied when there is a natural graph structure (such as a road network) or when an artificial graph can be constructed (such as a neighborhood graph in grid data). However, GNN-based solutions are inapplicable when the above graphs are not available, e.g., traffic data collected in a single loop detector only. GNNs are mainly used to forecast speeds and volumes in urban networks and freeways. However, prediction in urban networks is far more challenging than that in freeways because of complex spatiotemporal traffic patterns caused by various reasons, such as complex road structures, different vehicle types, and time-varying user demands.
Although there have been some surveys of deep learning for traffic forecasting problems, most of them are not GNN-focused, with only a few exceptions [46][47][48][49][50][51][52][53]. This study serves as an extension of existing GNN-relevant surveys [44,45], summarizes the latest research progress in 2022, and aims to be the latest reference manual for researchers in related fields. In this survey, a total of 118 journal papers and 30 conference papers published in 2022 are reviewed, all of which are selected from prestigious journals and conferences in transportation, computer science, and multidisciplinary fields. Each paper is reviewed in a structured manner and lessons learned are discussed to reveal research trends. Based on the surveyed studies, the latest open datasets and code resources are also collected and organized in lists. Existing research challenges are identified, and corresponding research opportunities are further suggested.
The contributions of this survey are summarized as follows: • The remainder of this paper is organized as follows. Section 2 is a literature review of the latest relevant studies and a discussion of recent research trends. Then, the latest lists of open datasets and code resources for the research community are presented in Section 3. Section 4 discusses research challenges and opportunities when applying graph neural networks for traffic forecasting to inspire follow-up research. The conclusion is drawn in Section 5.

Literature Review and Research Trends
The studies covered in this survey were all selected from prestigious journals and conferences in transportation, computer science, and multidisciplinary fields. To share incremental knowledge and avoid repetition with existing similar surveys [44,45], this section only selected those published in 2022 for discussion, with a total of 118 journal papers and 30 conference papers. Source journals and conferences are listed in Tables A2 and A3, with the number of papers counted. The reviewed studies are summarized in Table 1. For each study, the specific traffic problem, graph type, dataset, model component (especially the GNN structures involved) and a summary of the main content are discussed. More relevant studies are tracked and updated in our GitHub repository (https://github.com/jwwthu/GNN4Traffic, accessed on 2 February 2023).
As discussed in the introduction, Section 1, we categorized traffic forecasting problems from two perspectives, namely, based on the data format or based on the model used. Furthermore, in Table 1, we provided another perspective based on transportation modes, such as road traffic, taxis, bikes, and subways. As shown in Table 1, we found that the road traffic flow and speed prediction problem was still the most popular traffic prediction problem in different traffic-related studies. There are two possible reasons for this trend. The first reason is that for the road traffic forecasting problem, open datasets and baseline models are more accessible with well-processed steps and instructions, which saves the workload of data collection and preprocessing. The second reason is that building graphs for road-network-related problems is more intuitive, making it more natural to use GNNs to solve road traffic flow and speed prediction problems, and thus more common in the scope of our investigation.
As shown in Table 1, there are two types of graphs listed in the graph column, static graphs and dynamic graphs. In the early research stages, static graphs were widely used because of their convenience. However, researchers realized that static graphs were insufficient to capture changes in network topology and traffic patterns. For example, traffic flow measurements and their correlations on road segments change dynamically in space and time, which is beyond the modeling capabilities of static graphs. Then, dynamic graphs were introduced. As the name implies, a dynamic graph is a graph that can evolve as new nodes or edges are added or removed. However, static graphs are still very useful when the traffic infrastructure remains unchanged for the time period considered. Therefore, some researchers use both dynamic and static graphs. The static graph is used to model the static road network, and the dynamic graph is used to consider the impact of dynamic traffic events and weather information.
Most of the collected datasets used in the surveyed studies are open datasets with only a few exceptions. Among those open datasets, some have made great contributions to support relevant studies, which can fairly evaluate and compare different models, e.g., PeMS-BAY and METR-LA. However, it also poses problems when existing datasets are overutilized and overfitted to GNN-based deep learning models and produce unreliable models for other traffic scenarios and datasets. To address this potential risk, new datasets were collected and are listed in Section 3 for further evaluation. Additionally, most of the surveyed studies used two or more datasets, a phenomenon worthy of further study.
For the model component part, the graph convolutional network (GCN) [54] and graph attention network (GAT) [55] are the two dominant networks used. It is difficult to go through all the GNN model details in the surveyed papers listed in Table 1. Interested readers are advised to read the original text of the surveyed papers.
A GCN is a pioneer in transferring the concept of convolution operations from Euclidean image data to non-Euclidean image data and has achieved great success in the past few years. The basic idea of a GCN is to aggregate the features from neighbors and then apply a linear transformation on the aggregated features. GCN layers can be stacked k times to capture k-hop neighbor information. However, a GCN requires the entire graph structure for training, which consumes a considerable amount of computer memory. In that case, GAT, based on the attention mechanism [56], was introduced as an alternative to GCN. The main difference between GAT and GCN is the introduction of importance scores for different neighbors based on the masked self-attention mechanism. Technical details about GCN and GAT are beyond the scope of this survey, which aims to identify research trends, and can be found in relevant surveys [57,58]. Designing more effective GCN or GAT variants is still a major research direction. Fundamental theoretical breakthroughs in the GNN research community will also help in the development of new traffic forecasting methods.
Both GCN and GAT are mainly used to capture spatial dependencies. To capture temporal dependencies, there are some classic models, e.g., temporal convolutional network (TCN), long short-term memory (LSTM), and gated recurrent unit (GRU). More recently, an attention-based model, i.e., the Transformer, has proven effective for capturing long-term dependency in time series [59]. Nevertheless, as indicated in Table 1, Transformer has only been used in a few surveyed studies, and there is still much room for research. GraphSAGE, GRU A transferable federated inductive spatial-temporal graph neural network (T-ISTGNN) is featured with the capability of cross-area traffic state forecasting when preserving the privacy of source areas.
[68] Regional taxi usage Static graph TaxiNYC GAT, GRU A spatiotemporal heterogeneous graph attention network (STHAN) is featured with a spatiotemporal heterogeneous graph in which multiple spatial relationships and temporal relationships are modeled and metapaths are used to depict compound spatial relationships.
[69] Road traffic flow Dynamic graph, static graph METR-LA, PEMS-BAY GCN, GRU A spatiotemporal prediction framework using high-order graph convolutional network (STHGCN) is featured with a dynamic adaptive spatial graph learning module to learn the high-order dependence. A dual graph gated recurrent neural network (DG 2 RNN) is featured with a bidirectional GRU layer for learning temporal dependency and a spatial attention mechanism for learning spatial dependency. The proposed approach features a GCN-based data imputation module and an adaptive approach of leveraging DRL for the dynamic graph's adjacency-matrix generation.
[93] Road traffic flow Dynamic graph PeMSD4, PeMSD8 GCN The proposed CRFAST-GCN features a conditional random field (CRF)-enhanced GCN to capture the semantic similarity globally.
[94] Road traffic speed Dynamic graph PeMSD8, METR-LA TCN, GCN A universal framework is proposed to transform the existing one-step-ahead models to multistep-ahead models.
[95] Road traffic speed Static graph METR-LA, PEMS-BAY GNN The proposed approach features a novel GNN layer with a location attention mechanism to aggregate traffic flow information from adjacent roads. A comodal graph attention network (CMGAT) is featured with a multiple-traffic-graphbased spatial attention mechanism and a multiple-time-period-based temporal attention mechanism.
[100] Road traffic speed Dynamic graph METR-LA, PEMS-BAY GCN, TCN An adaptive spatiotemporal graph neural network (Ada-STNet) is featured with a dedicated spatiotemporal convolution architecture and a two-stage training strategy. [103] Road traffic flow Dynamic graph PeMSD3, PeMSD4, PeMSD7, PeMSD8 GCN An improved dynamic Chebyshev GCN is proposed with a novel Laplacian matrix update method, the attention mechanism, and a novel feature construction method.
[104] Road traffic flow Static graph PeMSD4, PeMSD8 GCN, GLU A causal gated low-pass graph convolution neural network (CGLGCN) is featured with a causal convolution gated linear unit with less computation time and a GCN with a self-designed low-pass filter.
[105] Road traffic flow Dynamic graph PeMSD4, PeMSD8 GAT An attention-based spatiotemporal graph attention network (ASTGAT) is featured with multiple residual convolution and a high-low feature concatenation.
[106] Road traffic speed Dynamic graph METR-LA, PeMS-BAY, PeMS-S GCN An attention-based dynamic spatial-temporal graph convolutional network (ADST-GCN) is featured with the combination of a dynamic adjustment module, a gated dilated convolution module, and a spatial convolution module.  The proposed approach features novel deep graph Gaussian processes (DGGPs), which consist of the aggregation of a Gaussian process, temporal convolutional Gaussian process, and Gaussian process with a linear kernel. [116] Road traffic flow, road traffic speed Dynamic graph PeMSD3, PeMSD4, PeMSD7, PeMSD8, METR-LA, PeMS-BAY GCN A dynamic spatial-temporal adjacent graph convolutional network (DSTAGCN) is featured with the construction of a spatial-temporal graph and the integration of fuzzy systems and neural networks for uncertain relationship representation. [117] Road traffic flow, road traffic speed Dynamic graph PeMS-BAY, TaxiBJ, PeMSD4, PeMSD8 GCN, GRU A dynamic spatial-temporal graph convolutional network (DSTGCN) is featured with a dynamic graph generation module with geographical proximity and spatial heterogeneity.
[118] Road traffic flow Dynamic graph The proposed approach features a new temporal vector CNN module and a new dynamic correlation graph construction method.
[119] Regional travel demand Static graph TaxiNYC GCN, GRU The proposed approach features a geographic similarity graph, functional similarity graph, and road similarity graph. A memory-attention-enhanced graph convolution long short-term memory network (MAEGCLSTM) is featured with the combination of a memory attention mechanism and LSTM.

GCN
The proposed approach features a graph construction method for cross-time and crossspace correlations. [204] Road traffic speed Static graph METR-LA, PeMS-BAY GCN, GRU The proposed approach features a novel local context-aware spatial attention mechanism. [205] Road traffic speed Dynamic graph PeMS-BAY, private data

GCN
The proposed approach features the combination of a GCN and attention mechanism for multidimensional information aggregation.
The problems considered in Table 1 were grouped into different transportation modes, e.g., road traffic, taxis, bikes, and subways. Previous studies have also shown that joint forecasting of multimode data is beneficial [206]. GNN-based solutions are applicable and have already been used for multimode forecasting cases. In [152], a multimode dynamic residual graph convolution network (MDRGCN) model was proposed for regional taxi and bike flow forecasting, in which cross-mode relationships were learned by multimode dynamic GCN, GRU, and residual modules. In [99], a comodal graph attention network (CMGAT) was proposed for bike and taxi demand forecasting, which was based on a multiple-traffic-graph-based spatial attention mechanism and a multiple-time-period-based temporal attention mechanism. In these studies, it was demonstrated that the GNN-based joint forecasting of multimode traffic data was more effective than individual forecasts.
We also noticed that the traffic occupancy prediction problem was not seen in the studies reviewed in this paper. Some possible reasons are discussed below. Traffic occupancy is often modeled as a decision variable rather than using continuous variables such as traffic speed or volume. While GNN-based solutions have been shown to be effective in predicting continuous variables, as described in this survey, decision-tree-based models are still powerful for making binary decisions, e.g., XGBoost and LightGBM [207][208][209]. Another possible reason is that traffic occupancy can be detected more efficiently with computer vision methods based on images or videos, in which case convolutional neural networks and Transformers still dominate [210]. A similar problem is lane-occupancy-rate prediction, which is also rare in the literature due to the high cost of collecting real-world laneoccupancy data, e.g., deploying loop detectors for each lane in large-scale road segments. For example, only simulated traffic data can be used for lane-occupancy measurement and prediction in [211].
For model evaluation and comparison, different evaluation metrics are used, e.g., root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Forecast horizons also differ per study, such as 5, 10, 30, or 60 min, and it was found that the larger the horizon, the harder the forecasting problem, and the greater the error observed with larger horizons. Due to the different evaluation metrics and forecast horizons, it is nearly impossible to fairly compare all surveyed studies and quantify the difficulty of the available datasets. It was also found that for some common baselines, e.g., DCRNN [212], STGCN [213], and Graph WaveNet [214], their reported performance in different studies could vary when the training variables were different.

New Dataset and Code Resources
This section provides up-to-date lists of open datasets and code resources for the research community.

New Datasets
Open datasets are the basis for evaluating and comparing different forecasting models [215]. As discussed in Section 2, several open datasets have been widely used in the surveyed studies, such as METR-LA, PeMS, and NYC Open Data. Despite the availability of these datasets, developing new datasets is still beneficial for the following two reasons. The first reason is the risk of overfitting of deep learning models on existing datasets, especially those that are relatively small compared to datasets in other domains, such as large collections of images and natural language corpora. The second reason is that models trained using datasets collected many years ago may suffer from data drift as traffic facilities change. The data-shift problem means that the traffic patterns in the historical training data could be totally different from those in the newly collected test data, and the performance of trained deep learning models can degrade significantly in unseen cases. Therefore, here, we update the community with new, publicly available traffic datasets in Table 2 to facilitate future research and encourage constant updates of high-quality traffic datasets.

New Code Resources
Open-code resources facilitate the replication of published results and migration of proposed models to new problems. We summarize here the new publicly available code resources in Table 3 and list the implementation frameworks, including TensorFlow (https: //www.tensorflow.org, accessed on 2 February 2023) and PyTorch (https://pytorch.org/, accessed on 2 February 2023). It is observed from Table 3 that PyTorch is more popular than TensorFlow for developing new graph neural network models in traffic forecasting research.

Research Challenges and Opportunities
This section discusses research challenges and opportunities when applying GNNs to traffic forecasting problems in order to inspire follow-up research.

Research Challenges
Several challenges can be observed from the surveyed studies, which can be categorized into data, model, and system perspectives. From a data perspective, challenges include data quality and cold-start issues. From a model perspective, challenges include complex graph structure and model robustness concerns. From a system perspective, the real-world deployment of GNNs in transportation systems is a challenge that cannot be ignored.
The first challenge is the training data quality. When utilizing graph neural networks, some issues related to data quality may arise. On the one hand, high-quality datasets are expensive to build, as the data collection process can be time-consuming and costly. As extreme or urgent traffic events such as traffic jams and accidents are rare, collecting comprehensive datasets is more difficult. On the other hand, data privacy is also non-negligible if we want to create more comprehensive datasets, since most existing traffic datasets are collected from public transportation modes (e.g., taxis and shared bikes) or road sensors, rather than from private vehicles [224].
The second challenge is the cold-start problem [136] when initializing GNNs for traffic prediction. Deep learning models, including GNNs, usually require a large quantity of training data to efficiently train the model and obtain satisfactory predictions. However, data collection in the traffic field is often time-consuming and labor-intensive, for example, by installing loop detectors for traffic flow and speed information collection. The cold-start problem arises when the developed GNN models are to be used in a new area or station, especially for a growing urban network.
The third challenge is the diverse and complicated graph structures that exist in the real-world traffic infrastructure. Most surveyed studies consider only dense graphs, e.g., in downtown areas or on closely connected highways, when traffic activities are active. However, the complete traffic graph of a city may be sparse, with some nodes having no or few connections to other nodes. This real-world condition has received insufficient attention in the surveyed studies. Another limitation of the surveyed studies is that the graphs considered are relatively small, e.g., less than 1,000 nodes. For example, the most popular PeMS datasets are a collection of subsets from a large dataset collected from more than 40,000 individual detectors spread over a wider geographic area, since the size of the original dataset exceeds the computing abilities for some research groups.
The fourth challenge is the robustness of GNN models. Deep learning models have long been criticized for their black-box nature with little or no interpretation paired with predicted outcomes. This black-box problem exists for graph neural networks as well, and there are few systematic methods for interpreting GNNs in traffic forecasting settings. Many anomalies or outliers in the data are removed during processing steps or do not appear in the training dataset. When these anomalies are encountered during the testing or deployment phase, the performance of the trained GNN model degrades, leading to large deviations in model predictions. Given such risks, it is important to enhance the robustness and interpretability of GNN models to increase user confidence in the models.
The fifth challenge is the real-world deployment of GNNs in transportation systems. The real-world implementation of the surveyed GNN solutions requires substantial computing, communication, and storage resources. However, most of the surveyed studies only consider empirical evaluations based on offline datasets without testing their models on real-world transportation systems. Several obstacles arise in the real-world deployment of GNNs. To effectively utilize graph-based structures, a centralized deployment mode is required to collect global information and compute predictions in a single server. Although deep learning models, including GNNs, can be trained offline, the online inference process still requires considerable computing and storage resources when the considered traffic graph is very large. When the considered graph becomes larger, the communication overhead also increases. To achieve more efficient and safe transportation systems, complex GNN architectures may not be necessary for traffic-related tasks if their marginal performance improvement fails to cover the increased computational, communication, and storage costs.

Research Opportunities
Some promising research opportunities are discussed to address the above challenges and inspire future research.
The first research opportunity is the introduction of traffic simulation tools for creating unseen complex situations as training data. Two specific approaches, model-driven and data-driven approaches, can be further investigated. Model-driven approaches are based on macroscopic or microscopic traffic simulators, where macroscopic tools focus on the high-level deterministic relationships of flow, speed, and the density of traffic flows, while microscopic tools focus on individual details. On the other hand, data-driven methods do not rely on traffic domain knowledge but create more data samples from existing methods, e.g., generative adversarial network (GAN)-based studies [85][86][87]170,225]. Regarding the black-box nature of neural networks, the use of physics-informed neural network approaches is gaining popularity in research. These approaches combine both modeldriven and data-driven methods and have been successfully applied in the transportation domain [226,227].
The second research opportunity is to introduce new learning schemes to traffic forecasting problems, e.g., transfer learning, meta learning, and federated learning. Transfer learning has been proven effective for transferring cross-city knowledge, which will help address the cold-start problem in new cities [191]. Furthermore, meta learning has been shown to be useful for building new graph structures through efficient structure-aware learning during cross-city knowledge transfer. Privacy-preserving schemes are further proposed to be combined with transfer learning, protecting the sensitive information from the source domain [67]. Federated learning is another effective learning approach for maintaining data privacy while training effective deep learning models [159,189].
The third research opportunity is the combination of knowledge graphs under different road conditions or transportation modes to establish connections among them [63]. More external data can be used when constructing traffic knowledge graphs, e.g., the activity calendar from social media for potential traffic demands. Additionally, the knowledge between different transportation modes, e.g., interchange hubs, would be useful for multimodal prediction [137,152,155].
The fourth research opportunity is a distributed learning approach for training largescale graph neural networks for traffic forecasting [228,229]. When the application of GNNs for traffic prediction scales to larger graphs, a distributed training of graph neural networks is necessary. In those cases, improvements in training and runtime efficiency is even more beneficial and important. Another similar idea is to leverage cloud computing for model training and edge computing for runtime inference [160,230] to accelerate the distributed training and inference process.
The fifth research opportunity is the Bayesian learning approach for uncertainty quantification. Uncertainty in traffic forecasting may not be as critical as uncertainty in other domains, e.g., wireless communication problems. However, it is still important to account for uncertainty in the transportation domain when noisy or missing data could impair predictive capabilities and lead to unusual forecasts. Bayesian neural networks have been shown to be effective in dealing with data uncertainty caused by noisy or missing data in road traffic flow forecasting [66]. Another similar idea is to incorporate the physical mechanism of traffic flow dynamics as constraints, such as neural controlled differential equations [188] and Poisson processes [84], to avoid unreasonable predicted values [196] and help to improve the model interpretability.
The sixth research opportunity is the combination of graph neural networks and reinforcement learning, which is rarely considered in the surveyed studies, with only one exception [90]. The ensemble of these two models can sometimes produce brilliant sparks. For example, some relevant studies leverage reinforcement learning techniques for a more efficient graph neural network structure search [231]. On the other hand, reinforcement learning itself is useful for making optimal decisions in the traffic domain with properly designed rewards, e.g., traffic light control and autonomous driving. There is still a large research gap in applying reinforcement learning to graph data structures [232,233].
The last but not the least research opportunity is the deployment of GNNs based on cloud computing and B5G/6G communication techniques. Cloud computing can provide the required computing and storage resources. GNN models can be trained, deployed, and updated in the cloud with a scalable infrastructure. The B5G/6G communication technique is designed to have the ability to support massive machine-type communication scenarios and can be used for reliable and massive traffic data collection and transmission.
In summary, the first and second research opportunities are proposed to address the first and second research challenges. The third and fourth research opportunities are proposed to address the third research challenge. The fifth research opportunity is proposed to address the fourth research challenge. The last research opportunity is proposed to address the fifth research challenge.

Conclusions
In 2022, the number of studies on the topic of applying graph neural networks for traffic forecasting grew rapidly. In this survey, we summarized the progress made by these studies and listed their targeted problem, graph types, datasets, and neural networks used. We observed that the road traffic flow and speed prediction problem was still the most popular traffic forecasting problem. The GNN family, GCN and GAT, was one of the promising solutions to these problems. To further motivate follow-up research, new collections of datasets and code resources were presented. Research challenges and opportunities were further discussed in this study.  Acknowledgments: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A. Abbreviation List
The abbreviations used in this manuscript are listed in Table A1 with their full names. Table A1. Abbreviations used in this manuscript.

Abbreviation
Full Name

Appendix B. The Source Journal list
The source of the journals for the surveyed studies are listed in Table A2 with the number of papers counted.

Appendix C. The Source Conference List
The source conferences for the surveyed papers are listed in Table A3 with the number of papers counted.