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Eliminating Propagation Delay: Attention-Based Spatial-Temporal Fusion Graph Convolution Network for Traffic Flow Prediction
Jinpeng Chen, Ziyu Yu, Tao Wang, Jun Ma, Hongbo Gao, Senzhang Wang, Zufeng Zhang, Kaimin Wei
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 91%
Last extracted: 8/1/2026, 10:41:29 AM
Summary
The paper proposes the Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN) for traffic flow prediction. It addresses limitations in existing models by eliminating information propagation delay errors and reducing computational complexity. The method utilizes spectral clustering to create a macro-graph for regional context, a transmit block to fuse macro and micro features, and a spatial-temporal fusion block that combines delay-aware graph convolutions with multi-head self-attention to capture both long-term and short-term temporal characteristics.
Entities (7)
Relation Signals (5)
A-STFGCN → addresses → Propagation Delay
confidence 95% · We design a spatial-temporal fusion block to extract the spatial-temporal feature correlations with propagation delay errors removed
A-STFGCN → performs → Traffic Flow Prediction
confidence 95% · A-STFGCN for traffic flow prediction
A-STFGCN → uses → Spectral Clustering
confidence 92% · we first build a macro graph to reduce the complexity of large road networks... we apply spectral clustering to the adjacency matrix
A-STFGCN → uses → Multi-head Self-Attention
confidence 92% · capture both long-term and short-term temporal characteristics of the data within a multi-head self-attention mechanism
Dynamic Time Warping → estimates → Propagation Delay
confidence 90% · We estimate the temporal similarity between node pairs using the Dynamic Time Warping (DTW) algorithm... we regard this pair as exhibiting a k-step propagation delay.
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Abstract
Abstract:Predicting traffic flow is crucial to optimizing transportation systems and improving urban mobility. Many graph convolution-based models have been proposed to extract spatial-temporal features and predict traffic flow. However, most focus on spatial-temporal and semantic correlation in topological relationships. There are two primary problems to address. Firstly, the convolutional structure in the model focuses on utilizing static spatial dependencies and spatial-temporal relationships in topological structures, while neglecting the different information propagation delays between adjacent nodes in the convolution. Secondly, these methods often stack a large number of complex structures, resulting in a substantial increase in computational time during the model training phase, thereby disregarding the model's requirements for timeliness. In this paper, we propose a novel network called the Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN). We design a spatial-temporal fusion block to extract the spatial-temporal feature correlations with propagation delay errors removed and to capture both long-term and short-term temporal characteristics of the data within a multi-head self-attention mechanism based on a mask matrix. Extensive experiments on five real-world datasets demonstrate that our method achieves the best overall performance while having good computation and data utilization efficiency compared with the eight baseline methods.
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- Source: https://arxiv.org/abs/2607.24885v1
- Canonical: https://arxiv.org/abs/2607.24885v1
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Eliminating Propagation Delay: Attention-Based Spatial-Temporal Fusion Graph Convolution Network for Traffic Flow Prediction Jinpeng Chen School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and TelecommunicationsBeijingChina jpchen@bupt.edu.cn , Ziyu Yu 2022140861@bupt.edu.cn School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and TelecommunicationsBeijingChina , Tao Wang kkkwt1998@163.com School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and TelecommunicationsBeijingChina , Jun Ma majun@bupt.edu.cn School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and TelecommunicationsBeijingChina , Hongbo Gao ghb48@ustc.edu.cn Department of Automation, School of Information Science and Technology, University of Science and Technology of ChinaHefeiChina , Senzhang Wang szwang@csu.edu.cn School of Computer Science and Engineering, Central South UniversityChangshaChina , Zufeng Zhang zhangzufeng@tsari.tsinghua.edu.cn Department of Automation, Tsinghua UniversityBeijingChina and Kaimin Wei kaiminwei@jnu.edu.cn College of Information Science and Technology, Jinan UniversityGuangzhouChina Abstract. Predicting traffic flow is crucial to optimizing transportation systems and improving urban mobility. Many graph convolution-based models have been proposed to extract spatial-temporal features and predict traffic flow. However, most focus on spatial-temporal and semantic correlation in topological relationships. There are two primary problems to address. Firstly, the convolutional structure in the model focuses on utilizing static spatial dependencies and spatial-temporal relationships in topological structures, while neglecting the different information propagation delays between adjacent nodes in the convolution. Secondly, these methods often stack a large number of complex structures, resulting in a substantial increase in computational time during the model training phase, thereby disregarding the model’s requirements for timeliness. In this paper, we propose a novel network called the Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN). We design a spatial-temporal fusion block to extract the spatial-temporal feature correlations with propagation delay errors removed and to capture both long-term and short-term temporal characteristics of the data within a multi-head self-attention mechanism based on a mask matrix. Extensive experiments on five real-world datasets demonstrate that our method achieves the best overall performance while having good computation and data utilization efficiency compared with the eight baseline methods. Traffic flow prediction, Propagation delay, Attention mechanism, Spatial-temporal graph convolutional network †ccs: Computing methodologies Neural networks†ccs: Applied computing Transportation 1. Introduction The widespread application of Intelligent Transportation Systems (ITS) in urban traffic management signifies a profound integration of technology into the transportation sector. Combining advanced information technology, communication systems, and data processing techniques, ITS aims to optimize the operation of urban transportation systems, improving efficiency, safety, and sustainability(Yin et al., 2015). However, the complexity and unpredictability of urban traffic systems still pose challenges, making accurate traffic management a continuous endeavor. Within this dynamic context, the exploration of traffic flow prediction has emerged as an imperative and progressively vital area of study. Traffic flow, a key indicator of road conditions, is crucial in guiding the management and control of urban traffic. Within the domain of Intelligent Transportation Systems (ITS), precise and reliable traffic flow prediction serves as a valuable tool for route planning and congestion prevention. So far, many deep learning-based short-term traffic flow prediction models have been proposed (Xu et al., 2022; Z, 2024; Chen et al., 2024a). However, most models focus on the topological structure of the entire transportation network in large cities or regions, which means that modeling and training may concentrate more on capturing the temporal pattern of adjacent nodes in the topological structure, ignoring the spatial-temporal heterogeneity in transportation data, making it difficult to accurately capture and model complex and dynamic spatial-temporal correlations in transportation data (Yin et al., 2021). For example, in the long term, traffic flow exhibits notable variations at different times of the day. During peak commute hours, road traffic typically experiences a rapid surge, while it tends to be sparser during off-peak hours. Urban nodes with diverse functions often manifest analogous patterns in traffic flow changes, such as congestion in shopping centers during weekends and evenings. On the other hand, traffic conditions are significantly influenced by events. Special events such as sports games, concerts, or emergency road maintenance can have a considerable impact on traffic flow in specific areas and during particular periods. Moreover, due to the varying physical distances between different nodes, the time it takes for traffic information to propagate between nodes often also varies. Existing models and methodologies face challenges in effectively capturing the characteristics of highly dynamic spatial-temporal data. In the initial phase of traffic data analysis, Convolutional Neural Networks (CNNs) were applied to grid-based traffic data, effectively capturing spatial correlations (Zhang et al., 2019; Shao et al., 2021). Parallel to this, the temporal dynamics of the traffic were deciphered using Recurrent Neural Networks (RNNs) and Long Short-Term Memory (LSTM) networks (Tian and Pan, 2015; Du et al., 2017; Kang et al., 2017; Lu et al., 2021). This bifurcated approach evolved with the introduction of Graph Neural Networks (GNNs). GNNs, which aligned more closely with the inherent graph structure of traffic networks, offered a more nuanced understanding of spatial dependencies (Yu et al., 2018). GNN-based models predominantly model spatial dependencies in a statical way, either predefined (Li and Zhu, 2021; Guo et al., 2022; Song et al., 2020) or through self-learning (Wu et al., 2019). This approach exhibits limitations in comprehending the dynamic and often unpredictable patterns of urban traffic. The static nature of these models fails to capture the temporal variability and evolution inherent in traffic flows. In recent research, there has been a shift towards integrating self-attention mechanisms with GNN models to extract temporal features more accurately (Jiang et al., 2023; Yan et al., 2021; Ye et al., 2022; Xu et al., 2020; Veličković et al., 2018). These models employ different spatial graphs to establish more precise spatial relationships, enhancing the model’s ability to predict traffic patterns. However, these GNN-based models with instant messaging mechanisms often neglect the potential impact of time delay in the propagation of spatial information (Chen et al., 2024b). For example, the time that takes for a traffic incident in one location to affect adjacent areas is frequently overlooked. This aspect underlines the necessity for models that can adequately account for time delays in spatial information propagation, ensuring a more realistic representation of traffic dynamics. To address the above issues, we propose an Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN) for traffic flow prediction. To facilitate the simultaneous modeling of time dependencies at different granularities, we have designed a novel multi-head temporal self-attention module to capture dynamic spatial correlations. This module integrates local neighborhood information and global information influenced by various factors into self-attention interactions through different graph masking methods, allowing it to capture both short-term and long-term temporal features in traffic data simultaneously. Building on this module, we have further designed a delayed perception feature-based spatial-temporal fusion graph convolution module, calculating temporal correlation matrices with different time steps and revealing hidden spatial-temporal dependencies through fusion graph convolutions of sequential time step data. In summary, the main contributions of this paper are as follows: • We propose a novel A-STFGCN framework based on the multi-head self-attention mechanism and Spatial-Temporal Fusion convolution for accurate traffic flow prediction. Our approach fully addresses the issues of obtaining Spatial-Temporal relationships in topological structures of traffic data. • We design a multi-head temporal self-attention module to effectively and efficiently extract and fuse long- and short-range temporal features of the data via different graph masking methods. Then, we propose a spatial-temporal fusion graph module to eliminate information propagation delay errors and synchronously capture spatial-temporal correlations in topological relationships. • We evaluate the proposed A-STFGCN framework on five real-world traffic speed prediction datasets, which achieves the best overall performance but also has good computational efficiency and data utilization efficiency compared to the eight baseline methods. 2. Related Work 2.1. Spatial-Temporal Traffic Forecasting and Dynamic Graph Learning Traffic flow prediction is a classic spatial-temporal forecasting task for intelligent transportation systems. Early deep models usually handled temporal and spatial dependencies with separate components, such as recurrent networks for time series and graph convolution for road topology. Representative GNN-based models, including DCRNN, STGCN, T-GCN, and Graph WaveNet, improved traffic forecasting by propagating information on physical or learned road graphs (Li et al., 2018; Yu et al., 2018; Zhao et al., 2019; Wu et al., 2019). Later, localized and fusion spatial-temporal graph models, such as STSGCN and STFGNN, further improved cross-time graph propagation (Song et al., 2020; Li and Zhu, 2021). However, a fixed road graph or a purely synchronous spatial-temporal graph may still be insufficient when traffic states propagate with different time lags across road segments. Recent studies therefore increasingly focus on adaptive and dynamic graph learning. DSTAGNN learns dynamic spatial-temporal aware graphs, MVDGCN models multi-view dynamic station relations, and FEDDGCN further decouples traffic signals while enhancing dynamic graph learning with frequency-domain information (Lan et al., 2022; Huang et al., 2023; Zhang et al., 2025). MetaDG extends dynamic graph modeling by generating dynamic node representations, adjacency matrices, and meta-parameters for spatio-temporal prediction (Zou et al., 2026). These methods demonstrate the importance of dynamic spatial dependencies, but their learned graph structures are often implicit. In contrast, A-STFGCN explicitly constructs delay-temporal graphs with DTW-based shifted alignment, making the cross-node propagation delay more interpretable and reusable as an offline graph prior. 2.2. Attention, Transformer and Decomposition-based Forecasting Self-attention and Transformer-style models have also become important tools for traffic forecasting because they can capture long-range temporal and spatial dependencies (Vaswani et al., 2017; Xu et al., 2020; Yan et al., 2021; Ye et al., 2022; Reza et al., 2022). ASTGCN introduces spatial-temporal attention for traffic forecasting, SAST-GNN applies self-attention to spatio-temporal graph prediction, GDFormer learns graph diffusion attention, and Bi-STAT uses spatial-adaptive and temporal-adaptive Transformer modules (Guo et al., 2019; Xie et al., 2020; Su et al., 2022; Chen et al., 2022). PDFormer is particularly relevant because it studies propagation-delay-aware long-range Transformer modeling (Jiang et al., 2023). Compared with these Transformer-oriented methods, our model uses a lighter GCN-based backbone with masked temporal self-attention: the delay relation is first encoded into explicit fusion graphs, and the attention branch is then used to complement local convolution with DTW-guided temporal dependencies. Another recent trend is to decompose traffic signals into more interpretable components. STDN disentangles trend-cyclical and seasonal patterns with spatio-temporal embeddings, FEDDGCN separates prominent periodic and perturbative components with frequency filters, and DualCast explicitly separates intrinsic traffic patterns from aperiodic environmental events (Cao et al., 2025; Zhang et al., 2025; Su et al., 2025). These works show that traffic forecasting benefits from modeling heterogeneous temporal patterns rather than treating all observations uniformly. A-STFGCN is complementary to this line of research: instead of decomposing the input series into frequency or event components, it focuses on the propagation pathway by aligning node pairs under short time shifts and injecting the resulting delay-aware relations into graph convolution and temporal attention. 2.3. Hierarchical and Large-scale Graph Modeling Large road networks bring additional challenges because full node-level message passing can be computationally expensive and may obscure regional traffic patterns. Hierarchical models introduce regional or macro-micro graph structures for traffic forecasting, and STAGCN-EC combines attention with graph convolution for efficient traffic forecasting (Wang et al., 2022; Guo et al., 2021; Lai et al., 2022). More recently, latent graph structure learning has been proposed for large-scale traffic forecasting by learning adaptive patch assignments in a data-driven manner (Wang et al., 2025). These approaches motivate the use of coarser spatial abstractions for large-scale scenarios. A-STFGCN follows this direction but keeps the macro graph construction simple and interpretable: spectral clustering produces a static cluster graph, and the transmit block dynamically sends macro-level regional trends back to node-level features. Table 1 summarizes the above model families from the perspective of the components most relevant to this work. Rather than claiming novelty from self-attention or graph convolution alone, A-STFGCN is positioned as a combined design that integrates macro-micro spatial abstraction, explicit delay-aware graph construction, and DTW-guided masked temporal self-attention. Table 1. Comparison of representative traffic forecasting models and recent related studies. Models Key modeling components GCN Adaptive/ Dynamic Graph Macro/ Patch Graph Delay-aware Attention/ Decomposition ARIMA / GRU - - - - - DCRNN / STGCN / T-GCN ✓ - - - - Graph WaveNet / DSTAGNN ✓ ✓ - - - STFGNN ✓ - - ✓ - ASTGCN / GDFormer / Bi-STAT ✓ ✓ - - ✓ PDFormer ✓ ✓ - ✓ ✓ HGCN / STAGCN-EC ✓ - ✓ - ✓ STDN / FEDDGCN / DualCast ✓ ✓ - - ✓ Latent Graph Learning - ✓ ✓ - - MetaDG ✓ ✓ - - - A-STFGCN (ours) ✓ ✓ ✓ ✓ ✓ 3. Preliminaries 3.1. Notations and Definitions Definition 1 (Traffic Road Network): We represent the traffic road network as an undirected graph =(,ℰ,)G=(V,E, A), where =v1,…,vNV=\v_1,...,v_N\ is the set of N sensor nodes and ℰ⊆×E ×V is the set of physical road connections. ∈ℝN×N A ^N× N is the adjacency matrix of G. In this paper, ij=1 A_ij=1 indicates that nodes viv_i and vjv_j are directly connected. Definition 2 (Traffic Graph Signal): We use t∈ℝN×D X_t ^N× D to denote the traffic observations of all nodes at time step t, where D is the feature dimension collected by sensors. The historical traffic tensor is denoted by =(1,…,T)∈ℝN×T×D X=( X_1,..., X_T) ^N× T× D. Definition 3 (Propagation Delay): We estimate the temporal similarity between node pairs using the Dynamic Time Warping (DTW) algorithm. For two nodes viv_i and vjv_j, if the DTW similarity between the time series of viv_i and the k-step shifted time series of vjv_j is higher than their synchronous similarity, we regard this pair as exhibiting a k-step propagation delay. 3.2. Problem Formalization Traffic flow prediction aims to predict future traffic states from historical observations on a road network. Given the graph G, an input window of length T1T_1, and a prediction horizon of length T2T_2, our goal is to learn a mapping function f such that (1) (t−T1+1),…,t;→(t+1),…,t+T2;\ X_(t-T_1+1),..., X_t;G\ f\ X_(t+1),..., X_t+T_2;G\ Table 2. Core notations used in A-STFGCN. Symbol Shape/Type Meaning =(,ℰ,)G=(V,E, A) Graph Traffic road network with node set, edge set, and adjacency matrix. N,NCN,N^C Scalars Number of sensor nodes and number of macro nodes in the cluster graph. T1,T2,DT_1,T_2,D Scalars Input sequence length, prediction horizon, and feature dimension. ,C X, X^C ℝN×T1×DR^N× T_1× D, ℝNC×T1×DR^N^C× T_1× D Node-level input tensor and macro-graph input tensor. T,Td Mat_T, Mat_T^d ℝN×NCR^N× N^C Static cluster assignment matrix and dynamic transmit matrix. X ℝN×T1×2DR^N× T_1× 2D Node representation after fusing node-level and macro-level features. sg A_sg ℝN×NR^N× N Spatial adjacency matrix derived from the physical road network. tg1,tg2 A_tg^1, A_tg^2 ℝN×NR^N× N Delay-temporal graphs corresponding to 1-step and 2-step propagation delays. tc A_tc ℝN×NR^N× N Temporal self-correlation matrix in the spatial-temporal fusion graph. stfg A_stfg Graph / matrix set Spatial-temporal fusion graph used by GSTF-GCN. t M_t ℝT1×T1R^T_1× T_1 DTW-based temporal similarity mask for masked temporal self-attention. Y ℝN×T2×DR^N× T_2× D Predicted future traffic flow. 4. Methodology Figure 1 summarizes the high-level data flow of A-STFGCN, while Figure 2 provides the detailed module-level architecture. Given raw traffic observations ∈ℝN×T1×D X ^N× T_1× D, the model first constructs a macro graph by spectral clustering, then transfers macro-level features back to the node-level branch through a transmit block, next extracts delay-aware spatial-temporal features with STF-Blocks, and finally outputs ^∈ℝN×T2×D Y ^N× T_2× D. Therefore, the core of A-STFGCN is not a simple stack of modules, but the combination of macro-micro spatial abstraction, a delay-aware fusion graph, and masked temporal self-attention. The original graph branch and the cluster graph branch are processed in parallel. The macro graph provides stable regional context for large-scale road networks, while the node-level branch preserves fine-grained local dynamics. Their interaction allows the model to jointly capture regional propagation patterns and road-segment-level temporal variations. Raw input∈ℝN×T1×D X ^N× T_1× DSpectral clustermacro graph C X^CNode branchlocal traffic statesTransmit blockmacro-micro fusionSTF-Blocksdelay-aware graph+ masked attentionOutput block^∈ℝN×T2×D Y ^N× T_2× D Figure 1. High-level data flow of A-STFGCN. Historical observations are processed by a node-level branch and a macro-graph branch, then fused before the STF-Blocks generate future traffic predictions. A flow diagram showing raw traffic input branching into a spectral clustering branch and a node branch, followed by a transmit block, STF-Blocks, and an output block that predicts future traffic flow. Figure 2. Detailed framework of A-STFGCN. (a) shows the parallel node-level and cluster-graph branches. (b) shows the detailed architecture of an STF-Block. (c) illustrates a spatial-temporal fusion graph composed of delay-temporal graphs tg1 A_tg^1 and tg2 A_tg^2, the spatial graph sg A_sg, and the temporal self-correlation graph tc A_tc. A detailed architecture diagram of A-STFGCN showing node-level and cluster-level branches, transmit blocks, STF-Blocks, and the spatial-temporal fusion graph components. 4.1. Spectral Cluster Given the raw input =(1,2,…,T1)∈ℝN×T1×D X=( X_1, X_2,..., X_T_1) ^N× T_1× D, we first build a macro graph to reduce the complexity of large road networks and to capture propagation patterns at the region-level. This step provides a more stable spatial context for subsequent node-level prediction. Our motivation is that traffic propagation is usually more coherent within locally connected regions than across the entire city-scale graph. Therefore, adjacent nodes with similar structural roles can be grouped into macro nodes without losing the dominant regional dynamics. This macro representation complements the original graph by emphasizing coarse-grained spatial organization. To obtain the macro graph, we apply spectral clustering to the adjacency matrix of the original road network. As shown in Figure 3, the Laplacian of the adjacency matrix is used to partition the road network, and each partition is treated as a macro node. If there exists a node vi∈cluster1v_i∈ cluster_1 and a node vj∈cluster2v_j∈ cluster_2 such that viv_i and vjv_j are connected in the original graph, then the corresponding macro nodes are connected in the cluster graph. Because the road topology is static for a given dataset, the spectral clustering step is executed only once before training and reused throughout all training epochs and test-time predictions. The cluster number NCN^C controls a trade-off between regional abstraction and local fidelity: a very small NCN^C tends to over-smooth heterogeneous road segments, whereas an excessively large NCN^C makes the macro graph too close to the original graph and weakens the efficiency gain. We therefore select NCN^C according to the validation-set performance for each dataset, and the resulting settings are summarized in Table 7. Figure 3. The sketch map of the clustering process. A road-network clustering sketch showing how original sensor nodes are partitioned into macro regions. The feature of each macro node is obtained by aggregating the average and minimum values of nodes in the same cluster. As a result, the clustered input is represented by C=(1C,2C,…,T1C)∈ℝNC×T1×D X^C=( X^C_1, X^C_2,..., X^C_T_1) ^N^C× T_1× D, where NCN^C is the number of macro nodes. Thus, the spectral clustering module transforms the original node-level input X into a macro-graph representation C X^C that is used together with the original branch in the following modules. 4.2. Transmit Blocks The transmit block sends region-level trends back to road-segment-level representations, so that each node can simultaneously observe its local state and the macro context of the region to which it belongs. Given ∈ℝN×T1×D X ^N× T_1× D and C∈ℝNC×T1×D X^C ^N^C× T_1× D, the block outputs fused node features ∈ℝN×T1×2D X ^N× T_1× 2D. We first define a static assignment matrix T∈ℝN×NC Mat_T ^N× N^C to encode the cluster membership of each node: (2) [T]ij=1if node i belongs to cluster j,0else.[ Mat_T]_ij= cases1&if node i belongs to cluster j,\\ 0&else. cases This matrix provides fixed mapping from node space to cluster space. In other words, each row selects the macro node that contains the sensor i. To adapt this fixed assignment to the time-varying traffic states, we further learn a dynamic transmit matrix Td∈ℝN×NC Mat_T^d ^N× N^C: (3) F =tanh((T1)2(C3)T+b) = (( X^T U_1) U_2( X^C U_3)^T+b) ′ F =−mean() = F-mean( F) Td Mat_T^d =′T = F Mat_T The matrix Td Mat_T^d reweights the node-to-cluster relations according to the current cross-scale affinity, so that the macro information transmitted can vary with traffic dynamics. Using Td Mat_T^d, we project the cluster features back into the node space and concatenate them with the original node features: (4) C X^C =TdC = Mat_T^d X^C X =⊕C = X X^C Here, C∈ℝN×T1×D X^C ^N× T_1× D is the macro feature projected into the node space, and ⊕ denotes the concatenation of the features rather than graph fusion. Therefore, X retains the local node information and the region-level context simultaneously. 4.3. STF-Blocks(Spatial-Temporal Fusion) As shown in Figure 2(b), each STF-Block contains three tightly coupled components: delay-aware graph construction, gated spatial-temporal fusion graph convolution (GSTF-GCN), and masked temporal self-attention. Given the fused node representation X, this block jointly models local spatial propagation, delay-aware interactions, and long-range temporal dependencies. 4.3.1. Gated Spatial-Temporal Fusion Graph Convolution Figure 4. Gated Spatial-Temporal Fusion Graph Convolution Block. A block diagram of GSTF-GCN showing graph convolution, spatial-temporal fusion graph convolution, gated temporal convolution, and residual output flow. The internal structure and information flow of GSTF-GCN are illustrated in Figure 4.We first construct a spatial-temporal fusion graph to relax the synchronous-propagation assumption made by conventional spatial graphs. In this graph, sg∈ℝN×N A_sg ^N× N denotes the physical spatial adjacency matrix, tg1 A_tg^1 and tg2 A_tg^2 denote the strongest 1-step and 2-step delay-temporal links discovered by DTW, and tc A_tc denotes the temporal self-correlation matrix. Their combination forms the spatial-temporal fusion graph stfg A_stfg, which preserves spatial neighbors, delay-aware cross-node relations, and temporal continuity in a unified structure. To estimate tg1 A_tg^1 and tg2 A_tg^2, we use FastDTW to compare delayed node sequences. Figure 5 gives an intuitive one-step delay example: the downstream series is better aligned after a temporal shift than at the same timestamp, which is exactly the pattern to capture the delay-temporal edges. We restrict the delay-temporal graph to 1-step and 2-step shifts because all datasets are sampled every 5 minutes, so these two graphs correspond to 5-minute and 10-minute propagation lags. For adjacent roads, the dominant spillback or downstream response is usually concentrated in this short window; larger shifts are more easily contaminated by unrelated temporal variations, while their longer-range effects can still be accumulated by stacked STF-Blocks and temporal attention. To keep the graph sparse and stable, we retain only the top-k delayed neighbors with the smallest alignment distance for each node. The following procedure summarizes this construction: Sensor viv_iSensor vjv_jxt−4x_t-4xt−3x_t-3xt−2x_t-2xt−1x_t-1xt−3x_t-3xt−2x_t-2xt−1x_t-1xtx_tA consistent shifted alignment indicates that the response of vjv_j lags behind viv_i,which motivates a delay-temporal edge in tg1 A_tg^1. Figure 5. Illustrative DTW-based delay alignment between two sensor series. A better alignment after a one-step shift indicates that downstream observations lag behind upstream changes. A two-row timeline diagram for sensors vi and vj. The lower row is shifted one step later, and arrows connect matching pattern positions to illustrate one-step propagation delay. Algorithm 1 Delay-Temporal Graphs Generation 1:Input: =1,2,…,T1∈ℝN×T1×D X=\ X_1, X_2,…, X_T_1\ ^N× T_1× D 2:for i←1i← 1 to N do 3: for j←1j← 1 to N do 4: disti,j1=TDL(i[:−1],j[1:])dist_i,j^1=TDL( X_i[:-1], X_j[1:]) 5: disti,j2=TDL(i[:−2],j[2:])dist_i,j^2=TDL( X_i[:-2], X_j[2:]) 6: Sort smallest k elements and their indices 7: 1=j11,j21,…,jk1 J^1=\j_1^1,j_2^1,…,j_k^1\, 2=j12,j22,…,jk2 J^2=\j_1^2,j_2^2,…,j_k^2\ 8: for j1j^1 in 1 J^1 do 9: ,←1 A_tg_i,j^1← 1 10: ,←1 A_tg_j,i^1← 1 11: for j2j^2 in 2 J^2 do 12: ,←1 A_tg_i,j^2← 1 13: ,←1 A_tg_j,i^2← 1 14:Return: Weighted Matrices 1,2 A_tg^1, A_tg^2 For a fixed FastDTW search radius, each pairwise delayed alignment is approximately linear in the sequence length, so constructing tg1 A_tg^1 and tg2 A_tg^2 is roughly proportional to N2T1N^2T_1, which is substantially lighter than repeatedly applying standard DTW inside model training. More importantly, this graph construction is performed offline once on the training split, and the resulting sparse graphs are reused during both training and inference. Therefore, the delay-aware modeling improves the receptive graph without introducing per-iteration overhead at deployment time. If the long-term traffic statistics drift, the same offline procedure can be rerun periodically to refresh the delay graph. Given ∈ℝN×T1×2D X ^N× T_1× 2D, GSTF-GCN first extracts local topological responses with the graph Laplacian, and then refines them with stfg A_stfg to reduce propagation-delay errors: (5) 1 H^1 =~1+b1 = A X W_1+b_1 2 H^2 =ReLU(stfg12+b2) =ReLU( A_stfg H^1 W_2+b_2) where 1,2 W_1, W_2 and b1,b2b_1,b_2 are trainable parameters, and ~ A is the Laplacian-based representation corresponding to the graph. Intuitively, 1 H^1 captures local spatial interactions, while 2 H^2 further aligns these interactions with delay-aware propagation patterns encoded in stfg A_stfg. To extract short-range temporal dynamics efficiently, we further apply a gated dilated convolution to 2 H^2. This step enlarges the temporal receptive field while keeping the computation lightweight: (6) [1,2] [ β_1, β_2 ] =split(Convdil=2(2)) =split(Conv_dil=2( H^2)) 3 H^3 =tanh(1)⊙σ(2) = ( β_1) σ( β_2) where Convdil=2Conv_dil=2 denotes the temporal dilated convolution and split divides the output into two equal parts. The gate selectively preserves useful local temporal responses, and 3∈ℝN×T11×D H^3 ^N× T_1^1× D, where T11=T1−2∗kc+2T_1^1=T_1-2*k_c+2 and kck_c is the temporal kernel size. To complement the above local modeling, we then apply attention to summarize more global temporal interactions: (7) 4 H^4 =3∗Attention() = W_3*Attention( X) =3∑i=1(i3⋅q⋅(i3⋅k)T⋅i3⋅v) = W_3 C _i=1 C ( H^3_i· W_q·( H^3_i· W_k)^T· H^3_i· W_v ) 4 H^4 =4+3+b3 = H^4+ H^3+b_3 output GCN_output =Linear(4⊕1) =Linear( H^4 H^1) The residual connection preserves local temporal information from 3 H^3, while the final linear layer fuses global temporal responses with the earlier spatial feature 1 H^1. 4.3.2. Masked Multi-head Self Attention The second temporal branch of STF-Block is a masked temporal self-attention module, which is used to capture non-local temporal dependencies beyond the convolutional receptive field. Different from a standard causal mask, t M_t is a DTW-based temporal similarity mask. Its role is to selectively strengthen interactions between time steps with similar traffic evolution patterns, so that unreliable temporal interactions are suppressed while more trustworthy long-range dependencies are preserved. For each attention head i, the fused feature X is projected into query, key, and value tensors: (8) i=iQ,i=iK,i=iV Q_i= X W_i^Q, K_i= X W_i^K, V_i= X W_i^V where iQ W_i^Q, iK W_i^K, and iV W_i^V are trainable projection matrices. The resulting i Q_i, i K_i, and i V_i preserve the temporal length T1T_1 and describe how each time step queries, matches, and aggregates information from the other time steps. We then perform multi-head self-attention along the temporal dimension: (9) MultiHead() ( X) =Concat(head1,…,headh)O =Concat(head_1,…,head_h) W^O headi _i =Attention(i,i,i) =Attention( Q_i, K_i, V_i) Attention(i,i,i) ( Q_i, K_i, V_i) =softmax(iiTdk)i =softmax ( Q_i K_i^T d_k ) V_i To balance selectivity and completeness, we keep both a masked branch and an unmasked branch. The masked branch emphasizes DTW-consistent temporal alignments, while the unmasked branch preserves global context that may still be useful for prediction: (10) output=Linear( MMS_output=Linear( (MultiHead()⊙t)⊕MultiHead()) (MultiHead( X) M_t) MultiHead( X)) The symbol ⊙ denotes the Hadamard product. Therefore, output MMS_output fuses a DTW-guided temporal representation with an unmasked global temporal representation. 4.4. Output Block To preserve multi-level information from different STF-Blocks, we add a skip connection with a 1×11× 1 convolution after each block. This design keeps features from different depths and alleviates information attenuation in deeper layers. Specifically, each STF-Block output outputi STF_output^i is projected to the skip dimension ski∈ℝN×T′×Dsk STF_sk^i ^N× T × D_sk. The skip features are then summed and convolved to obtain the final hidden state hid X_hid, which is mapped to the prediction ^∈ℝN×T2×D Y ^N× T_2× D: (11) ski STF_sk^i =Conv(outputi) =Conv( STF_output^i) hid X_hid =Conv(sk1+sk2) =Conv( STF_sk^1+ STF_sk^2) Y =ReLU(Linear(hid)) =ReLU(Linear( X_hid)) We optimize the model using the mean absolute error (MAE). Given the ground truth =(T1+1,T1+2,…,T1+T2) Y=( X_T_1+1, X_T_1+2,..., X_T_1+T_2), the loss is defined as (12) MAE(,^)=1N∑i=1N|^i−i|MAE( Y, Y)= 1N _i=1^N| Y_i- Y_i| Table 3. Experimental Results on PeMS04, PeMS07, and PeMS08. Datasets PEMS04 PEMS07 PEMS08 Metrics MAE RMSE Accuracy MAE RMSE Accuracy MAE RMSE Accuracy Models ARIMA 30.792 36.106 0.757 36.761 44.952 0.719 25.817 36.204 0.868 GRU 28.469 41.322 0.836 29.236 43.504 0.830 22.852 35.023 0.877 STGCN 27.190 34.166 0.851 30.108 44.050 0.833 20.125 32.589 0.878 T-GCN 28.963 44.487 0.835 28.624 41.368 0.832 20.717 33.004 0.883 STFGNN 21.045 33.003 0.878 24.015 37.011 0.869 17.636 25.985 0.906 ASTGCN 22.175 34.166 0.873 26.748 40.817 0.868 16.824 25.892 0.908 STAGCN-EC 22.445 33.689 0.876 26.236 37.811 0.869 — — — HGCN 22.210 33.823 0.872 29.052 39.942 0.872 17.428 26.122 0.908 A-STFGCN 20.515 31.974 0.878 22.208 34.599 0.874 16.018 25.465 0.924 Table 4. Experimental Results on CA and GLA. Datasets CA GLA Metrics MAE RMSE Accuracy MAE RMSE Accuracy Models ARIMA 37.052 52.114 0.754 40.704 57.861 0.702 GRU 30.178 44.747 0.798 32.246 44.650 0.772 STGCN 21.131 36.792 0.862 22.687 38.102 0.857 T-GCN 26.967 39.667 0.842 27.052 42.712 0.841 STFGNN 21.032 35.580 0.868 21.648 36.785 0.872 ASTGCN 28.052 44.623 0.820 27.989 42.783 0.822 GWNET 21.515 34.024 0.871 20.232 32.886 0.883 HGCN 20.986 33.475 0.881 21.015 33.768 0.878 A-STFGCN 19.883 31.213 0.886 20.252 32.526 0.883 5. Experiments In this section, we provide five traffic flow datasets to evaluate the method, then compare the proposed A-STFGCN with state-of-the-art existing work, and finally analyze the effectiveness of A-STFGCN through ablation studies. 5.1. Datasets We conducted our model evaluation using five highway traffic datasets: PeMS07, PeMS04, PeMS08, CA, and GLA. PeMS04, PeMS07, and PeMS08 are derived from real-time data collected by the California Department of Transportation’s Performance Measurement System (PeMS). After preprocessing, they provide traffic data every five minutes. In the experiment, we used traffic flow data from the past hour to predict traffic flow for the next hour. These three datasets contain distance information from adjacent sensors, so we can extract spatial features from both adjacent and distance information. CA and GLA are part of the LargeST benchmark dataset. CA includes a total of 8,600 sensors with data spanning five years (from 2017 to 2021), covering a wide area of California. GLA, a subset of CA, includes 3,834 sensors installed in 5 counties in the Greater Los Angeles area. The LargeST dataset provides comprehensive metadata for each sensor, including coordinates, highway category, number of lanes, and more, allowing detailed spatial-temporal analysis. Similar to PeMS datasets, CA and GLA provide traffic data every five minutes. Table 5 meticulously details the dataset specifications. We employ Z-score normalization for data processing from all datasets. We construct the adjacency matrix of the road network. Each dataset is divided into 60% for training, 20% for validation, and 20% for testing in chronological order. Table 5. Description of traffic datasets used in this study. Datasets #Nodes #Edges #Timesteps #Interval(min) PeMS04 307 340 16,992 5 PeMS07 883 866 28,224 5 PeMS08 170 290 17,856 5 CA 8600 201363 525,888 5 GLA 3834 98703 525,888 5 5.2. Evaluation In our experimental analysis, we assess performance using three pivotal metrics: (1) Mean Absolute Error (MAE), (2) Root Mean Squared Error (RMSE), and (3) Accuracy. It is important to note that missing values within the datasets have been excluded from these calculations to ensure the integrity and accuracy of our metric evaluations. 5.3. Experimental Settings All experiments in this work were carried out using PyTorch 1.2.0 on a workstation equipped with an NVIDIA RTX 3090 GPU (24 GB of memory). The best checkpoint was selected according to the validation-set performance, and the model was optimized with Adam using an initial learning rate of 0.0001. We trained the model for 80 epochs with a batch size of 32. For all five datasets, the sampling interval is 5 minutes. Therefore, using the past hour to predict the next hour corresponds to the input steps T1=12T_1=12 and the prediction steps T2=12T_2=12 . The delay-temporal graph ATGA_TG in Algorithm 1 was generated offline before model training and then reused during both training and inference. In our implementation, this preprocessing step took around 20 minutes for most public datasets. The FastDTW search length was set to 12, which is consistent with the longest forecasting horizon considered in this work. We use only 1-step and 2-step delay graphs because they correspond to the dominant 5-minute and 10-minute local propagation lags under our sampling rate, while longer effective dependencies are further modeled by stacked STF-Blocks and temporal attention. The sparsity parameter k in Algorithm 1 and the cluster number NCN^C were selected based on the validation-set performance. To simplify graph fusion, the entries of sg A_sg, tg1 A_tg^1, tg2 A_tg^2, and tc A_tc were binarized to 0,1\0,1\. Table 6. Reproducibility summary of A-STFGCN. Category Parameter Value Data setting Sampling interval 5 minutes for all datasets. Data setting Input / prediction horizon T1=12T_1=12 and T2=12T_2=12, corresponding to past 60 minutes for future 60-minute prediction. Data setting Data split Chronological split with 60% training, 20% validation, and 20% testing. Data setting Normalization Z-score normalization. Training Framework / hardware PyTorch 1.2.0 on an NVIDIA RTX 3090 GPU with 24 GB memory. Training Optimizer / learning rate Adam with initial learning rate 1×10−41× 10^-4. Training Batch size / epochs Batch size =32=32; training epochs =80=80. Delay graph Delay steps 1-step and 2-step delay-temporal graphs, i.e., tg1 A_tg^1 and tg2 A_tg^2. Delay graph FastDTW search length 12. Delay graph Construction mode Precomputed offline before training; typical preprocessing time is about 20 minutes on public datasets. Architecture STF-Block temporal dilation dil=2dil=2. Architecture Temporal kernel size ts=1t_s=1. Architecture Graph value type The entries of the fused subgraphs are binarized to 0,1\0,1\. Architecture Output skip mapping 1×11× 1 convolution after each STF-Block. Table 7. Dataset-specific cluster settings. Dataset N^C PeMS04 20 PeMS07 40 PeMS08 40 CA 400 GLA 200 The dataset-specific cluster counts are summarized in Table 7. In particular, we set NC=400N^C=400 for CA, NC=200N^C=200 for GLA, NC=20N^C=20 for PeMS04, and NC=40N^C=40 for PeMS07 based on validation-set performance. For datasets not explicitly listed in the tuning record, we followed the same validation-based selection protocol. 5.4. Baselines The proposed model A-STFGCN is compared with eight well-known baseline models as follows: ARIMA: The Auto-Regressive Integrated Moving Average model is a classical statistical approach used for predicting future values in time-series data, leveraging dependencies within the series. GRU: The Gated Recurrent Unit network, which represents an enhancement over the traditional Recurrent Neural Network (RNN), aims to solve the vanishing gradient problem commonly associated with standard RNNs(Cho et al., 2014). STGCN: Spatial-Temporal Graph Convolutional Networks incorporate both Gated Linear Unit (GLU) and graph convolution operations to address spatial and temporal data dependencies(Yu et al., 2018). T-GCN: The Temporal Graph Convolutional Network is designed to integrate temporal dynamics with graph convolutional methods to enhance prediction accuracy in network data(Zhao et al., 2019). STFGNN: The Spatial-Temporal Fusion Graph Neural Network utilizes the DTW algorithm to generate the temporal graph and designs the spatial-temporal fusion graph neural module to synchronously capture the spatial-temporal relation(Li and Zhu, 2021). ASTGCN: Attention Based Spatial-Temporal Graph Convolutional Network combines attention mechanisms with the characteristics of spatial-temporal data(Guo et al., 2019). HGCN: A novel Hierarchical Graph Convolution Networks for traffic forecasting by operating on both the micro and macro traffic graphs(Guo et al., 2021). STAGCN-EC: A Spatial-Temporal Attention Graph Convolution Network on Edge Cloud model, model training requires low computational resources and is efficient(Lai et al., 2022). 5.5. Experiment Results and Analysis Table 3 and Table 4 illustrate the average accuracy comparison of traffic flow predictions at 12 time steps (1 hour) between the proposed A-STFGCN model and the eight baseline models mentioned above on five datasets used. Models that perform poorly on the respective datasets are not included in the comparison. Traditional speed prediction methods mainly model temporal regularity and do not explicitly exploit the irregular spatial correlations of road networks. ARIMA therefore performs poorly, while GRU improves temporal modeling but still lacks graph-based spatial propagation. The graph-based baselines, including STGCN, T-GCN, STFGNN, ASTGCN, HGCN, STAGCN-EC, and A-STFGCN, achieve clear improvements because they encode spatial-temporal dependencies. Among them, STFGNN explores potential temporal correlations with FastDTW, ASTGCN and STAGCN-EC introduce attention-based temporal modeling, and HGCN incorporates hierarchical regional information. A-STFGCN further combines these useful directions by using a macro graph, a transmit block, delay-aware fusion graph convolution, and masked temporal self-attention. A detailed analysis of the experimental results shows that A-STFGCN achieves consistently competitive MAE and RMSE across the five datasets. On PeMS04, A-STFGCN reduces MAE by 7.49% and RMSE by 5.10% compared with the strongest baseline, indicating improved numerical prediction reliability even when the accuracy metric is close. On PeMS07, A-STFGCN obtains a larger improvement, with MAE reduced by 15.35%, RMSE reduced by 8.49%, and accuracy increased by 1.57%. PeMS07 contains many more sensors than PeMS04 and PeMS08, so this result suggests that the macro-micro feature interaction and delay-aware graph are particularly useful when the road network becomes larger and spatial propagation is more heterogeneous. On PeMS08, the model still outperforms all baselines, although the margin is smaller because the dataset contains fewer sensors and the spatial structure is less complex. The same trend can be observed on the LargeST subsets. For CA, A-STFGCN achieves the lowest MAE and RMSE, reducing MAE and RMSE by 5.26% and 6.75% compared with the next best model HGCN, while also improving accuracy by 0.57%. CA contains 8,600 sensors and covers a much larger road network, where relying only on local topology can miss long-range and region-level propagation. The cluster graph and transmit block provide stable regional context, while the delay-temporal graph helps align cross-node responses under short propagation lags. For GLA, A-STFGCN obtains the lowest RMSE of 32.526 and an accuracy of 0.883, which is comparable to the best baseline. Although its MAE is the second lowest, the lower RMSE indicates that A-STFGCN is more robust to large prediction errors and peak deviations, which are important in complex urban traffic conditions. Following common practice in the compared baselines, we report the results selected by validation-set performance. We did not add a separate multi-run standard deviation table in this revision because rerunning all baselines under the same protocol would require substantial additional experiments. We therefore focus the analysis on the observed performance trends and provide more detailed mechanism-level interpretation of the results. Table 8. Comparison of average training time (in hours) on PeMS04 and PeMS07 datasets. Datasets Training Time(h) A-STFGCN STAGCN-EC HGCN PeMS04 1.21 1.25 0.91 PeMS07 3.61 3.53 5.13 To achieve higher prediction accuracy, some baseline models rely on complex structures that require more time for training and occupy more GPU memory, especially on larger datasets. Excessive training and prediction time can limit practical deployment in urban transportation systems. Table 8 compares A-STFGCN with STAGCN-EC and HGCN, two representative baselines that also consider computational efficiency. A-STFGCN remains close to STAGCN-EC on PeMS04 and PeMS07 while being faster than HGCN on PeMS07, showing that the proposed macro-micro and delay-aware design does not introduce prohibitive training overhead. Moreover, the spectral clustering and delay-temporal graph construction are performed offline and reused during training and inference, so they do not increase the per-epoch or online prediction cost. 5.6. Ablation Study Figure 6. Ablation Study on PeMS04 and PeMS07. Each bar represents MAE performance under different ablation settings. A bar chart comparing A-STFGCN with ablated variants on PeMS04 and PeMS07 using MAE. Figure 7. MAE trend over training epochs on the PeMS08 dataset. The A-STFGCN shows stable convergence compared to baselines. A line chart showing the MAE trend over training epochs on the PeMS08 dataset. We conducted comparative experiments on three variants to analyze the effectiveness of different structures in A-STFGCN. (1) w/o GCN replaces the GSTF-GCN module with regular graph convolutional layers. This variant removes message passing on the spatial-temporal fusion graph and therefore weakens the ability to jointly exploit physical adjacency, temporal self-correlation, and delay-temporal links. (2) w/o mask removes the DTW-guided mask from the temporal multi-head self-attention module. Without this selective temporal filtering, the attention branch treats all temporal interactions more uniformly and may emphasize less reliable temporal alignments. (3) w/o Delay replaces the delay-temporal graph with a synchronous time-correlation matrix. This setting keeps temporal correlation modeling but removes explicit propagation-lag compensation, so it directly tests whether shifted DTW alignment contributes to prediction. Figure 6 compares these variants on the PeMS04 and PeMS07 datasets. The w/o GCN variant performs worse because regular graph convolution cannot fully exploit the fused delay-aware spatial-temporal graph. The w/o Delay variant also degrades, confirming that synchronous correlations alone are insufficient when traffic perturbations propagate across sensors with short time lags. The w/o mask variant shows that temporal self-attention benefits from DTW-guided selectivity rather than attending to all time steps uniformly. Overall, the ablation results indicate that A-STFGCN gains from the cooperation of the fusion graph convolution, the delay-temporal graph, and the masked temporal self-attention module. 6. Limitations and Future Work Although A-STFGCN improves the modeling of spatial-temporal propagation in traffic networks, several limitations remain. First, the spectral cluster graph and the delay-temporal graph are constructed offline from historical topology and traffic sequences. This design keeps online training and inference efficient, but the graphs may need to be periodically updated when the road network, sensor deployment, or long-term traffic pattern changes substantially. Second, the cluster number NCN^C and the sparsity of delay-temporal links are selected according to the validation performance. A fixed granularity is simple and reproducible, but may be suboptimal for cities with highly heterogeneous regional structures. Future work can explore adaptive multi-resolution clustering and dynamic update strategies while preserving the interpretability of the macro graph. Third, the current model relies mainly on historical traffic observations and graph topology. It does not explicitly incorporate external factors such as weather, holidays, incidents, or planned events, which may cause abrupt non-periodic fluctuations. Integrating such exogenous signals with the delay-aware graph is a promising direction to improve robustness under abnormal traffic conditions. Finally, we plan to extend A-STFGCN to other spatial-temporal prediction tasks, such as rainfall prediction and accident prediction, and investigate pre-training or data augmentation techniques for scenarios with insufficient temporal data. 7. Conclusion This study presents a novel network model, the Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN), to predict traffic flow. Traffic flow prediction is crucial for optimizing transportation systems, reducing congestion, and enhancing overall urban mobility. Although various graph convolution-based models have been proposed to extract spatial-temporal features and predict traffic flow, most of them emphasize static spatial dependencies and spatial-temporal relationships in topological structures, neglecting spatial-temporal heterogeneity issues. Our proposed A-STFGCN model addresses these challenges by introducing a Spatial-Temporal Fusion Block to extract spatial-temporal feature correlations. We leverage a Mask matrix-based multi-head self-attention mechanism to capture long-term and short-term temporal features of the data. Extensive experiments on five real-world datasets demonstrate that our method not only achieves the overall best performance, but also exhibits excellent computational efficiency and data utilization efficiency compared to the eight baseline methods. 8. 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