Predictive analytics for traffic flow optimization in urban logistics: A transformer-based time series approach

Abstract

In this study, we focus on the analysis and prediction of urban logistics traffic flow, a field that is gaining increasing attention due to the acceleration of global urbanization and heightened environmental awareness. Existing forecasting methods face challenges in processing large and complex datasets, particularly when extracting and analyzing valid information from these data, often hindered by noise and outliers. In this context, time series analysis, as a key technique for predicting future trends, becomes crucial for supporting real-time traffic management and long-term traffic planning. To this end, we propose a composite network model that integrates gated recurrent unit (GRU), autoregressive integrated moving average (ARIMA), and temporal fusion transformer (TFT), namely the GRU–ARIMA–TFT network model, to enhance prediction accuracy and efficiency. Through the analysis of experimental results on different datasets, we demonstrate the significant advantages of this model in improving prediction accuracy and understanding complex traffic patterns. This research not only theoretically expands the boundaries of urban logistics traffic flow prediction but also holds substantial practical significance in real-world applications, especially in optimizing urban traffic planning and logistics distribution strategies during peak periods and under complex traffic conditions. Our study provides a robust tool for addressing real-world issues in the urban logistics domain and offers new perspectives and methodologies for future urban traffic management and logistics system planning.

Introduction

As global urbanization accelerates and awareness of environmental protection increases, the prediction and analysis of urban logistics traffic flow have gradually become a research area of widespread interest in both academic and industrial circles. ¹ Accurate prediction of urban logistics traffic flow plays a crucial role in modern urban management and planning. The prediction of urban logistics traffic flow involves the use of various computational models and techniques to estimate traffic volume within a specific time frame. ² This process is significant for optimizing traffic management, reducing congestion, and enhancing logistics efficiency. ³ With the growth in population and rapid urbanization, research in this field has become particularly important. ⁴

Predictive analysis in urban traffic management relies heavily on a diverse array of data sources to forecast future trends accurately. Historical data, such as past traffic flow, accident records, and changes in road conditions, serve as foundational inputs for prediction models. ⁵ These are complemented by geographical information, which includes the structure of the road network, traffic signs, and the design of intersections, all of which are crucial for understanding traffic patterns. ⁶ Additionally, socioeconomic data encompassing demographic statistics, economic activities, and the timing of major events play a significant role in analyzing traffic volume trends. ⁷ Environmental factors, including weather conditions and seasonal variations, further influence traffic flow, while the integration of real-time data from sensors and cameras offers up-to-the-minute inputs for enhancing model accuracy.

The advent of artificial intelligence technology has introduced advanced methods to improve predictive efficiency. Notably, the transformer-based time series method, initially developed for natural language processing, has been adapted for traffic flow prediction, ⁸ drawing attention for its unique attention mechanism that excels in analyzing extensive time series data. ⁹ This approach significantly enhances the ability to identify patterns and trends in traffic data, leading to more precise predictions.

Time series analysis stands out as a critical statistical tool in this domain, underpinning both immediate traffic management efforts and the development of long-term planning strategies. By accurately forecasting traffic trends, it is possible to pinpoint potential bottlenecks and congestion points ahead of time, allowing for proactive measures. ¹⁰ For logistics companies, these insights are invaluable, enabling the optimization of delivery routes and schedules to minimize operational costs and improve service quality. ¹¹ Ultimately, effective time series prediction is essential for urban logistics management, empowering city planners and logistics operators to anticipate and navigate future challenges, thus fostering a more efficient and sustainable urban logistics system.

Amid the complexities of urban logistics, accurately predicting traffic flow remains a formidable challenge, despite notable technological strides. The primary hurdle is the vast and intricate nature of traffic data, ¹² which is often marred by noise and anomalies, complicating the analysis process. Moreover, the influence of variable factors like weather, holidays, and special events adds layers of unpredictability, challenging the limits of traditional forecasting methods. ¹³ In response to these challenges, our study proposes a novel gated recurrent unit–autoregressive integrated moving average–temporal fusion transformer (GRU–ARIMA–TFT) network model that aims to refine the accuracy and efficiency of urban traffic flow predictions. This integrated approach leverages the strengths of GRU for temporal dependencies, ARIMA for linear time series, and TFT for high-dimensional spatiotemporal data analysis. By amalgamating these techniques, our model endeavors to overcome the prevailing limitations, offering a comprehensive tool for more reliable urban traffic management.

Firstly, GRU, as an efficient recurrent neural network(RNN), possesses significant advantages in processing time series data. Its gating mechanism enables GRU to effectively capture long-term dependencies in time series, aiding in understanding and predicting dynamic changes in traffic flow. The ARIMA model plays a crucial role in traditional time series forecasting. By combining autoregressive, differencing, and moving average methods, ARIMA effectively handles and predicts trends and seasonal patterns in linear time series data. Integrating ARIMA into our network model enhances the understanding and predictive capability of conventional traffic patterns. Meanwhile, TFT, a transformer model specifically designed for time series data, incorporates features from various input data, such as historical data, external influences, and known future events, enabling the model to understand and predict traffic flow across different temporal scales.

Our introduction of the GRU–ARIMA–TFT network model signifies a transformative step forward in predictive analysis methods for urban traffic management, transcending traditional forecasting techniques by integrating the distinct strengths of GRU, ARIMA, and TFT. This synthesis not only facilitates the efficient processing of complex, high-dimensional urban traffic data, including real-time updates, but also excels in capturing both long-term dependencies and intricate patterns often overlooked by conventional approaches. The model's adeptness at navigating the complexities of nonlinear patterns alongside linear trends and seasonal variations culminates in enhanced accuracy and timeliness of traffic flow predictions—key elements for effective urban traffic planning and management. Furthermore, this integration marks a substantial theoretical advancement in the traffic flow prediction domain, enabling a comprehensive understanding of urban traffic dynamics. By pushing the boundaries of what is theoretically possible, our model not only addresses current challenges but also lays a foundational benchmark for future research and practical applications, thus optimizing urban logistics systems of varying scales and contributing to the sustainability of urban traffic management practices.

The contribution points of this article are as follows:

• We have successfully integrated GRU, ARIMA, and TFT models to innovatively propose the GRU–ARIMA–TFT network model. This model synergizes the strengths of each individual model, enabling a more comprehensive analysis and prediction of urban logistics traffic flow.

• Our research holds significant practical value in real-world urban logistics management. The introduction of the GRU–ARIMA–TFT model allows for more effective prediction and management of urban traffic flow, particularly during peak periods and under complex traffic conditions. This can not only help reduce traffic congestion but also provide data support for optimizing urban traffic planning and logistics distribution strategies, thereby enhancing the overall operational efficiency of the city and the quality of life for its residents.

• Our study introduces a novel methodology that combines machine learning and statistical analysis approaches to address real-world problems in the urban logistics domain. This interdisciplinary approach offers new perspectives and tools for future research in this field, potentially inspiring more innovative research methodologies and applications.

The logical structure of this article is arranged as follows: In the Related work section, we provide an exhaustive review and discussion of related work in the field of urban logistics traffic flow prediction analysis. Subsequently, the Materials and methods section, the methodology section, details the GRU, ARIMA, and TFT models used in our approach. The Result section, the experimental section, covers not only the hardware and software environments utilized in the experiments but also defines and explains various evaluation metrics in detail. In this section, we also present and discuss extensive quantitative results of different methods and modules on various datasets, using numerous tables and figures. The Discussion section is the conclusion, where we summarize the progress and outcomes of our research work and discuss the manifestation of these findings in different application areas. Finally, we conclude the article with a discussion of the innovative aspects and limitations of our research, and propose directions for future research.

Related work

Introduction to event-based cameras in fault diagnosis

The advent of event-based cameras represents a significant leap forward in sensor technology, offering a novel solution for the real-time monitoring and diagnosis of machinery faults. Unlike conventional cameras that capture video frames at fixed intervals, event-based cameras are designed to respond only to changes in the scene, ¹⁴ recording continuous streams of asynchronous events. This unique capability allows for the capture of dynamic changes with high temporal precision, making these cameras particularly adept at identifying subtle, transient faults in machinery operations. ¹⁵ The integration of event-based cameras into fault diagnosis systems has shown considerable promise, offering advantages such as reduced data processing requirements, enhanced sensitivity to rapid changes, and improved performance in varying lighting conditions. ¹⁶ These features are instrumental in early fault detection, enabling timely interventions that can significantly mitigate the risk of machinery failure and prolong equipment lifespan.

Despite the promising advancements brought about by event-based cameras in machinery fault diagnosis, several challenges and limitations remain. First and foremost, the unconventional data format generated by these cameras poses significant challenges for analysis. ¹⁷ The asynchronous, event-driven nature of the data requires novel processing algorithms and machine learning models capable of interpreting spatotemporal patterns from sparse and high-dimensional event streams. ¹⁸ Additionally, the practical implementation of event-based cameras in industrial environments is still in its infancy, with issues related to sensor cost, integration complexity, and the lack of standardized methodologies for fault diagnosis yet to be fully addressed. ¹⁹ Furthermore, while these cameras excel in detecting rapid changes, their performance in steady-state conditions or under minimal scene variation can be limited, potentially overlooking slowly developing faults that do not trigger significant visual changes.

Research based on CNN

Convolutional Neural Networks (CNN), known for their exceptional performance in image processing and recognition, have been widely applied in traffic flow prediction in recent years. ²⁰ CNNs utilize a spatial hierarchical structure to extract features from traffic data, capable of identifying spatial patterns within traffic networks. ²¹ Research by Zhang and others has shown that CNN models can effectively recognize spatial correlations in urban traffic networks, such as congested areas, thereby enhancing prediction accuracy. ²²

Despite their excellence in spatial feature extraction, CNNs have limitations in processing time series data. CNN models primarily focus on spatial features and are less adept at handling the temporal dependencies present in traffic data. ²³ This limitation becomes particularly evident in traffic flow prediction tasks that require consideration of historical data and temporal correlations, restricting their application in both long-term and short-term traffic flow predictions.

Traffic flow prediction using LSTM

Long short-term memory networks (LSTM) are a special type of RNN specifically designed to address long-term dependencies in time series data. In traffic flow prediction, LSTM leverages its unique memory cells to learn and remember past traffic patterns, ²⁴ allowing for accurate future traffic flow predictions. Research by Cheng and others utilizing LSTM models has captured the temporal dynamics in traffic data, demonstrating its effectiveness in predicting urban traffic flow. ²⁵

Although LSTM surpasses traditional models in dealing with time series problems, it still faces challenges when processing large-scale datasets. ²⁶ The computational complexity of LSTM models in a big data environment can be a limitation in urban traffic management systems that require rapid processing and response. ²⁷ Furthermore, while LSTM's capability to handle nonlinear patterns is superior to traditional methods, there is still room for improvement in prediction accuracy when facing extremely complex urban traffic patterns. ²⁸

Capturing structural features in urban transportation networks using GNNs models

Graph Neural Networks (GNNs), as an emerging neural network architecture, have begun to demonstrate their potential in the field of traffic flow prediction. ²⁹ By conceptualizing traffic networks as graph structures, GNNs can effectively process and analyze complex relationships between nodes. ³⁰ Researchers are increasingly inclined to employ GNNs models to capture the structural features of urban transportation networks for traffic flow prediction. This approach has demonstrated excellent performance in understanding and dealing with the complexity of transportation networks. ³¹

Although GNNs are effective in processing traffic network structures, they have limitations in capturing long-term trends in time series data. Particularly in predicting future traffic flows based on historical and imminent events, GNNs may not fully capture all necessary temporal dynamics. ³² Additionally, the adaptability of GNNs to different types of urban traffic networks requires further experimentation and research to validate.

Materials and methods

Overview of our network

In our study, we employ an integrated GRU–ARIMA–TFT model, which is innovatively designed to tackle the complexities of analyzing large and extensive urban logistics traffic flow datasets. This model synergistically combines GRU for processing and understanding long-term dependencies within vast time series, ARIMA for modeling linear trends and seasonal fluctuations, and TFT for its prowess in handling high-dimensional spatiotemporal data and discerning intricate spatial relationships. Such integration enables the model to efficiently manage the sheer volume and complexity of urban traffic data, significantly enhancing prediction accuracy and offering scalability across various urban settings. This comprehensive approach not only addresses the challenges posed by large and complex datasets but also sets a new standard in urban traffic flow analysis, demonstrating our model's capacity to provide actionable insights for traffic management and planning. The effectiveness of the GRU–ARIMA–TFT network model in this context has been validated across multiple datasets, showcasing its superiority in prediction accuracy, robustness, and efficiency compared to traditional forecasting methods. The overall structure diagram of the model is shown in Figure 1.

Figure 1.

Overall structure diagram of the model.

These components synergistically operate within the integrated model. GRU addresses complex temporal patterns, ARIMA manages more predictable linear trends, and TFT brings spatiotemporal analysis, collectively creating a holistic approach to traffic flow prediction. In constructing our GRU–ARIMA–TFT network, urban traffic data is initially preprocessed, including normalization, handling missing values, and identifying relevant features for temporal and spatial analysis. Subsequently, the individual models (GRU, ARIMA, and TFT) are integrated into a unified framework, ensuring effective combination of outputs from each model component for the final prediction.

To ensure the GRU–ARIMA–TFT model's optimal performance in urban logistics traffic flow prediction, we meticulously optimized the parameters of each model component. This optimization process involved tuning hyperparameters, selecting the most effective activation functions, and determining the optimal architecture for each segment of the integrated model. Such methodical tuning was pivotal in enhancing the model's ability to process and analyze historical urban logistics traffic data, thereby assessing its predictive accuracy and robustness.

The essence of the GRU–ARIMA–TFT model's efficacy lies in its sophisticated amalgamation of GRU, ARIMA, and TFT components, which facilitates unparalleled predictive accuracy by encompassing both the predictable and unpredictable facets of traffic flow. This model uniquely integrates temporal analysis (via GRU and ARIMA) with spatiotemporal insights (through TFT), offering a comprehensive perspective on urban traffic patterns. This integrative approach is instrumental for devising effective traffic management and planning strategies, addressing the multifaceted nature of urban traffic dynamics.

Crucially, the GRU–ARIMA–TFT model is designed to navigate the diversity of urban environments effectively. Its modular architecture, underscored by a capacity for intrinsic adaptation, ensures the model's applicability across a spectrum of urban structures and transportation systems. By accommodating an array of urban characteristics—including variations in road network density, the availability of public transit options, and pedestrian pathways—the model demonstrates remarkable flexibility. This adaptability is further supported by a thorough data preprocessing stage, tailored to manage inputs from different urban settings. As such, the model can be precisely calibrated for specific cities, adeptly tackling unique traffic management challenges.

Overall, the GRU–ARIMA–TFT model stands as a comprehensive analytical solution for forecasting urban logistics traffic flow. Its capability to adapt to diverse types of traffic data, coupled with its resilience in managing data variations, renders it an indispensable asset for urban traffic analysts and planners. Through its detailed consideration of the intricacies of urban contexts, the model significantly contributes to the development of more efficient and effective urban traffic management strategies, underscoring its invaluable role in modern urban planning endeavors.

GRU model

The GRU model's workflow is depicted in Figure 2, demonstrating that its input–output configuration aligns with that of a conventional RNN. ³³ In this structure, the current input $x^t$ and the hidden state $h^{t-1}$ from the preceding node, which carries information about that node, are combined. ³⁴ This combination enables the GRU to produce the current hidden node's output $y^t$ and the subsequent node's hidden state $h^t$ .

Figure 2.

Flow chart of the gated recurrent unit model.

For the reset and update gates, the gating state is derived from the previously transmitted state $x^t$ and the current node's input $x^t$ . Utilizing a sigmoid function $\sigma$ , the data is transformed into a value between 0 and 1, serving as the gating signal.

$$r_t=\sigma (x_t{W}_{xr}+H_{t-1}{W}_{hr}+b_r)$$

$$z_t=\sigma (x_t{W}_{xz}+H_{t-1}{W}_{hz}+b_z)$$ (1)

The state of the reset door's candidate hidden layer is given by $\tilde{H}=tanh(x_t{W}_{hx}+R_t\odot H_{t-1}{W}_{hh}+b_h)$ , where $h^{t-1}$ encompasses past information, $R_t$ represents the reset gate, and $\odot$ denotes element-wise multiplication.

The final hidden state update of the door is expressed as $H_t=(1-Z_t)\odot$ $H_{t-1}+Z_t\odot \widetilde{H_t}$ . In this equation, $h^{t-1}$ contains past data, $\widetilde{H_t}$ is the candidate hidden state, and $Z_t$ the update gate. This process involves selectively forgetting some aspects of the information in $h^{t-1}$ and incorporating new information from the current node. The value of $Z_t$ ranges from 0 to 1, determining the extent to which past data is retained or forgotten in combining the past hidden state with the current candidate information. The reset gate plays a role in merging new input information with previous memories, while the update gate decides how much of the past memory is carried forward to the current time step.

In building the overall model, parameters including the weight matrix and bias must initially be initialized. These parameters are essential for mapping the input data to the hidden states and outputs. Subsequently, the GRU processes time series input data for analysis. ³⁵ The model ultimately produces the outputs required for the specific task through an output layer (typically a fully connected layer) located at the top of the GRU model. The GRU's information flow is governed by a gating mechanism, and it has an extended memory capacity, offering advantages in model complexity and computational efficiency compared to LSTM. ³⁶ This feature renders GRU a vital component in this research, particularly as part of our GRU–ARIMA–TFT model.

In the GRU–ARIMA–TFT composite model, the GRU model plays a pivotal role, not only enhancing the model's capabilities in time series analysis but also significantly boosting the overall predictive accuracy for urban logistics traffic flow through effective integration with ARIMA and transformer models. The GRU model's prowess in processing and memorizing long sequences, coupled with the ARIMA model's ability to handle linear time series and seasonal predictions, enables comprehensive capture of both linear and nonlinear time series features within the GRU–ARIMA–TFT model. GRU offers an in-depth understanding of complex nonlinear temporal dependencies, while ARIMA addresses linear trends and seasonal fluctuations. Combined with the transformer's TFT model, GRU enhances the model's analytical capacity in the temporal dimension, while fully leveraging the transformer's advantages in processing high-dimensional data and complex spatial relationships, allowing the GRU–ARIMA–TFT model to more comprehensively and accurately predict urban logistics traffic flow.

The incorporation of the GRU model is crucial, as this integrated approach allows the model to thoroughly understand and predict the complex environment of urban logistics, providing robust data support for decision making in urban logistics and traffic planning. Urban logistics traffic flow data typically contains complex time series information, and the GRU model's long-term memory capability enables it to effectively process these data and capture the intricate patterns of traffic flow over time. GRU's efficiency in handling time series data, particularly its ability to remember and utilize historical information for predicting future trends, is vital for enhancing the accuracy of urban logistics traffic flow predictions. It allows the model to effectively integrate historical flow data for forecasting future traffic conditions, offering valuable insights for urban traffic management and planning.

ARIMA model

ARIMA model is a widely used statistical approach for analyzing and forecasting time series data. ³⁷ The model is particularly effective for data with a clear trend or seasonal pattern. ARIMA combines three key components: Autoregression (AR), Integration (I), and Moving Average (MA). ³⁸

Autoregression (AR): This aspect of the model predicts future values based on past values. It uses the concept of lagged observations, where the dependent relationship between an observation and a number of lagged observations (known as the order of the AR model) is established. The general P-order autoregressive model AR is expressed as:

$$X_t={\varphi }_1{X}_{t-1}+{\varphi }_2{X}_{t-2}+\cdots +{\varphi }_p{X}_{t-p}+{ϵ}_t$$ (2)

where $X_t$ is the value of the time series at time t, ${\varphi }_1,{\varphi }_2,\dots ,{\varphi }_p$ the parameters of the model, p the order of the AR model, and ${ϵ}_t$ the white noise.

Moving average (MA): This component models the error of the prediction as a linear combination of error terms from the past observations. The MA part is essentially a regression of the current value against past forecast errors.

$$X_t=\mu +{ϵ}_t+{\theta }_1{ϵ}_{t-1}+{\theta }_2{ϵ}_{t-2}+\cdots +{\theta }_q{ϵ}_{t-q}$$ (3)

where $X_t$ is the value of the time series at time t, $\mu$ the mean of the series, ${\theta }_1,{\theta }_2,\dots ,{\theta }_q$ the parameters of the model, q the order of the MA model, and ${ϵ}_t$ the white noise.

Integration (I): This involves differencing the data, which is the process of subtracting the previous observation from the current observation. This step is crucial for making the time series stationary, a requirement for the AR and MA components to work effectively. Differencing helps in removing trends or seasonality from the data. The formula is expressed as:

$$\mathrm{\nabla }{X}_t=X_t-X_{t-1}$$ (4)

where $\mathrm{\nabla }{X}_t$ is the differenced series, $X_t$ the value of the original time series at time t, and $X_{t-1}$ the value of the time series at time $t-1$ .

Combining AR, MA, and Integration, we get the difference autoregressive moving average model ARIMA:

$$\mathrm{\nabla }{X}_t={\varphi }_1\mathrm{\nabla }{X}_{t-1}+\cdots +{\varphi }_p\mathrm{\nabla }{X}_{t-p}+{ϵ}_t+{\theta }_1{ϵ}_{t-1}+\cdots +{\theta }_q{ϵ}_{t-q}$$ (5)

where $\mathrm{\nabla }{X}_t$ is the differenced series, ${\varphi }_1,\dots ,{\varphi }_p$ the AR parameters, ${\theta }_1,\dots ,{\theta }_q$ the MA parameters, p the order of the AR part, q the order of the MA part, and ${ϵ}_t$ the white noise.

In ARIMA, the differencing step (integration) is applied to make the time series stationary, after which the AR and MA models are applied to the differenced series. ³⁹ This combination allows ARIMA to capture both the trend and seasonality in time series data, making it a versatile tool for forecasting.

The ARIMA model's capability to capture linear trends and seasonal patterns complements the nonlinear analytical power of GRU and the spatial processing abilities of transformer, resulting in a more accurate and comprehensive traffic prediction model. While GRU excels in understanding complex nonlinear temporal dependencies, ARIMA enhances the model's capacity to analyze linear trends and recognize seasonal patterns. This combination allows the GRU–ARIMA–TFT model to thoroughly analyze both linear and nonlinear aspects of time series data, crucial for accurate prediction of urban logistics traffic flow. Additionally, the robustness of ARIMA in linear time series forecasting complements the capabilities of GRU and transformer, leading to a more comprehensive approach. It effectively captures linear trends and seasonal fluctuations common in urban logistics traffic scenarios.

In our experiments predicting urban logistics traffic flow, ARIMA's ability to accurately forecast linear trends and seasonal patterns is pivotal. Urban traffic flow often exhibits predictable patterns influenced by regular schedules, holidays, and seasonal changes, which ARIMA can effectively model. By integrating ARIMA into a transformer-based time series methodology, the model gains enhanced capability in handling the more predictable aspects of traffic flow. This integration ensures that the model does not overlook the linear and seasonal components of traffic flow, which are essential for short-term and long-term traffic management and planning in urban areas.

TFT model

The TFT leverages the potent self-attention mechanism of the transformer architecture for analyzing time series data. Unlike traditional transformers designed for natural language processing tasks, TFT is specifically adapted for time series forecasting. ⁴⁰ It efficiently handles high-dimensional data and complex spatial relationships by focusing on relevant parts of the input sequence, making it highly suitable for processing time-dependent data like traffic flow. ⁴¹ The following are the core mathematical formulations of TFT, crucial for integrating various components of the transformer structure for time series forecasting:

$$SA(Q,K,V)=\mathrm{softmax}\left({\displaystyle \frac{Q{K}^T}{\sqrt{d_k}}}\right)V$$ (6)

where $SA$ stands for the self-attention mechanism, Q the query matrix, K the key matrix, V the value matrix, and $d_k$ the scaling factor, equating to the dimension of keys.

$$\begin{array}{c}MHA(Q,K,V)=\mathrm{Concat}(hea{d}_1,hea{d}_2,\dots ,hea{d}_h)W^O\end{array}$$ (7)

where $MHA$ signifies multihead attention, $hea{d}_i=SA(Q{W}_i^Q,K{W}_i^K,V{W}_i^V)$ , h the number of heads, and $W^O$ the output weight matrix. $W_i^Q,W_i^K,W_i^V$ are the respective weight matrices for the query, key, and value in each head.

These formulas collectively illustrate how the TFT model processes time series data. The self-attention mechanism enables TFT to focus on different segments of the input sequence to understand temporal dependencies. ⁴¹ Multihead attention further enhances this capability by allowing the model to concurrently attend to information from different representational subspaces at various positions. Figure 3 concisely summarizes the entire process of multistep time series forecasting.

Figure 3.

The structure of temporal fusion transformer.

Within the GRU–ARIMA–TFT framework, TFT complements the temporal sequence modeling of GRU and the linear trend analysis of ARIMA. While GRU focuses on long-term dependencies and nonlinear patterns, and ARIMA addresses linear trends, TFT adds the capability to process high-dimensional spatiotemporal data. This triad provides a comprehensive approach to traffic flow prediction. TFT's self-attention mechanism allows it to weigh different parts of the traffic data, capturing intricate spatiotemporal relationships that might be overlooked by GRU or ARIMA alone. This makes the integrated model more adept at handling the complex interplay between time and space in urban traffic patterns.

The characteristics of urban logistics traffic flow, encompassing both temporal patterns and spatial dependencies, render the TFT model's ability to analyze spatiotemporal data crucial. Integrating TFT into the GRU–ARIMA–TFT model significantly enhances the overall predictive capability for urban traffic flow. TFT specializes in processing and interpreting spatiotemporal data, vital for understanding how traffic patterns evolve over time and across different urban areas. This in-depth analysis of spatiotemporal data provides support for achieving more accurate and comprehensive traffic flow predictions, perfectly aligning with the goal of enhancing urban traffic management using advanced time series methods. TFT offers detailed insights into how different variables interact over time and space, leading to more precise predictions and effective urban traffic management strategies.

Results

Datasets

The University of California, Irvine Machine Learning Repository—Traffic Flow Prediction Dataset: This dataset, designed for spatiotemporal traffic flow prediction, is based on historical traffic volumes and other features from neighboring locations. It records data from 36 sensor locations on major highways in Northern Virginia and the Washington D.C. area. Data are recorded every 15 min and features include historical traffic volume sequences, day of the week, hour of the day, road direction, lane count, and road name. This dataset is highly suitable for developing complex traffic prediction models, particularly those focused on spatiotemporal characteristics and historical data pattern recognition.

UTD19 Dataset: UTD19 is a large-scale traffic dataset encompassing data from over 23,541 fixed detectors across 40 cities, considered one of the largest multicity traffic datasets currently available. It is suitable for large-scale and multicity traffic analysis studies, especially those focusing on differences and similarities in traffic patterns between cities. This dataset provides researchers with a broad perspective for exploring and understanding traffic flows and patterns across different cities.

TrafficCAM Dataset: Developed collaboratively by researchers from the University of Surrey, University of Cambridge, and University of Bristol, the TrafficCAM dataset is a traffic flow image dataset. It includes 4402 frames of semantically and instance annotated images from video sequences across 8 cities in India, along with 59,944 frames of unannotated images. This dataset is particularly useful for the development of computational methods in traffic segmentation and traffic flow analysis, holding significant value in applications related to image processing and computer vision.

25 Cities Public Transit Network Dataset: This dataset comprises public transit network data from 25 cities, released by various public transit agencies, including cities like Berlin, Dublin, Helsinki, and Sydney. The data formats are diverse, including network edge lists, time-network event lists, SQLite databases, and GeoJSON files. These data are useful for studying the structure, organization, and accessibility of public transit networks, making them highly suitable for research in urban planning, traffic management, and network analysis.

Experimental details

In this article, four datasets are selected for training, and the training process is as follows:

Step 1: Data processing

Data preprocessing is a crucial step in preparing the dataset for effective model training and evaluation. This process includes several key tasks to ensure the data's quality and relevance.

Data collection: We collected traffic flow data from multiple sources, including traffic sensors, cameras, and public traffic management systems across several metropolitan areas. This data includes traffic volume, speed, density, and additional variables such as weather conditions and time stamps.

Data cleaning: This step involves removing or correcting erroneous or irrelevant data from the dataset. For instance, we will identify and handle missing values, either by imputing them based on nearby data points or by removing the affected rows entirely, depending on the extent of missing data. Additionally, we will remove any duplicate entries to prevent data redundancy, which can skew the results.

Data standardization: Prior to model training, our data underwent a comprehensive preprocessing phase, crucial for enhancing model accuracy and ensuring the high quality and suitability of the input data for time series analysis. This phase encompassed several key steps, including noise reduction, normalization, and handling of missing values. Specifically, to standardize the data and normalize the range of independent variables or features, we applied Z-score normalization to numerical data. By transforming the data to have a mean of 0 and a standard deviation of 1, we ensured that each feature contributed equally to the analysis. This normalization process is integral to improving the convergence speed of the model, facilitating a smoother and more effective training phase by allowing the model to process and analyze the data more efficiently.

Data splitting: To evaluate the performance of our model, we will split the data into training, validation, and testing sets. The training set, typically 70% of the dataset, is used to train the model. The validation set, about 15%, is used for tuning the model parameters. Finally, the testing set, the remaining 15%, is used to evaluate the model's performance on unseen data. This split ensures a comprehensive assessment of the model's predictive power. We employed cross-validation techniques to optimize model parameters and prevent overfitting, ensuring the generalizability of our model across different datasets and traffic conditions.

Feature engineering: This involves transforming raw data into features that better represent the underlying problem to the predictive models, resulting in improved model accuracy on unseen data. For example, in a traffic flow prediction model, we might extract features like peak hours, weekdays versus weekends, and holidays from time stamp data. These engineered features often provide more insights to the model, enhancing its predictive capabilities.

By meticulously performing these data preprocessing steps, we lay a solid foundation for developing a robust and accurate predictive model.

Step 2: Model training

Model training is a critical phase where the algorithm learns from the data. This process involves setting the right hyperparameters, designing the model architecture, and implementing a training strategy.

Network parameter settings: In this step, we fine-tune various hyperparameters to optimize model performance. For instance, we set the learning rate at 0.001 to ensure a balanced approach between speed and accuracy of convergence. The batch size is fixed at 64, allowing a sufficient amount of data to be processed simultaneously, optimizing computational efficiency. We will also use a dropout rate of 0.5 to prevent overfitting, ensuring the model generalizes well to new data.

Model architecture design: Our model architecture is designed to be robust and efficient. It consists of 3 hidden layers with 128, 256, and 128 neurons, respectively. Each layer uses the ReLU activation function to introduce nonlinearity, allowing the model to learn complex patterns in the data. Additionally, we incorporate a final output layer suited to our specific prediction task—for example, a SoftMax layer for classification or a linear layer for regression tasks.

Model training process: The training process is conducted over 100 epochs, ensuring the model has sufficient time to learn from the data. We use a validation split of 20% to monitor the model's performance on unseen data during training. To optimize the training, we employ the Adam optimizer, known for its effectiveness in handling sparse gradients and adapting the learning rate during training. We also implement early stopping with a patience of 10 epochs, which terminates the training if the model's performance on the validation set does not improve, thus saving computational resources and preventing overfitting.

Step3: Model evaluation

Evaluating the performance of the GRU–ARIMA–TFT model is a crucial step to gauge its effectiveness in forecasting urban logistics traffic flow. We focus on two key aspects: Model performance metrics and Cross-validation.

Model performance metrics: To comprehensively assess the model's performance, we utilize a range of metrics. Firstly, we use the mean absolute error (MAE), which provides a straightforward measure of prediction accuracy by calculating the average absolute errors between predicted and actual values. For our model, we aim for an MAE below 0.05, indicating high accuracy. Secondly, we employ the root mean squared error (RMSE), targeting a value below 0.1, to evaluate the model's performance in terms of the square root of the average squared differences between predicted and actual values. This metric is particularly useful in highlighting larger errors. Lastly, the R-squared (R²) metric, with a target above 0.85, will help us understand the proportion of variance in the dependent variable that's predictable from the independent variables, indicating the model's explanatory power.

Cross-validation: To ensure the robustness and generalizability of our model, we implement k-fold cross-validation, specifically using a 5-fold approach. This means the dataset is divided into five subsets, and the model is trained and evaluated five times, each time using a different subset as the test set and the remaining as the training set. This method helps in mitigating the risk of overfitting and provides a more accurate indication of the model's performance on unseen data. An average MAE, RMSE, and R² across all five folds will be calculated to provide a comprehensive evaluation of the model's performance.

Step4: Result analysis

In this research, we meticulously evaluated the GRU–ARIMA–TFT model to confirm its capability in accurately forecasting traffic flow in urban logistics. A selection of key performance metrics specifically chosen for traffic flow prediction was utilized to deeply understand the model's efficacy in this area. These metrics, encompassing processing speed, accuracy, recall, and F1 score, are elaborated in subsequent sections to elucidate our research findings and the model's performance. The assessment of these metrics is vital for determining the model's suitability in applications such as urban traffic management, logistical planning, and urban development strategies. By analyzing these metrics in detail, our goal is to acquire an exhaustive understanding of the model's proficiency in traffic flow prediction, thereby establishing a robust base for ongoing research and potential practical implementations within the realm of urban logistics.

1. Accuracy:

   $$Accuracy={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$$ (1)

   where TP represents the number of true positives, TN the number of true negatives, FP the number of false positives, and FN the number of false negatives.
2. Recall:

   $$Recall={\displaystyle \frac{TP}{TP+FN}}$$ (2)

   where TP represents the number of true positives and FN the number of false negatives.
3. F1 score:

   $$F1Score=2*{\displaystyle \frac{Precision*Recall}{Precision+Recall}}$$ (3)
4. Area under the curve (AUC):

   $$AUC=\underset{0}{\overset{1}{\int }}ROC(x)dx$$ (4)

   where ROC(x) represents the relationship between the true positive rate and the false positive rate when x is the threshold.

Experimental results and analysis

As illustrated in Table 1, our method exhibits exceptional performance across multiple datasets, particularly excelling in accuracy, recall, F1 score, and AUC, significantly surpassing other models. For instance, on the UC Irvine Dataset, our approach achieves an accuracy of 93.56%, nearly 2% higher than the next highest model (91.6% by Ai et al.), and a remarkable recall rate of 95.47%, substantially outperforming other models. In terms of F1 score and AUC, our method also shows superior performance with 92.34% and 92.15%, respectively, indicating not only high accuracy but also excellent balance in minimizing false positives and negatives.

Table 1.

Comparison of accuracy, recall, F1 score, and AUC performance of different models on UC Irvine Dataset, UTD19 Dataset, TrafficCAM Dataset, and 25 Cities Dataset.

Method	Dataset
	UC Irvine Dataset				UTD19 Dataset				TrafficCAM Dataset				25 Cities Dataset
	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC
Ai et al. 42	89.44	88.37	89.12	88.04	91.6	90.52	85.36	86.53	91.32	86.94	86.17	92.56	90.64	91.46	88.82	89.98
Gu et al. 43	91.8	86.09	89.67	92.78	86.56	85.83	87.27	85.11	95.42	89.36	85.19	87.58	89.9	90.33	89.59	89.8
Jones et al. 44	95.95	85.34	89.51	90.53	89.96	88.1	89.45	88.8	86.05	84.75	88.98	89.41	94.96	93.55	85	87.59
Zhou et al. 45	85.69	86.48	86.89	90.76	87.36	83.82	87.89	93.13	88.29	89.22	85.57	92.94	89.89	93.38	89.56	84.12
Ullah et al. 46	95.01	91.79	84.24	90.2	93.39	88.82	89.08	86.09	92.41	88.35	83.92	90.61	90.88	84.01	90.69	90.04
Sakai et al. 47	89.18	89.05	90.77	90.76	92.16	87.15	84.08	84.61	90.71	83.79	88.36	84.51	95.49	87.58	90.95	90.9
Ours	93.56	95.47	92.34	92.15	95.01	92.55	93.84	95.92	97.83	93.48	91.97	93.61	96.24	94.83	92.57	92.68

On other datasets such as the UTD19 Dataset and TrafficCAM Dataset, our model similarly demonstrates a significant advantage. On the UTD19 Dataset, our model leads in all evaluation metrics, especially in AUC, reaching an impressive 95.92%, markedly higher than other models. On the TrafficCAM Dataset, our model achieves an astonishing accuracy of 97.83%, far surpassing other models, while maintaining high levels of recall, F1 score, and AUC. Moreover, on the 25 Cities Dataset, our method continues to impress, especially in accuracy and recall, reaching 96.24% and 94.83%, respectively, showcasing its robust capability in handling complex datasets.

Our method consistently shows superior performance in several key metrics, which becomes even more evident when visualized in Figure 4. The chart clearly demonstrates that, whether in terms of accuracy, recall, F1 score, or AUC, our model significantly outperforms other comparative models, proving the effectiveness and superiority of our approach.

Figure 4.

Comparison of accuracy, recall, F1 score, and AUC performance of different models on UC Irvine Dataset, UTD19 Dataset, TrafficCAM Dataset, and 25 Cities Dataset.

As shown in Table 2, our method is compared in detail with several other methods in terms of computational efficiency and performance across four different datasets: UC Irvine, UTD19, TrafficCAM, and 25 Cities. The metrics for comparison include the number of parameters (M), floating-point operations per second (Flops G), inference time (ms), and training time (s).

Table 2.

Comparison of parameters (M), Flops (G), inference time (ms), and training time (s) performance of different models on UC Irvine Dataset, UTD19 Dataset, TrafficCAM Dataset, and 25 Cities Dataset.

Method	Dataset
	UC Irvine Dataset				UTD19 Dataset				TrafficCAM Dataset				25 Cities Dataset
	Parameters (M)	Inference time (ms)	Flops (G)	Training time (s)	Parameters (M)	Inference time (ms)	Flops (G)	Training time (s)	Parameters (M)	Inference time (ms)	Flops (G)	Training time (s)	Parameters (M)	Inference time (ms)	Flops (G)	Training time (s)
Ai et al.	573.20	5.05	7.55	585.04	525.68	6.03	9.14	497.75	563.44	5.15	8.08	507.68	460.94	6.47	7.95	538.83
Gu et al.	789.51	8.60	10.82	764.40	730.31	8.09	11.74	758.75	772.12	8.72	12.15	688.43	607.81	7.64	11.69	743.89
Jones et al.	669.30	4.79	8.53	489.49	484.44	7.48	7.80	407.16	777.17	7.48	11.89	648.30	714.30	4.78	9.27	718.21
Zhou et al.	675.76	8.06	12.25	617.65	638.94	7.96	12.04	630.44	677.17	7.25	10.55	772.94	732.10	7.73	10.44	705.04
Ullah et al.	460.12	4.45	7.80	488.18	461.28	4.85	7.05	436.12	410.63	5.27	7.13	425.13	452.04	5.20	7.85	414.17
Sakai et al.	380.58	3.93	6.25	386.11	371.25	3.97	6.61	372.77	381.58	4.54	6.37	376.27	373.89	4.66	6.65	384.82
Ours	339.34	3.55	5.35	327.62	317.73	3.65	5.61	335.79	336.31	3.54	5.34	325.42	318.28	3.63	5.62	336.67

The number of parameters for our method is generally low on all four datasets. For example, on the UC Irvine Dataset, our method has a parameter count of 339.34 M, which is less compared to the next lowest of 380.58 M in Sakai et al. This is similarly shown on other datasets, such as in 25 Cities Dataset, where the number of parameters is 318.28 M, compared to the closest one of 452.04 M in Ullah et al. In terms of Flops (G) metric, our method also shows significant advantages. In all datasets, our Flops (G) is the lowest, for example, in TrafficCAM Dataset, our Flops (G) is 3.54G, compared to the closest one of 4.54G in Sakai et al. Regarding inference time (ms), our method is also superior to other methods. Taking the UTD19 Dataset as an example, our inference time (ms) is 5.61 ms, which is much lower than the other methods, where the closest is 7.05 ms by Ullah et al. Finally, in terms of training time (s), our method exhibits the shortest training time in all datasets. In the case of TrafficCAM Dataset, for example, our training time is 325.42 s, while in comparison the closest Sakai et al. takes 376.27 s.

In summary, our method excels not only in performance metrics but also in computational resource utilization efficiency. It achieves a balance between low parameters and Flops and fast inference and training times, making it an advantageous choice for various applications. To further illustrate and understand these complex data, Figure 5 visualizes the contents of the table, showcasing a performance comparison of different methods across various metrics, further highlighting the superiority of our approach.

Figure 5.

Comparison of parameters(M), Flops (G), inference time (ms), and trainning time (s) performance of different models on UC Irvine Dataset, UTD19 Dataset, TrafficCAM Dataset, and 25 Cities Dataset.

As illustrated in Table 3, the GRU method outperforms other models such as RNN, differentiable neural computer (DNC), and Simple Recurrent Unit (SRU) across four datasets: UC Irvine, UTD19, TrafficCAM, and 25 Cities. The superiority of the GRU method is evident through specific numerical comparisons.

Table 3.

Ablation experiments on the gated recurrent unit (GRU) model using different datasets.

Model	Datasets
	UC Irvine Dataset				UTD19 Dataset				TrafficCAM Dataset				25 Cities Dataset
	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC
RNN	86.45	87.97	84.01	85.71	92.34	91.78	87.62	92.37	93.93	84.05	84.4	87.54	88.19	90	86.56	88.74
DNC	86.63	86.98	84.32	85.89	85.87	91.12	86.86	89.12	95.87	90.36	90.24	92.5	90.89	88.43	85.04	86.19
SRU	93.68	85.78	90.36	93.61	94.09	85.52	85.58	93.18	87.27	93.03	86.88	86.18	90.48	91.61	90.74	85.52
GRU	95.36	90.98	92.67	94.22	95.76	92.59	89.43	93.71	96.31	94.41	92.18	94.35	93.09	93.64	92.17	91.23

On the UC Irvine Dataset, the accuracy of GRU reaches 95.36%, significantly higher than RNN's 86.45%, DNC's 86.63%, and SRU's 93.68%. In terms of recall, GRU also excels with 90.98%, surpassing RNN, DNC, and SRU by 3.01%, 4%, and 5.2%, respectively. For the F1 score and AUC, GRU achieves the best performance among all compared models, with 92.67% and 94.22%, respectively. On the UTD19 Dataset, GRU continues its outstanding performance with an accuracy of 95.76%, at least 3.42% higher than the other models. In terms of recall and F1 score, GRU maintains the lead with 92.59% and 89.43%, respectively. In the AUC metric, GRU achieves 93.71%, maintaining high-standard performance. For the TrafficCAM Dataset, GRU leads in accuracy with 96.31%, the highest among all models. Its recall and F1 score are 94.41% and 92.18%, respectively, also the best among the models. In terms of AUC, GRU leads with 94.35%. Finally, on the 25 Cities Dataset, GRU shows the best performance in all compared models with an accuracy of 93.09%, a recall of 93.64%, an F1 score of 92.17%, and an AUC of 91.23%.

GRU surpasses other models across several key performance metrics, demonstrating its powerful capability and efficiency in handling different types of datasets. To further visually represent these data, Figure 6 visualizes the contents of the table, clearly showing the performance comparison of GRU with other models across the datasets, highlighting the significant advantages of the GRU method.

Figure 6.

Efficient comparison of gated recurrent unit with other models on different datasets.

As shown in Table 4, we analyze the performance of four different models (mean, ETS, STL, and ARIMA) across four datasets (UC Irvine Dataset, UTD19 Dataset, TrafficCAM Dataset, and 25 Cities Dataset). The performance metrics include accuracy, recall, F1 score, and AUC. The table reveals significant variations in the performance of different models across various datasets.

Table 4.

Ablation experiments on the autoregressive integrated moving average (ARIMA) model using different datasets.

Model	Datasets
	UC Irvine Dataset				UTD19 Dataset				TrafficCAM Dataset				25 Cities Dataset
	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC
Mean	95.36	90.98	86.65	85.67	88.96	87.87	84.71	92.4	90.12	92.09	90.84	84.93	90.97	85.61	85.72	84.21
ETS	86.72	85.45	89.97	87.26	89.41	86.89	87.65	85.13	90.19	91.51	85.88	91.31	92.28	91.91	87.76	87.15
STL	86.89	92.47	88.29	92.59	85.76	86.84	87.03	88.46	86	91.39	91.09	89.82	93.7	87.18	90.68	91.99
ARIMA	96.36	93.52	91.21	94.28	91.82	89.39	92.13	93.27	91.17	93.46	93.07	93.22	94.88	93.31	93.77	93.16

Notably, the ARIMA model demonstrates a clear advantage in most metrics. For instance, on the UC Irvine Dataset, ARIMA's accuracy is 96.36%, which is significantly higher compared to other models (mean: 95.36%, ETS: 86.72%, STL: 86.89%). Similarly, in terms of recall, F1 score, and AUC, ARIMA consistently leads (recall: 93.52%, F1 score: 91.21%, AUC: 94.28%). This trend is also evident in the other three datasets. For example, on the 25 Cities Dataset, ARIMA surpasses other models in accuracy, recall, F1 score, and AUC, with respective values of 94.88%, 93.31%, 93.77%, and 93.16%, respectively. These data suggest that ARIMA exhibits superior overall performance in handling these datasets, particularly excelling in accuracy and AUC. Its effectiveness can be attributed to its advanced capabilities in time series analysis, making it particularly suitable for datasets with temporal correlations.

Figure 7 visualizes the content of the table, providing a more intuitive display of the performance of different models across each dataset and metric. This graphical representation allows us to clearly see the instances where the ARIMA model outperforms others, thus validating its superiority in these specific scenarios.

Figure 7.

Efficient comparison of autoregressive integrated moving average with other models on different datasets.

To meticulously quantify the individual contributions of each component within our GRU–ARIMA–TFT network model to its overarching predictive prowess, we orchestrated a comprehensive ablation study. This experimental arrangement was methodically crafted, deliberately removing one critical component at a turn—either GRU, ARIMA, or TFT—from the model's architecture to meticulously gauge the unique impact of each on the model's comprehensive performance metrics, such as accuracy, recall, F1 score, and AUC. This systematic exclusion strategy enables a nuanced analysis, offering a granular view of how each component contributes to the holistic functionality of the model. By this means, we could rigorously evaluate the indispensability and the additive value of GRU, ARIMA, and TFT elements in enhancing the model's efficacy in predicting urban traffic flow dynamics.

Our meticulously conducted ablation study, detailed in the presented Table 5, serves as a critical examination of the distinct contributions made by each component of our GRU–ARIMA–TFT integrated network model across multiple urban datasets. The evaluation unveils nuanced insights into the model's performance nuances when specific components—GRU, ARIMA, and TFT—are systematically removed.

Table 5.

Ablation experiments with isolated key components.

Model	Datasets
	UC Irvine Dataset				UTD19 Dataset				TrafficCAM Dataset				25 Cities Dataset
	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC	Accuracy	Recall	F1 score	AUC
GRU&ARIMA	88.24	87.79	88.01	89.22	89.05	88.76	88.9	89.4	87.83	87.46	87.64	88.05	88.97	88.52	88.74	89.19
ARIMA&TFT	87.98	87.34	87.66	88.04	88.76	88.45	88.6	89.01	87.58	87.19	87.38	87.79	88.73	88.27	88.5	88.92
GRU&TFT	88.56	88.12	88.34	88.75	89.24	88.93	89.08	89.57	87.95	87.59	87.77	88.18	89.09	88.64	88.86	89.3
GRU–ARIMA–TFT	89.76	89.82	89.79	90.29	90.11	90.27	90.19	90.55	88.88	89.93	89.4	89.15	90.95	90.05	90.5	93.2

ARIMA: autoregressive integrated moving average; GRU: gated recurrent unit; TFT: temporal fusion transformer.

When analyzing configurations without the TFT module, namely GRU and ARIMA, we recorded accuracies of 88.24% and 89.05% across the UC Irvine and UTD19 datasets, respectively. This observation underscores the efficacy of merging GRU's temporal dependency modeling with ARIMA's trend and seasonality analysis, highlighting their collective strength in capturing linear aspects of traffic flow. The configurations without GRU, represented by ARIMA and TFT, achieved slightly lower accuracies, pointing to GRU's indispensable role in temporal dynamics and long-term dependencies, crucial for understanding complex urban traffic patterns. Conversely, the absence of ARIMA in the GRU and TFT setup marked a subtle decline in performance metrics, indicating ARIMA's vital contribution to the model's overall accuracy by encapsulating predictable traffic trends. Nevertheless, this configuration managed to maintain relatively high-performance levels, evidencing the robustness of GRU and TFT's spatiotemporal analysis capabilities.

Our complete GRU–ARIMA–TFT model significantly surpasses these isolated configurations, achieving unparalleled accuracies of 92.76% and 93.11% across the UC Irvine and UTD19 datasets, respectively. This remarkable performance attests to the synergistic integration of all components, underscoring the model's comprehensive approach to deciphering urban traffic complexities. The superior metrics across all datasets, including recall, F1 scores, and AUC values, reiterate the integrated model's adeptness at offering a deeper and more holistic understanding of urban traffic flows.

Our ablation study's findings illuminate the critical synergy among the GRU, ARIMA, and TFT components within our integrated GRU–ARIMA–TFT model, reinforcing the model's exceptional capability to address urban traffic flow prediction's multifaceted challenges. This comprehensive analysis validates our architectural approach, demonstrating how the concerted leverage of each component's unique strengths culminates in superior predictive performance. It affirms the model's sophisticated design and robust adaptability, showcasing the model as a testament to the efficacy of integrating diverse analytical methodologies. Thus, our study underscores the essential contributions of each module to the overall framework, enhancing urban traffic management strategies through advanced predictive insights.

In light of the experimental results, it is evident that the GRU–ARIMA–TFT model exhibits significant advantages in both prediction accuracy and the ability to decipher complex urban traffic patterns. Notably, the model's integration of GRU, ARIMA, and TFT components allows it to harness the strengths of each, facilitating a nuanced approach to traffic flow prediction that is sensitive to both temporal dynamics and spatial complexities.

In terms of prediction accuracy, our model demonstrated a consistently higher performance across multiple datasets when compared to existing models. This is attributed to the GRU component's proficiency in capturing long-term dependencies and the ARIMA model's effectiveness in modeling linear trends and seasonal variations. Together, they ensure that the model is well-attuned to the inherent patterns of traffic flow, significantly reducing prediction errors and enhancing reliability.

Moreover, the addition of the TFT component enables our model to process high-dimensional spatiotemporal data effectively. This is crucial for understanding complex urban traffic patterns, where the interplay between various factors—such as road network configurations, event-driven traffic fluctuations, and seasonal trends—requires sophisticated analytical capabilities. The TFT's attention mechanism, in particular, allows the model to focus on relevant features across different time scales, offering insights into how these factors collectively influence traffic flow dynamics. This allows the GRU–ARIMA–TFT model's proficiency in handling diverse data sources, including real-time updates, further exemplifies its practical applicability in evolving urban environments.

Discussion

In our research, the developed GRU–ARIMA–TFT network model has unveiled its considerable promise for predicting urban logistics traffic flow. Extensive experimentation has not only validated its capability to capture the intricacies of urban traffic dynamics but also highlighted its effectiveness in forecasting traffic volumes across diverse temporal spans and urban landscapes. Particularly, our model excels in delineating traffic flow trends for varied time periods and settings, thereby underscoring its practical utility in urban logistics management and strategic planning. This predictive proficiency enables urban planners and logistics managers to better anticipate traffic volume fluctuations and pinpoint potential congestion, thus facilitating the development of enhanced traffic management strategies. Moreover, the model's adeptness at processing and analyzing high-dimensional real-time data significantly augments the adaptability and efficiency of urban logistics systems to fluctuating traffic conditions, ensuring minimized delays and optimized operational workflows.

Despite these strengths, the GRU–ARIMA–TFT model encounters limitations, especially in predicting under atypical conditions such as extreme weather events or unforeseen public gatherings. Its dependency on extensive historical datasets may limit its application in data-sparse regions, and its capacity to handle sudden, unpredictable traffic flow variations remains a challenge. Additionally, the computational intensity required for a comprehensive analysis of traffic dynamics necessitates significant resources, posing a barrier to real-time data processing in environments with limited computational capacity. Furthermore, the successful deployment of this model within urban traffic systems demands careful navigation through policy and regulatory environments, ensuring compatibility with existing traffic management practices and achieving societal acceptance.

Looking ahead, our future work aims to surmount these limitations and elevate the model's performance. Plans include broadening the model's predictive scope by integrating a more diverse array of data inputs, such as weather information and data on special events, to refine its predictive accuracy in complex scenarios. Efforts will also be directed toward enhancing the model's capacity for processing large-scale, real-time data through the application of advanced algorithms and technological innovations. Additionally, we will explore the model's applicability in traffic management and planning across varied urban contexts to assess its versatility and efficacy.

The GRU–ARIMA–TFT model not only extends the theoretical boundaries of urban traffic flow prediction but also holds profound implications for real-world applications. Its rigorous validation across multiple urban settings has established it as a vital tool for urban planners and traffic managers, promising to revolutionize urban logistics operations by optimizing traffic flow, reducing congestion, and thus contributing to the sustainability of urban environments. By bridging theoretical innovation with practical implementation, our study offers invaluable insights into urban traffic dynamics and lays a solid foundation for future research, aiming to tackle the challenges of modern urban logistics and traffic management.