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Register a new userGraph Theory for Metro Traffic Modelling
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Added by
Yao Lei Xu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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A unifying graph theoretic framework for the modelling of metro transportation networks is proposed. This is achieved by first introducing a basic graph framework for the modelling of the London underground system from a diffusion law point of view. This forms a basis for the analysis of both station importance and their vulnerability, whereby the concept of graph vertex centrality plays a key role. We next explore k-edge augmentation of a graph topology, and illustrate its usefulness both for improving the network robustness and as a planning tool. Upon establishing the graph theoretic attributes of the underlying graph topology, we proceed to introduce models for processing data on such a metro graph. Commuter movement is shown to obey the Ficks law of diffusion, where the graph Laplacian provides an analytical model for the diffusion process of commuter population dynamics. Finally, we also explore the application of modern deep learning models, such as graph neural networks and hyper-graph neural networks, as general purpose models for the modelling and forecasting of underground data, especially in the context of the morning and evening rush hours. Comprehensive simulations including the passenger in- and out-flows during the morning rush hour in London demonstrates the advantages of the graph models in metro planning and traffic management, a formal mathematical approach with wide economic implications.
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In this article we demonstrate how graph theory can be used to identify those stations in the London underground network which have the greatest influence on the functionality of the traffic, and proceed, in an innovative way, to assess the impact of a station closure on service levels across the city. Such underground network vulnerability analysis offers the opportunity to analyse, optimize and enhance the connectivity of the London underground network in a mathematically tractable and physically meaningful manner.
Traffic flow prediction, particularly in areas that experience highly dynamic flows such as motorways, is a major issue faced in traffic management. Due to increasingly large volumes of data sets being generated every minute, deep learning methods have been used extensively in the latest years for both short and long term prediction. However, such models, despite their efficiency, need large amounts of historical information to be provided, and they take a considerable amount of time and computing resources to train, validate and test. This paper presents two new spatial-temporal approaches for building accurate short-term prediction along a popular motorway in Sydney, by making use of the graph structure of the motorway network (including exits and entries). The methods are built on proximity-based approaches, denoted backtracking and interpolation, which uses the most recent and closest traffic flow information for each of the target counting stations along the motorway. The results indicate that for short-term predictions (less than 10 minutes into the future), the proposed graph-based approaches outperform state-of-the-art deep learning models, such as long-term short memory, convolutional neuronal networks or hybrid models.
Accurate prediction of metro passenger volume (number of passengers) is valuable to realize real-time metro system management, which is a pivotal yet challenging task in intelligent transportation. Due to the complex spatial correlation and temporal variation of urban subway ridership behavior, deep learning has been widely used to capture non-linear spatial-temporal dependencies. Unfortunately, the current deep learning methods only adopt graph convolutional network as a component to model spatial relationship, without making full use of the different spatial correlation patterns between stations. In order to further improve the accuracy of metro passenger volume prediction, a deep learning model composed of Parallel multi-graph convolution and stacked Bidirectional unidirectional Gated Recurrent Unit (PB-GRU) was proposed in this paper. The parallel multi-graph convolution captures the origin-destination (OD) distribution and similar flow pattern between the metro stations, while bidirectional gated recurrent unit considers the passenger volume sequence in forward and backward directions and learns complex temporal features. Extensive experiments on two real-world datasets of subway passenger flow show the efficacy of the model. Surprisingly, compared with the existing methods, PB-GRU achieves much lower prediction error.
Traffic forecasting is a classical task for traffic management and it plays an important role in intelligent transportation systems. However, since traffic data are mostly collected by traffic sensors or probe vehicles, sensor failures and the lack of probe vehicles will inevitably result in missing values in the collected raw data for some specific links in the traffic network. Although missing values can be imputed, existing data imputation methods normally need long-term historical traffic state data. As for short-term traffic forecasting, especially under edge computing and online prediction scenarios, traffic forecasting models with the capability of handling missing values are needed. In this study, we consider the traffic network as a graph and define the transition between network-wide traffic states at consecutive time steps as a graph Markov process. In this way, missing traffic states can be inferred step by step and the spatial-temporal relationships among the roadway links can be Incorporated. Based on the graph Markov process, we propose a new neural network architecture for spatial-temporal data forecasting, i.e. the graph Markov network (GMN). By incorporating the spectral graph convolution operation, we also propose a spectral graph Markov network (SGMN). The proposed models are compared with baseline models and tested on three real-world traffic state datasets with various missing rates. Experimental results show that the proposed GMN and SGMN can achieve superior prediction performance in terms of both accuracy and efficiency. Besides, the proposed models parameters, weights, and predicted results are comprehensively analyzed and visualized.
Spatial-temporal forecasting has attracted tremendous attention in a wide range of applications, and traffic flow prediction is a canonical and typical example. The complex and long-range spatial-temporal correlations of traffic flow bring it to a most intractable challenge. Existing works typically utilize shallow graph convolution networks (GNNs) and temporal extracting modules to model spatial and temporal dependencies respectively. However, the representation ability of such models is limited due to: (1) shallow GNNs are incapable to capture long-range spatial correlations, (2) only spatial connections are considered and a mass of semantic connections are ignored, which are of great importance for a comprehensive understanding of traffic networks. To this end, we propose Spatial-Temporal Graph Ordinary Differential Equation Networks (STGODE). Specifically, we capture spatial-temporal dynamics through a tensor-based ordinary differential equation (ODE), as a result, deeper networks can be constructed and spatial-temporal features are utilized synchronously. To understand the network more comprehensively, semantical adjacency matrix is considered in our model, and a well-design temporal dialated convolution structure is used to capture long term temporal dependencies. We evaluate our model on multiple real-world traffic datasets and superior performance is achieved over state-of-the-art baselines.
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