Graph Theory for Metro Traffic Modelling
This work addresses metro transportation planning and traffic management, offering a formal mathematical approach with potential economic implications, but it is incremental as it builds on existing graph theory and deep learning methods.
The authors tackled metro traffic modeling by proposing a graph theory framework, demonstrating its utility for network robustness and planning, and showing that commuter movement follows diffusion laws with graph Laplacian models, validated through simulations of London's morning rush hour passenger flows.
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 Fick's 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.