Resilience analytics: coverage and robustness in multi-modal transportation networks

A multi-modal transportation system of a city can be modeled as a multiplex network with different layers corresponding to different transportation modes. These layers include, but are not limited to, bus network, metro network, and road network. Formally, a multiplex network is a multilayer graph in which the same set of nodes are connected by different types of relationships. Intra-layer relationships denote the road segments connecting stations of the same transportation mode, whereas inter-layer relationships represent connections between different transportation modes within the same station. Given a multi-modal transportation system of a city, we are interested in assessing its quality or efficiency by estimating the coverage i.e., a portion of the city that can be covered by a random walker who navigates through it within a given time budget, or steps. We are also interested in the robustness of the whole transportation system which denotes the degree to which the system is able to withstand a random or targeted failure affecting one or more parts of it. Previous approaches proposed a mathematical framework to numerically compute the coverage in multiplex networks. However solutions are usually based on eigenvalue decomposition, known to be time consuming and hard to obtain in the case of large systems. In this work, we propose MUME, an efficient algorithm for Multi-modal Urban Mobility Estimation, that takes advantage of the special structure of the supra-Laplacian matrix of the transportation multiplex, to compute the coverage of the system. We conduct a comprehensive series of experiments to demonstrate the effectiveness and efficiency of MUME on both synthetic and real transportation networks of various cities such as Paris, London, New York and Chicago. A future goal is to use this experience to make projections for a fast growing city like Doha.