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.Other Information Published in: EPJ Data Science License: https://creativecommons.org/licenses/by/4.0See article on publisher's website: http://dx.doi.org/10.1140/epjds/s13688-018-0139-7</p

Statistics on the topological features of the eight networks.

<p> and denote the number of nodes and links. and are the average clustering coefficient and the density of the network, respectively. If a vertex has neighbours, edges could exist among the vertices within the neighbourhood. Thus, the local clustering coefficient for a network can be defined as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072908#pone.0072908-Adamic2" target="_blank">[39]</a>, where denotes the neighbours of . is defined as . is defined as . is the modularity of the network defined as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072908#pone.0072908-Clauset2" target="_blank">[26]</a>, where denotes a community which includes the vertice and if vertices and are connected and 0 otherwise and if and 0 otherwise. and denote the average degree and the average shortest distance.</p

Comparisons of computational efficiency on four networks.

<p>Each value of running time is the cumulative time for 100 implementations.</p

Accuracy and computational time comparisons between FBM and CAR-based approaches on two noisy PPI networks.

<p>(a) The upper plot illustrates the precision curves for all approaches on the PPI-1 network while the bars in the lower plot illustrate the corresponding AUP (area under precision curve) values for each approach. (b) The upper plot illustrates the precision curves for all approaches on the PPI-2 network while the bars in the lower plot illustrate the corresponding AUP (area under precision curve) values for each approach. The sampling parameter is tuned by 20, 30 and 50 for the FBM approach. The computational time (seconds) for each method is shown in the legend.</p

Three artificial networks illustrating the link formation mechanism in the communities.

<p>Three artificial networks illustrating the link formation mechanism in the communities.</p

Link density distributions for the four networks.

<p>The diagonal highlighted blocks are corresponding to communities with link densities which are not less than 0.8.</p

Accuracy comparisons between predicting links selectively removed from the communities by following the three link formation principles and predicting links removed randomly.

<p>The fraction of links removed is always 10 percent.</p

An example network illustrating the relationship between community distribution and link density matrix.

<p>(a) The community distribution of the network. (b) The link density matrix of the corresponding community distribution.</p