Multilayer public transport networks

Abstract

The introduction of network science approaches into public transport research has seen great advances in the past 15 years. However, it has become apparent that monolayer networks are often not sufficient to model and analyse real-world systems in sufficient detail. In the last decade, the theory of multilayer networks has proven to be an invaluable tool in various disciplines, including transport. Multilayer networks consist of layers of networks that are coupled among themselves. This enables modelling of complex systems with heterogeneous elements and relations between them. Although there is a body of work in public transport research that uses multilayer networks, the related literature is scattered, lacking unified terminology and agreed-upon approaches. We posit that there is vast uncovered potential in using multilayer network approaches to public transport modelling, planning, and operations. We first present the basic formalisms of multilayer networks with a focus on how they (may) relate to public transport networks. We then provide a systematic review of the literature on multilayer networks in public transport research. We identify and taxonomise ways in which public transport systems are modelled as multilayer networks. Based on the survey and drawing from the state and history of network science in public transport research as well as multilayer approaches across other application domains, we propose a research agenda for multilayer public transport networks for the upcoming decade(s).

Figures (5)

• Figure 1: An illustration of the standard PTN graph representations.
• Figure 2: An illustration of a simple multilayer network consisting of two layers. Intra-layer edges within a single layer are shown in bold lines and inter-layer edges connecting nodes from separate layers are shown in dashed lines.
• Figure 3: Types of multilayer networks. The upper plot shows the classification tree of MLNs as presented in the this review. Below each category is an example of a multilayer public transport network. The leftmost plot represents $\mathcal{M}^{I}$ represents an interdependent network where the bottom layer is the L-space metro and top layer L-space bus. The middle network $\mathcal{M}^{H}$, is an example of a heterogeneous network, where the bottom layer is again the L-space metro and the top layer is the C-space representation of the same network. The rightmost network, represents a multiplex network $\mathcal{M}^{M}$ where the bottom layer is the L-space representation of the toy metro network and the top layer is the OD layer. (See also descriptions in the text).
• Figure 4: Supra-adjacency matrices for the interdependent toy network $\mathcal{M}^I$ (left) and the multiplex toy network $\mathcal{M}^M$ (right). The networks are visualised in Figure \ref{['fig:mlntypes']}.
• Figure 5: A two-level taxonomy of MLPTNs.