Robustness of the public transport network against attacks on its routes

TL;DR

This paper investigates the robustness of public transport networks to attacks that remove entire bus routes, using three network representations (L-space, L'-space, and C-space) and a suite of route-attack strategies. It evaluates both a synthetic, SAW-based PTN model and a real-world Buenos Aires AMBA network to compare betweenness-based and one-step maximal-harm strategies against other centrality measures and random failures. The results show that betweenness-based attacks are particularly effective at fragmenting networks into several comparably sized components, while maximal one-step strategies can also be highly damaging to the giant component in certain regimes. The study highlights differences between synthetic and real networks, suggests refinements to synthetic models to better capture real-world robustness, and provides insights for designing more resilient PTNs and future mobility-focused analyses.

Abstract

We investigate the robustness of Public Transport Networks (PTNs) when subjected to route attacks, focusing specifically on public bus lines. Such attacks, mirroring real-world scenarios, offer insight into the multifaceted dynamics of cities. Our study delves into the consequences of systematically removing entire routes based on strategies that use centrality measures. We evaluate the network's robustness by analyzing the sizes of fragmented networks, focusing on the largest components and derived metrics. To assess the efficacy of various attack strategies, we employ them on both a synthetic PTN model and a real-world example, specifically the Buenos Aires Metropolitan Area in Argentina. We examine these strategies and contrast them with random, and one-step most and least harmful procedures. Our findings indicate that \textit{betweenness}-based attacks and the one-step most (\textit{maximal}) harmful procedure emerge as the most effective attack strategies. Remarkably, the \textit{betweenness} strategy partitions the network into components of similar sizes, whereas alternative approaches yield one dominant and several minor components.

Figures (8)

• Figure 1: Example of a PTN and their three different representations, $\mathbb{L}$, $\mathbb{L}$' and $\mathbb{C}$-spaces.
• Figure 2: Schematic representation of the removal procedure following the strategy of degree centrality measure for $N=25$ and $R=5$. Given a certain PTN, a centrality measurement is performed and the most important route is attacked, i.e., all its edge are removed from $\mathbb{L}$'-space and the node is removed from the $\mathbb{C}$-space.
• Figure 3: Illustration of the progressive process of synthetic networks generation for $a = 0$, $b = 5$, $S = 45$ and $X = 300$. In panel [A] a single route is shown and, as on the whole process, it is clearly a self-avoiding path. In panels [B], [C], [D], [E] and [F] a new route is subsequently added with a different color for clarity purpose. It is important to notice that there is a single connected component because the parameter $a$ is set to $0$.
• Figure 4: Illustration of the results of attacking a particular realization of a network generated with the synthetic model with $a=0$, $b=0.5$, $R=500$, $S=45$ a through a directed attack (using betweenness centrality strategy) and a random attack. The original $\mathbb{L}$’-space is plotted on the panel [A]. Panels [B], [C], and [D] represent the first components resulting from different stages of the network random attack, with the corresponding fraction $\Phi$ of removed routes. Panels [E], [F], and [G] represent the results of the network- betweenness directed attack for the same $\Phi$ values. Different colors represent the first five components into which the network is disassembled. Isolated nodes are plotted in gray.
• Figure 5: Average fraction of nodes on the two main components $S_1$ and $S_2$, and the normalized entropy $\Sigma_S$ are depicted as functions of $\Phi$ in the top, middle, and bottom panels, respectively. The estimation of the averages and their corresponding errors are taken over $10$ realizations of the synthetic network. The shaded areas correspond to the errors associated with the estimation of the averages. The different proposed removal processes are represented by colored lines for the synthetic PTN network with $a = 0$, $b = 5$, $S = 45$, and $R = 500$. "Max" and "Min" account for $maximal$ and $minimal$ strategies, respectively. This holds for next figures also.