Vulnerability of Transport Networks Under Disruption of Their Collaborations : A Multi-Layer Network Model

Collaborative transport creates synergies as it enables efficient use of decentrally operated transport resources. However, extensive collaboration between carriers also comes with vulnerabilities, which can make disruptions very impactful. While the synergies of collaborative transport are widely addressed in the literature, existing transportation research models are not able to capture the vulnerabilities to disruption induced by collaboration. We aim to fill this gap by establishing a novel multi-layer network model capturing the functional dependence between the physical transport network, of which performance is impacted by the disruptions, and the network of carrier collaborations, which is being disrupted. The model is applicable to particular instances of collaborative transport networks generated from data or from random graphs. Moreover, by integrating the constraints imposed by collaborations into existing analytical methods for the analysis of network properties, the model allows for an analytical derivation of the impact of structural properties of characteristic random network populations on vulnerability. Using the model on a mix of probabilistic network populations and populations of networks generated through simulation, we show that market structure, represented by disparity in carrier sizes, has a non-trivial impact on the vulnerability of a collaborative transport network to targeted disruption at the collaborative level, resulting from the interplay between a system’s dependence on collaboration and its susceptibility to targeted disruption. Networks are most vulnerable if they have intermediate disparity in carrier sizes