On the Induction of Cascading Failures in Transportation Networks

We examine the effect of malicious attacks in disrupting optimal routing algorithms for transportation networks. We model traffic networks using the cell transmission model, which is a spatiotemporal discretization of kinematic wave equations. Here, vehicles are modeled as masses and roads as cells, and traffic flow is subject to conservation of mass and capacity constraints. At time zero a resource-constrained malicious agent reduces the capacities of cells so as to maximize the amount of time mass spends in the network. For the resulting set of capacities the network router then solves a linear program to determine the flow configuration that minimizes the amount of time mass spends in the network. Our model allows for the outright or partial failure of road cells at time zero, the effects of which can cause cascading failure in the network due to irreversible blockages resulting from congestion. This two-player problem is written as a max-min optimization and is reformulated to an equivalent nonconvex optimization problem with a bilinear objective and linear constraints. Linearization techniques are applied to the optimization problem to find local solutions. Analyzing illustrative examples shows that attackers with relatively small resource budgets can cause widespread failure in a traffic network.