On the Resilience of Traffic Networks under Non-Equilibrium Learning

We investigate the resilience of learning-based $\mathit{\text{Intelligent}}\mathit{\text{Navigation}}\mathit{\text{Systems}}$ (INS) to informational flow attacks, which exploit the vulnerabilities of IT infrastructure and manipulate traffic condition data. To this end, we propose the notion of $\mathit{\text{Wardrop}}\mathit{\text{Non-Equilibrium}}\mathit{\text{Solution}}$ (WANES), which captures the finite-time behavior of dynamic traffic flow adaptation under a learning process. The proposed non-equilibrium solution, characterized by target sets and measurement functions, evaluates the outcome of learning under a bounded number of rounds of interactions, and it pertains to and generalizes the concept of approximate equilibrium. Leveraging finite-time analysis methods, we discover that under the mirror descent (MD) online-learning framework, the traffic flow trajectory is capable of restoring to the Wardrop non-equilibrium solution after a bounded INS attack. The resulting performance loss is of order $\tilde{\mathcal{O}}(T^{\beta })$ ($-\frac{1}{2}\le \beta <0)$), with a constant dependent on the size of the traffic network, indicating the resilience of the MD-based INS. We corroborate the results using an evacuation case study on a Sioux-Fall transportation network.