Optimal allocation of protective resources in urban rail transit networks against intentional attacks

•Introduce a tri-level defender-attacker-user game-theoretic model for optimally allocating protection resources.•Consider sophisticated attacking behavior on multiple locations and intensities.•Develop a nested variable neighborhood search method.•Conduct a case study based on the Singapore rail transit network.

This paper advances the field of network interdiction analysis by introducing an application to the urban rail transit network, deploying protective resources against intentional attacks. The resource allocation problem for urban rail transit systems is considered as a game between two players, the attacker interdicting certain rail stations to generate greatest disruption impact and the system defender fortifying the network to maximize the system’s robustness to external interdictions. This paper introduces a game-theoretic approach for enhancing urban transit networks’ robustness to intentional disruptions via optimally allocating protection resources. A tri-level defender–attacker–user game-theoretic model is developed to allocate protective resources among rail stations in the rail transit network. This paper is distinguished with previous studies in that more sophisticated interdiction behaviors by the attacker, such as coordinated attack on multiple locations and various attacking intensities, are specifically considered. Besides, a more complex multi-commodity network flow model is employed to model the commuter travel pattern in the degraded rail network after interdiction. An effective nested variable neighborhood search method is devised to obtain the solution to the game in an efficient manner. A case study based on the Singapore rail transit system and actual travel demand data is finally carried out to assess the protective resources’ effectiveness against intentional attacks.