Optimal allocation of defensive resources in regional railway networks under intentional attacks

Railway network is one of the busiest regional transportation infrastructures, which is exposed to a high risk of intentional attacks. Given the railway network stations have a larger service area, attackers may have different biases toward the valuation of railway stations or lines. This paper proposes a method for optimally allocating defensive resources based on a Bayesian game model and a comprehensive importance evaluation model of stations by multi-layer network models, aiming to reduce the losses of defenders. The attack strategy was made according to the importance of railway stations evaluated by three-layer network models, namely topology layer, the ridership layer and the travel time layer, which depict the features of railway networks and also reflect the variety of attacker's biases. The optimal allocation of defensive resources was obtained under the Nash equilibrium of Bayesian game. The proposed method is implemented in a regional railway network in north China, and the case network's risk under various attack strategies were compared to validate the applicability of this model. The application results show that the optimal defensive resources allocation based on the importance evaluation by three-layer models has the lowest risk considering the variety in the attacker's biases.