An origin–destination based road pricing model for static and multi-period traffic assignment problems

•We analytically derived origin–destination (OD)-based tolls for elastic demand.•We derived user equilibrium conditions for multi-period static traffic assignment.•OD-based toll pricing model for the multi-period static traffic assignment problems.•Practical advantages of the proposed OD-based pricing over existing schemes.•The origin–destination based pricing scheme outperforms the no-toll scenario. To mitigate traffic externalities, we propose an origin–destination (OD) based road pricing model for traffic assignment problems. For elastic demand, we derive explicit optimal tolls for the OD-based pricing scheme. We also extend the model to a multi-period static traffic assignment (MSTA) where we derive analytically the route and OD-dependent tolls based on equilibrium conditions. We present some examples to show that the OD-based tolling scheme could improve the system welfare significantly, compared to the no-toll scenario (user equilibrium – UE).