Circuit system analogy to equilibrium models and its application in one-way transportation networks

Equilibrium models have extremely important application in traffic assignment, but it is difficult to provide the objective function of equilibrium models with intuitive or economic explanation. After establishing an analogy between one-way transportation networks and circuit networks, this paper directly derives the mathematical programming formula of user equilibrium model and system optimum model in the traffic assignment from the perspective of circuit-balance and power-minimizing principles. The concept of effective resistance is introduced to clearly explain the principle of Braess's paradox, which shows the practical value of circuit network analogy in the transportation network research.