A new network equilibrium flow model: User-equilibrium with quantity adjustment

Travelers’ route choice behaviors affect the distribution of network flow. The paper presents an unconventional equilibrium flow model that extends the well-known non-Walrasian equilibrium theory of economics to the analysis of route choice behavior. With the introduction of path residual capacity as the quantity signal, a quantity adjustment user equilibrium flow model depicts the route choice dynamics based on the maximum path residual capacity, and thus differs from the traditional traffic equilibrium pattern regulated by path travel time. An equivalent nonlinear complementary problem to the proposed model is developed, and further reformulated as an unconstrained mathematical program using a gap function, which permits many efficient solution algorithms. The maximum residual capacity path algorithm and the maximum residual capacity traffic assignment algorithm are developed, and the gradient descent algorithm is used to solve the unconstrained mathematical program. Numerical results show that the proposed model and solution algorithm are feasible and effective. The paper proposes that both price adjustment and quantity adjustment are special cases of the price-quantity adjustment principle, and the equilibrium flow model based on which can capture route choice behaviors that has not been modeled in previous studies.