Dynamic Traffic Network Equilibrium System with Elastic Demands

We discuss the dynamic traffic network equilibrium system problem with elastic demands by way of a quasi-variational inequality.We introduce the equilibrium definition with elastic demands based on Wardrops principles when there are some internal relationships between different kinds of goods which transported through the same traffic network. Moreover, we also prove that the equilibrium conditions of this problem with elastic demands can be equivalently expressed as a system of evolutionary variational inequalities. By using the fixed point theory and projected dynamic system theory, we get the existence and uniqueness of the solution for this equilibrium problem with elastic demands. Finally, some numerical examples are given to illustrate our results.

Traffic Network Equilibrium Problems with Capacity Constraints of Arcs and Linear Scalarization Methods

Traffic network equilibrium problems with capacity constraints of arcs are studied. A (weak) vector equilibrium principle with vector-valued cost functions, which are different from the ones in the work of Lin (2010), and three kinds of parametric equilibrium flows are introduced. Some necessary and sufficient conditions for a (weak) vector equilibrium flow to be a parametric equilibrium flow are derived. Relationships between a parametric equilibrium flow and a solution of a scalar variational inequality problem are also discussed. Some examples are given to illustrate our results.