An intersection-movement-based dynamic user optimal route choice problem.

*(English)*Zbl 1291.90038Summary: In this paper a novel variational inequality (VI) formulation of the dynamic user optimal (DUO) route choice problem is proposed using the concept of approach proportion. An approach proportion represents the proportion of travelers that select a turning or through movement when leaving a node. Approach proportions contain travelers’ route information so that the realistic effects of physical queues can be captured in a formulation when a physical-queue traffic flow model is adopted, and so that route enumeration and path-set generation can be avoided in the solution procedure. In addition, the simple structure of the approach proportion representation allows us to decompose the constraint set for solving large-scale DUO route choice problems. This paper also discusses the existence and uniqueness of the solutions to the VI problem and develops a solution algorithm based on the extragradient method to solve the proposed VI problem. This solution algorithm makes use of the decomposition property of the constraint set and is convergent if the travel time functions are pseudomonotone and Lipschitz continuous. It is not necessary to know the Lipschitz constant of the travel time functions in advance. Finally, numerical examples are given to demonstrate the properties of the proposed model and the performance of the solution algorithm.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |