A new class of instantaneous dynamic user-optimal traffic assignment models.

*(English)*Zbl 0771.90039Summary: The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. We introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solution of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first- order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints, they have unique solutions. A numerical example is presented indicating that this class of models yields realistic results.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

93C95 | Application models in control theory |

90C25 | Convex programming |

90B10 | Deterministic network models in operations research |