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**A variational inequality formulation of the dynamic network user equilibrium problem.**
*(English)*
Zbl 0771.90037

Summary: We are concerned with developing more realistic dynamic models of route choice and departure time decisions of transportation network users than have been proposed in the literature heretofore. We briefly review one class of models that is a dynamic generalization of the static Wardropian user equilibrium, the so-called Boston traffic equilibrium. In contrast, we then propose a new class of models that is also a dynamic generalization of the static Wardropian user equilibrium. In particular, we show for the first time that there is a variational inequality formulation of dynamic user equilibrium with simultaneous route choice and departure time decisions which, when appropriate regularity conditions hold, preserves the first in, first out queue discipline.

### MSC:

90B06 | Transportation, logistics and supply chain management |

49J40 | Variational inequalities |

91B52 | Special types of economic equilibria |

90B10 | Deterministic network models in operations research |

90B22 | Queues and service in operations research |

60K25 | Queueing theory (aspects of probability theory) |