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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)
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