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Zbl 0771.90037
Friesz, Terry L.; Bernstein, David; Smith, Tony E.; Tobin, Roger L.; Wie, B.W.
A variational inequality formulation of the dynamic network user equilibrium problem. (English)
[J] Oper. Res. 41, No.1, 179-191 (1993). ISSN 0030-364X; ISSN 1526-5463/e

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 2000:: *90B06 Transportation, logistics
49J40 Variational methods including variational inequalities
91B52 Special types of equilibria in economics
90B10 Flows in networks
90B22 Queues and service
60K25 Queueing theory

Keywords: variational inequality; route choice; departure time decisions; transportation network; Wardropian user equilibrium; Boston traffic equilibrium

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