A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem

In the present paper 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.

[1]  André de Palma,et al.  Some Circumstances in Which Vehicles Will Reach Their Destinations Earlier by Starting Later: Revisited , 1986, Transp. Sci..

[2]  Lester B. Lave,et al.  Highway congestion and congestion tolls , 1977 .

[3]  M. Wohl,et al.  New directions for passenger demand analysis and forecasting , 1967 .

[4]  André de Palma,et al.  Dynamic Model of Peak Period Traffic Congestion with Elastic Arrival Rates , 1986, Transp. Sci..

[5]  R. J. Smeed,et al.  Some Circumstances in Which Vehicles Will Reach Their Destinations Earlier by Starting Later , 1967, Transp. Sci..

[6]  Malachy Carey,et al.  A Constraint Qualification for a Dynamic Traffic Assignment Model , 1986, Transp. Sci..

[7]  Malachy Carey,et al.  Optimal Time-Varying Flows on Congested Networks , 1987, Oper. Res..

[8]  Terry L. Friesz,et al.  TRANSPORTATION NETWORK EQUILIBRIUM, DESIGN AND AGGREGATION: KEY DEVELOPMENTS AND RESEARCH OPPORTUNITIES. IN: THE AUTOMOBILE , 1985 .

[9]  M. Ben-Akiva,et al.  STOCHASTIC EQUILIBRIUM MODEL OF PEAK PERIOD TRAFFIC CONGESTION , 1983 .

[10]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[11]  Chris Hendrickson,et al.  Schedule Delay and Departure Time Decisions in a Deterministic Model , 1981 .

[12]  Mosher,et al.  A CAPACITY-RESTRAINT ALGORITHM FOR ASSIGNING FLOW TO A TRANSPORT NETWORK , 1963 .

[13]  George L. Nemhauser,et al.  Optimality Conditions for a Dynamic Traffic Assignment Model , 1978 .

[14]  W. Vickrey.  Congestion Theory and Transport Investment , 1969 .

[15]  Terry L. Friesz,et al.  Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem , 1989, Oper. Res..

[16]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[17]  Gordon F. Newell,et al.  Applications of queueing theory , 1971 .

[18]  Moshe Ben-Akiva,et al.  Dynamic model of peak period congestion , 1984 .

[19]  Deepak K. Merchant,et al.  A Model and an Algorithm for the Dynamic Traffic Assignment Problems , 1978 .

[20]  Hani S. Mahmassani,et al.  Experiments with departure time choice dynamics of urban commuters , 1986 .