Traffic Equilibrium and Variational Inequalities

@article{Dafermos1980TrafficEA,
  title={Traffic Equilibrium and Variational Inequalities},
  author={Stella Dafermos},
  journal={Transportation Science},
  year={1980},
  volume={14},
  pages={42-54}
}
  • S. Dafermos
  • Published 1 February 1980
  • Computer Science
  • Transportation Science
We consider the general traffic equilibrium network model where the travel cost on each link of the transportation network may depend on the flow on this as well as other links of the network. The model has been designed in order to handle situations where there is interaction between traffic on different links e.g., two-way streets, intersections or between different modes of transportation on the same link. For this model, we use the techniques of the theory of variational inequalities to… 

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References

SHOWING 1-10 OF 10 REFERENCES

An Extended Traffic Assignment Model with Applications to Two-Way Traffic

An extended traffic assignment model where the traveling cost on a link becomes a function of the entire flow pattern in the network is introduced and appears particularly suitable for application to networks containing two-way streets.

An Algorithm for the Traffic Assignment Problem

An efficient algorithm is developed, an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way, using a node-arc formulation of the problem.

The Traffic Assignment Problem for Multiclass-User Transportation Networks

It is shown that this model is also capable of handling the case of several classes of users in the same transportation network each of which has an individual cost function and, at the same time, contributes to its own and other classes' cost functions in an individual way.

Studies in the Economics of Transportation.

THE CAPABILITIES AND EFFICIENT OPERATION OF SEVERAL TYPES OF TRANSPORTATION SYSTEMS ARE STUDIED. FOR HIGHWAY TRAFFIC THE MAIN EMPHASIS IS ON CONGESTION AND ITS CONSEQUENCES. QUEUING MODELS ARE USED

A Column Generation Algorithm for Optimal Traffic Assignment

A column generation algorithm for solving a class of nonlinear traffic assignment problems and Computational experience that contrasts column generation with the a priori generation of all paths and compares two different quadratic programming algorithms is reported.

Traffic assignment problem for a general network

A tra ns portatio n network is formulated, and a lgo rithms are co ns truc ted for the so lutio n of these prob lems of finding the traffi c patte rn s.