Traffic Network Equilibrium and the Environment

A Multicriteria Decision-Making Perspective
  • Anna Nagurney
  • June Dong
  • Patricia L. Mokhtarian
Part of the Applied Optimization book series (APOP, volume 74)


A traffic network equilibrium model is developed in which the users or travelers on the network are assumed to be multicriteria decision-makers with an explicit environmental criterion. The members of a class of traveler perceive their generalized cost on a route as a weighting of travel time, travel cost, and the emissions generated. The model allows the weights to be not only class-dependent but also link-dependent. The multiclass, multicriteria network equilibrium conditions are shown to satisfy a finite-dimensional variational inequality problem. Qualitative properties of the solution are obtained. A special case of the model is then used to obtain sharper results and to illustrate the relationship between the weights and the attainment of a desired environmental quality standard. An algorithm is proposed for the computation of the equilibrium pattern, along with convergence results, and then applied to solve a numerical example. The multiclass, multicriteria network equilibrium model is the first to incorporate an environmental criterion.


Multicriteria decision-making traffic network equilibrium environmental criteria variational inequalities 


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  1. Allen W. G. (1996). Model improvements for evaluating pricing strategies. Transportation Research Record 1498, 75–81.Google Scholar
  2. Anderson W. P., Kanaroglou P. S., Miller E. J., and Buliung R. N. (1996). Simulating automobile emissions in an integrated urban model. Transportation Research Record 1520, 71–80.CrossRefGoogle Scholar
  3. Beckmann M. J., McGuire C. B. and Winsten C. B. (1956). Studies in the Economics of Transportation, Yale University Press, New Haven, Connecticut.Google Scholar
  4. Button K. J. (1990). Environmental externalities and transport policy. Oxford Review of Economic Policy 6, 61–75.CrossRefGoogle Scholar
  5. Dafermos S. (1980). Traffic equilibria and variational inequalities. Transportation Science 114 42–54.CrossRefGoogle Scholar
  6. Dafermos S. (1981). A multicriteria route-mode choice traffic equilibrium model. Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island.Google Scholar
  7. Dafermos S. C. and Sparrow F. T. (1969). The traffic assignment problem for a general nerwork. Journal of Research of the National Bureau of Standards 73B, 91–118.Google Scholar
  8. DeCorla-Souza P., Everett J., Cosby J., and Lim P. (1995). Trip-based approach to estimate emissions with Environmental Protection Agency’s MOBILE model. Transportation Research Record, 1444, 118–125.Google Scholar
  9. Dial R. B. (1979). A model and algorithms for multicriteria route-mode choice. Transportation Research 13B, 311–316.CrossRefGoogle Scholar
  10. Dial R. B. (1996). Bicriterion traffic assignment: Basic theory and elementary algorithms. Transportation Science 30, 93–11.CrossRefGoogle Scholar
  11. Kinderlehrer D. and Stampacchia G. (1980). An Introduction to Variational Inequalities and Their Applications. Academic Press, New York.Google Scholar
  12. Korpelevich G. M. (1977). The extragradient method for finding saddle points and other problems. Matekon 13, 35–49.Google Scholar
  13. Leurent F. (1993a). Modelling elastic, disaggregate demand. In J. C. Moreno Banos, B. Friedrich, M. Papageorgiou, and H. Keller, editors, Proceedings of the First Meeting of the Euro Working Group on Urban Traffic and Transportation, Technical University of Munich, Munich, Germany.Google Scholar
  14. Leurent F. (1993b). Cost versus time equilibrium over a network. European Journal of Operations Research 71, 205–221.CrossRefGoogle Scholar
  15. Leurent F. (1996). The theory and practice of a dual criteria assignment model with continuously distributed values-of-times. In J. B. Lesort, editor, Transportation and Traffic Theory, pp. 455–477, Pergamon, Exeter, England.Google Scholar
  16. Leurent F. (1998). Multicriteria assignment modeling: making explicit the determinants of mode or path choice. In P. Marcotte and S. Nguyen, editors, Equilibrium and Advanced Transportation Modelling, pp. 153–174, Kluwer Academic Publishers, Boston, Massachusetts.CrossRefGoogle Scholar
  17. Nagurney A. (1999). Network Economics: A Variational Inequality Approach. Second and revised edition, Kluwer Academic Publishers, Dordrecht, The Netherlands.Google Scholar
  18. Nagurney A. (2000a). Sustainable Transportation Networks. Edward Elgar Publishers, Cheltenham, England.Google Scholar
  19. Nagurney A. (2000b). A multiclass, multicriteria traffic network equilibrium model. Mathematical and Computer Modelling 32, 393–411.CrossRefGoogle Scholar
  20. Nagurney A. and Dong J. (2000). A multiclass, multicriteria traffic network equilibrium model with elastic demand. To appear in Transportation Research B.Google Scholar
  21. Nagurney A., Dong J. and Mokhtarian P. L. (2000a). Integrated multiclass network equilibrium models for commuting versus telecommuting. Isenberg School of Management, University of Massachusetts, Amherst.Google Scholar
  22. Nagurney A., Dong J. and Mokhtarian P. L. (2000b). Teleshopping versus shopping: A multicriteria network equilibrium framework. To appear in Mathematical and Computer Modelling.Google Scholar
  23. Quandt R. E. (1967). A probabilistic abstract mode model. In Studies in Travel Demand VIII, Mathematica, Inc., Princeton, New Jersey, pp. 127–149.Google Scholar
  24. Rilett L. R., and Benedek, C. M. (1994). Traffic assignment under environmental and equity objectives. Transportation Research Record 1443, 92–99.Google Scholar
  25. Schneider M. (1968). Access and land development. In Urban Development Models, Highway Research Board Special Report 97, pp. 164–177.Google Scholar
  26. The Economist (1996). Living with the car. June 22, 3–18.Google Scholar
  27. The Economist (1997). Living with the car. December 26, 21–23.Google Scholar
  28. Tzeng G. H. and Chen C. H. (1993). Multiobjective decision making in traffic assignment. IEEE Transactions on Engineering Management 40, 180–187.CrossRefGoogle Scholar
  29. United States Department of Transportation (1992a). A summary: Transportation programs and provisions of the Clean Air Act Amendments of 1990. Publication number: FHWA-PD-92–023.Google Scholar
  30. United States Department of Transportation (1992b). A summary: Air quality programs and provisions of the Intermodal Surface Transportation Efficiency Act of 1991, 1992. Publication Number: FHWA-PD-92022.Google Scholar
  31. Wardrop J. G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institute of Civil Engineers, Part II, pp. 325–378.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Anna Nagurney
    • 1
  • June Dong
    • 2
  • Patricia L. Mokhtarian
    • 3
  1. 1.Department of Finance and Operations Management, Isenberg School of ManagementUniversity of MassachusettsAmherstUSA
  2. 2.School of BusinessState University of New York at OswegoOswegoUSA
  3. 3.Department of Civil and Environmental EngineeringUniversity of CaliforniaDavisUSA

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