Abstract
We formulate the network equilibrium problem with mixed demand which generalizes the problems of network equilibrium with fixed and elastic demand. We prove the equilibrium conditions for this problem and propose some conditions of existence of a solution that are based on the coercivity property.We establish a connection between the problem of network equilibrium with mixed demand and the problem of auction equilibrium. The results of test calculations are presented for a model example.
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References
I. V. Konnov, Nonlinear Optimization and Variational Inequalities (Kazan. Univ., Kazan, 2013) [in Russian].
M. J. Beckmann, C. B. McGuire, and C. B. Winsten, Studies in the Economics of Transportation (Yale Univ. Press, New Haven, CT, 1956).
D. P Bertsekas and E. M. Gafni, “Projection Methods for Variational Inequalities with Application to the Traffic Assignment Problem,” in Nondifferential and Variational Techniques in Optimization (North-Holland, Amsterdam, 1982), pp. 139–159.
S. Dafermos, “Traffic Equilibrium and Variational Inequalities,” Transp. Sci. 14 (1), 42–54 (1980).
S. Dafermos, “The General Multimodal Network Equilibrium Problem with Elastic Demand,” Networks 12 (1), 57–72 (1982).
J. de Dios Ortúzar and L. G. Willumsen, Modeling Transport (JohnWiley & Sons, Chichester, 2011).
F. Giannessi and A. Maugeri, Variational Inequalities and Network Equilibrium Problems (Plenum Press, New York, 1995).
I. V. Konnov, Equilibrium Models and Variational Inequalities (Elsevier, Amsterdam, 2007).
I. V. Konnov, ‘On Auction Equilibrium Models with Network Applications,” Netnomics 16 (1), 107–125 (2015).
I. V. Konnov, “An Alternative Economic Equilibrium Model with Different Implementation Mechanisms,” Adv. Model. Optim. 17 (2), 245–265 (2015) [Available at http://camo.ici.ro/journal/vol17/v17b7.pdf (accessed Apr. 6, 2017)].
P. Mailléand B. Tuffin, Telecommunication Network Economics: From Theory to Applications, (Cambridge Univ. Press, New York, 2014).
A. Nagurney, Network Economics: A Variational Inequality Approach (Kluwer Acad. Publ., Dordrecht, 1999).
M. Patriksson, The Traffic Assignment Problem: Models and Methods (Dover,Mineola, NY, 2015).
O. V. Pinyagina, “On a Network Equilibrium Problem withMixed Demand,” in Discrete Optimization and Operations Research: Proceedings of the 9th International Conference DOOR, Vladivostok, Russia, September 19–23, 2016 (Springer, Cham, 2016), pp. 578–583.
M. J. Smith, “Existence, Uniqueness, and Stability of Traffic Equilibria,” Transp.Res. Part B:Methodological 13 (4), 295–304 (1979).
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Original Russian Text © O.V. Pinyagina, 2017, published in Diskretnyi Analiz i Issledovanie Operatsii, 2017, Vol. 24, No. 4, pp. 77–94.
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Pinyagina, O.V. The network equilibrium problem with mixed demand. J. Appl. Ind. Math. 11, 554–563 (2017). https://doi.org/10.1134/S1990478917040135
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DOI: https://doi.org/10.1134/S1990478917040135