The author presents a general framework for formulating network equilibrium problems in which the equilibrium conditions are given by a system of nonlinear equations. Existence and uniqueness results are presented, and iterative solution techniques with well-defined convergence properties are suggested. For illustrative purposes, these techniques are applied to a specific two-mode equilibrium model; a discussion comparing some aspects of this approach with other existing approaches is included.
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References
1.
AashtianiH, 1979The Multi-modal Traffic Assignment Problem PhD dissertation, Operations Research Center, MIT, Cambridge, MA
2.
AashtianiHMagnantiT, 1981, “Equilibria on a congested transportation network”Siam Journal on Algebra and Discrete Methods2213–226
3.
AbdulaalMLeBlancL J, 1979, “Methods for combining modal split and equilibrium assignment models”Transportation Science13292–314
4.
BeckmannM JMcGuireC BWinstenC B, 1956Studies in the Economics of Transportation (Yale University Press, New Haven, CT)
5.
BensoussanALionsJ LTemanT, 1972, “Sur les méthodes de décomposition, de décentralisation, et de coordinations et d'applications”Cahiers d'IRIA115–1890
6.
DafermosS C, 1972, “An extended traffic assignment model with implications to two-way traffic”Transportation Science673–87
7.
DafermosS C, 1982, “The general multimodal network equilibrium problem with elastic demand”Networks1257–72
8.
FangS, 1980, “Fixed point models for equilibrium problems on transportation networks” report 80–7, Department of Mathematics, University of Maryland, College Park, MD
9.
FiskCBoyceD, 1983, “Alternative variational inequality formulations of the network equilibrium-travel choice problem”Transportation Science17 (forthcoming)
10.
FiskCNguyenS, 1979, “Properties of the two mode equilibrium model with flow dependent transit costs” publication 121, Centre de Recherche sur les Transports, Université de Montréal, Montréal, Canada
11.
FiskCNguyenS, 1981, “Existence and uniqueness properties of an asymmetric two-mode equilibrium model”Transportation Science4318–328
12.
FiskCNguyenS, 1982, “Solution algorithms for network equilibrium models with asymmetric user costs”Transportation Science16361–381
13.
FiskCPittaMLinK T, 1982, “Network equilibrium with junction interactions: Model and solution methods” presented at the 1981 meeting of TIMS/ORSA, Detroit, MI; available from the author
14.
FlorianM, 1977, “A traffic equilibrium model of travel by car and public transit modes”Transportation Science11166–179
15.
FlorianMChapleauRNguyenSAchimCJames-LefebvreLGalarneauSLefebvreJFiskC, 1980, “Validation and application of EMME: An equilibrium based two-mode urban transportation planning method”Transportation Research Record72814–23
