Abstract
We consider a traffic equilibrium problem in which each route has two attributes, time delay and monetary outlay, which are combined into a generalized time through a nonlinear relation. It is shown that this problem can be stated as a convex optimization model. Two simplicial decomposition type methods are proposed for its solution. The subproblem of these methods, which is a two-attribute shortest route problem, can be efficiently solved by the multi-labelling technique which has previously been applied to resource-constrained shortest path problems. Our numerical experiments show that both methods are feasible approaches to the equilibrium problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M.S. Bazaraa, H.D. Sherali and C.M. Shetty. Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New York, NY, 1993.
D. Bernstein and S.A. Gabriel. Solving the nonadditive traffic equilibrium. In P.M. Pardalos, D.W. Hearn, and W. Hager, editors, Network Optimization, volume 450 of Lecture Notes in Economics and Mathematical Systems, pages 72–102. Springer-Verlag, 1997.
J. Desrosiers, Y. Dumas, M.M. Solomon, and R. Soumis. Time constrained routing and scheduling. In M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser, editors, Handbook in Operations Research and Management Science, Network Models. North-Holland, 1995.
S.A. Gabriel and D. Bernstein. The traffic equilibrium problem with nonadditive path costs. Transportation Science, 31:337–348, 1997.
D.W. Hearn, S. Lawphongpanich, and J.A. Ventura. Restricted simplicial decomposition: Computation and extensions. Mathematical Programming Study, 31:99–118, 1987.
D.A. Hensher and T.P. Truong. Valuation of travel savings. Journal of Transport Economics and Policy, pages 237–260, 1985.
L. Hultkranz and R. Mortazavi. The value of travel time changes in a random nonlinear utility model. CTS working paper 1997:16., Submitted.
T. Larsson and M. Patriksson. Simplicial decomposition with disaggregated representation for the traffic assignment problem. Transportation Science, 26:4–17, 1992.
T. Larsson, M. Patriksson, and A-B. Strömberg. Ergodic, primal convergence in dual subgradient schemes for convex programming. Mathematical Programming, 86:283–312, 1999.
M. Patriksson. The Traffic Assignment Problem — Models and Methods. VSP, Utrecht, 1994.
Y. Sheffi. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Englewood Cliffs, NJ, 1985.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
Larsson, T., Lindberg, P.O., Patriksson, M., Rydergren, C. (2002). On Traffic Equilibrium Models with a Nonlinear Time/Money Relation. In: Patriksson, M., Labbé, M. (eds) Transportation Planning. Applied Optimization, vol 64. Springer, Boston, MA. https://doi.org/10.1007/0-306-48220-7_2
Download citation
DOI: https://doi.org/10.1007/0-306-48220-7_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-0546-6
Online ISBN: 978-0-306-48220-5
eBook Packages: Springer Book Archive