Abstract
In this paper we present mathematical programming models for the problem of estimating a trip matrix from network data. The models presented are based on the results of Nguyen (1977) who has shown that trip matrices that reproduces observed linkflows in a congested network can be obtained by solving an elastic demand traffic assignment problem with a specific linear demand function.
It can be shown that this elastic traffic assignment problem has a unique optimal solution with respect to the linkflows but that the resulting trip matrix not necessarily is unique.
The mathematical programming models presented will deal with the problem of deriving one of the optimal trip matrices from Nguyens elastic demand traffic assignment problem.
Models with different choice criteria will be discussed and solution methods based on decomposition techniques will be presented for the various models.
The presented models will all be examples of implicit optimization models, i.e. optimization models in which the constraints involve another optimization model.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Beckman M, McGuire, C B, Winsten, C (1956), Studies in the economics of transportation, Yale Univ. Press, New Haven, Conn.
Brenninger-Göthe, M, Jörnsten, K O (1983), A note on a cutting plane algorithm for estimating a trip matrix from network data, Linköping Institute of Technology, Report LiTH-MAT-R-83-14.
Brenninger-Göthe, M, Jörnsten, K O, (1985), A bicriterion model for estimation of a trip matrix from network data, Linköping Institute of Technology, Report (forthcoming).
Brenninger-Göthe, M, Larsson, T (1985), A note on the traffic equilibrium problem, Linköping Institute of Technology, Report (forthcoming).
Erlander, S (1980), Optimal spatial interaction and the gravity model, Lecture Notes in Economics and Mathematical Systems, 173, Springer-Verlag, Berlin, Heidelberg, New York.
Evans, S P (1976), Derivation and analysis of some models for combining trip distribution and assignment, Transportation Research, Vol 10, 37–57.
Florian, M, Nguyen, S, Ferland, J (1975), On the combined distribution-assignment of traffic, Transportation Science, Vol. 9, 43–53.
Florian, M, Nguyen, S (1977), A method for computing network equilibrium with elastic demands, Transportation Science 11, 166–179.
Gartner, G H (1980), Optimal traffic assignment with elastic demands: A Review, Part I. Analysis Framework, Part II. Algorithmic Approaches, Transportation Science Vol. 14, 174–208.
Jörnsten, K O, Nguyen, S (1979), On the estimation of a trip matrix from network data, Linköping Institute of Technology, Report LiTH-MAT-R-79-36.
Jörnsten, K O, Nguyen, S (1983), Estimation of an trip matrix from network data; dual approaches, Linköping Institute of Technology, Report LiTH-MAT-R-83-10.
LeBlanc, L J, Farhangian, K (1982), Selection of a trip table which reproduces observed link flows. Transportation Research, Vol. 16B, 83–88.
Nguyen, S (1976), Procedures for equilibrium traffic assignment with elastic demand, Centre de Recerche sur les Transport, Université de Montréal, Publication No. 39.
Nguyen, S (1977), Estimating an OD-matrix from network data. A network equilibrium approach, Centre de Recherche sur les Transport, Université de Montréal, Publication No. 60.
Snickars, F, Weibull, J W (1977), A minimum information principle, theory and practice, Regional Science and Urban Economics 7, 137–168.
Tanner, J C (1961), Factors affecting the amount of travel, Road Research Technical Paper 51, HMSO, London.
Turnquist, M Gur, Y (1979), Estimation of trip tables from observed volumes, Proceeding 58th annual meeting of the Transportation Research Board.
Wardrop, J G (1952), Some theoretical aspects of road traffic research, Proc. Inst. of Civil Eng. Part II, 325–378.
Wilson, A G (1970), Entropy in urban and regional modelling, Pion, London.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Brenninger-Göthe, M., Jörnsten, K. (1986). Models and methods for estimating an origin-destination trip matrix from network data. In: Prékopa, A., Szelezsáan, J., Strazicky, B. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 84. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043830
Download citation
DOI: https://doi.org/10.1007/BFb0043830
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16854-6
Online ISBN: 978-3-540-47138-7
eBook Packages: Springer Book Archive