An Algorithm for Traffic Equilibrium Flow with Capacity Constraints of Arcs
Zhi Lin

Abstract

In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equilibrium with capacity constraints of arcs.

Share and Cite:

Lin, Z. (2015) An Algorithm for Traffic Equilibrium Flow with Capacity Constraints of Arcs. Journal of Transportation Technologies, 5, 240-246. doi: 10.4236/jtts.2015.54022.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Wardrop, J. (1952) Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institute of Civil Engineers, Part II, 1, 325-378. http://dx.doi.org/10.1680/ipeds.1952.11362 [2] Beckmann, M.J., McGuire, C.B. and Winsten, C.B. (1956) Studies in the Economics of Transportation. Yale University Press, New Haven. [3] Chen, G.Y. and Yen, N.D. (1993) On the Variational Inequality Model for Network Equilibrium [Internal Report 3. 196 (724)]. Department of Mathematics, University of Pisa. [4] Lin, Z. (2010) The Study of Traffic Equilibrium Problems with Capacity Constraints of Arcs. Nonlinear Analysis: Real World Applications, 11, 2280-2284. http://dx.doi.org/10.1016/j.nonrwa.2009.07.002 [5] Lin, Z. (2010) On Existence of Vector Equilibrium Flows with Capacity Constraints of Arcs. Nonlinear Analysis, 72, 2076-2079. http://dx.doi.org/10.1016/j.na.2009.10.007 [6] Xu, Y.D. and Li, S.J. (2014) Vector Network Equilibrium Problems with Capacity Constraints of Arcs and Nonlinear Scalarization Methods. Applicable Analysis: An International Journal, 93, 2199-2210. http://dx.doi.org/10.1080/00036811.2013.875160 [7] Chiou, S.W. (2010) An Efficient Algorithm for Computing Traffic Equilibria Using TRANSYT Model. Applied Mathematical Modelling, 34, 3390-3399. http://dx.doi.org/10.1016/j.apm.2010.02.028 [8] Xu, M., Chen, A., Qu, Y. and Gao, Z. (2011) A Semismooth Newton Method for Traffic Equilibrium Problem with a General Nonadditive Route Cost. Applied Mathematical Modelling, 35, 3048-3062. http://dx.doi.org/10.1016/j.apm.2010.12.021 [9] Chen, A., Zhou, Z. and Xu, X.D. (2012) A Self-Adaptive Gradient Projection Algorithm for the Nonadditive Traffic Equilibrium Problem. Computers & Operations Research, 39, 127-138. http://dx.doi.org/10.1016/j.cor.2011.02.018