zbMATH — the first resource for mathematics

A combinatorial user optimal dynamic traffic assignment algorithm. (English) Zbl 1156.90324
Summary: This paper introduces a polynomial combinatorial optimization algorithm for the dynamic user optimal problem. The approach can efficiently solve single destination networks and can be potentially extended to heuristically solve multidestinational networks. In the model, traffic is propagated according to sound traffic flow theoretical models rather than link exit functions; thereby allowing link queue evolution to be modeled more precisely. The algorithm is designed, proven, implemented and computationally tested.

90B20 Traffic problems in operations research
90B80 Discrete location and assignment
Full Text: DOI
[1] Boyce, D., D.-H. Lee, and B. Janson. (1996). ”A Variational Inequality Model of an Ideal Dynamic User-Optimal Route Choice Problem.” Presented at the 4th Meeting of the EURO Working Group on Transportation, Newcastle, UK.
[2] Carey, M. (1986). ”A Constraint Qualification for a Dynamic Traffic Assignment Model.” Transportation Science 20, 55–88.
[3] Carey, M. (1987). ”Optimal Time-Varying Flows on Congested Networks.” Operations Research, 35, 58–69. · Zbl 0629.90033
[4] Carey, M. (1992). ”Nonconvexity of the Dynamic Traffic Assignment Problem.” Transportation Research, 26B, 127–133.
[5] Daganzo, C. (1994). ”The Cell Transmission Model: A Simple Dynamic Representation of Highway Traffic Consistent with the Hydrodynamic Theory.” Transportation Research 28B(4), 269–287.
[6] Daganzo, C. (1995). ”The Cell Transmission Model, Part II: Network Traffic.” Transportation Research 29B(2), 79–93.
[7] Friesz, T., et al. (1989). ”Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem.” Operations Research 37, 893–901. · Zbl 0691.49029
[8] Friesz, T., et al. (1993). ”A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem.” Operations Research 41, 179–191. · Zbl 0771.90037
[9] Janson, B. (1992). ”Dynamic Traffic Assignment for Urban Networks.” Transportation Research 25B, 143–161.
[10] Lee, D.-H. (1996). ”Formulation and Solution of a Dynamic User-Optimal Route Choice Model on a Large-Scale Traffic Network.” Ph.D. Thesis in Civil Engineering, University of Illinois, Chicago.
[11] Merchant, D.K., and G. Nemhauser. (1978a). ”A Model and an Algorithm for the Dynamic Traffic Assignment Problem.” Transportation Science 12, 183–199.
[12] Merchant, D.K. and G. Nemhauser. (1978b). ”Optimality Conditions for a Dynamic Traffic Assignment Model.” Transportation Science, 12 (1978b) 200–207.
[13] Sheffi, Y. (1984). Urban Transportation Networks: Equilibirum Analysis with Mathematical Progeamming Methoods. Prentice-Hall, Englewood Cliffs, N.J.
[14] Smith, M. (1993). ”A New Dynamic Traffic Model and the Existence and Calculation of Dynamic user Equilibria on Congested Capacity-Constrained Road Networks.” Transportation Research 27B, 49–63.
[15] Waller, S.T. and A. Ziliaskopoulos. (2001). ”A Dynamic and Stochastic Approach to Network Design.” Journal of the Transportation Research Board No. 1771, pp. 106–114.
[16] Wie, B.-W. (1995). ”Discrete Time, Nested Cost Operator AApproach to the Dynamic Network User Equilibrium Problem.” Transportation Science 28, 79–92. · Zbl 0826.90050
[17] Ziliaskopoulos A. (2001). ”A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem.” Transportation Science 34, 37–49. · Zbl 1002.90013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.