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A cell-based dynamic traffic assignment model: Formulation and properties. (English) Zbl 1001.90016
Summary: This paper developed a cell-based dynamic traffic assignment formulation that follows the ideal Dynamic User Optimal (DUO) principle. Through defining an appropriate gap function, we transformed a formulation based on the nonlinear complementarity problem to an equivalent mathematical program. To improve the accuracy of dynamic traffic modelling, this formulation encapsulates a network version of the cell transmission model. We set up four scenarios to evaluate the properties of this formulation, in the aspects of traffic dynamics, traffic interactions across multiple links, and the ideal DUO principle. This formulation produced outputs that are in agreement with what the results ought to be. Namely, the formulation is able to capture dynamic traffic phenomena, such as shock-waves, queue formation, and dissipation. Moreover, it is capable of capturing dynamic traffic interactions across multiple links. Both of these characteristics are inherent from the underlying traffic model adopted in this formulation. The results also demonstrate that this cell-based formulation follows the ideal DUO principle.

90B20 Traffic problems in operations research
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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[1] Ran, B.; Boyce, D., ()
[2] Ran, B.; Lo, H.; Boyce, D., A formulation and solution algorithm for a multi-class dynamic traffic assignment problem, (), 195-216
[3] Lo, H.; Ran, B.; Hongola, B., A multi-class dynamic traffic assignment model: formulation and computational experiences, Transportation research record, 1537, 74-82, (1996)
[4] Lo, H., A dynamic traffic assignment formulation that encapsulates the cell-transmission model, (), 327-350
[5] Jayakrishnan, R.; Tsai, W.K.; Chen, A., A dynamic traffic assignment model with traffic flow relationship, Transportation research, 3C, 51-82, (1995)
[6] Janson, B., Dynamic traffic assignment with arrival time costs, Transportation research, 25B, 143-161, (1991)
[7] Friesz, T.; Bernstein, D.; Smith, T.; Tobin, R.; Wie, B., A variational inequality formulation of the dynamic network user equilibrium problem, Operations research, 41, 179-191, (1993) · Zbl 0771.90037
[8] Smith, M.J., A new dynamic traffic and the existence and calculation of dynamic user equilibria on congestion capacity-constrained road networks, Transportation research, 27B, 49-63, (1993)
[9] Wie, B.; Friesz, T.; Tobin, R., Dynamic user optimal traffic assignment on congestion multidestination networks, Transportation research, 24B, 431-442, (1990)
[10] Wardrop, J., Some theoretical aspects of road traffic research, (), 325-378
[11] Daganzo, C.F., The cell-transmission model: A simple dynamic representation of highway traffic, Transportation research, 28B, 4, 269-287, (1994)
[12] Daganzo, C.F., The cell-transmission model, part II: network traffic, Transportation research, 29B, 2, 79-93, (1995)
[13] Lighthill, M.J.; Whitham, J.B., On kinematic waves. I. flow movement in long rivers. II. A theory of traffic flow on long crowded road, Proceedings of royal society, A229, 281-345, (1955) · Zbl 0064.20906
[14] Richards, P.I., Shockwaves on the highway, Operations research, 4, 42-51, (1956)
[15] H. Lo and W.Y. Szeto, A cell-based variational inequality formulation of the dynamic user optimal assignment problem, Tranaportation Research B (to appear). · Zbl 1001.90016
[16] Daganzo, C.F., Fundamental of transportation and traffic operations, (1999), Elsevier Britain
[17] Aashtiani, H., The multi-modal traffic assignment problem, () · Zbl 0967.90500
[18] Kanzow, C.; Fukushima, M., Equivalence of the generalized complementarity problem to differentiable unconstrained minimization, Journal of optimization theory and applications, 90, 2, 581-603, (1996) · Zbl 0866.90124
[19] Facchinei, F.; Soares, J., Testing a new class of algorithms for nonlinear complementarity problems, () · Zbl 0849.90118
[20] Fischer, A., A special Newton-type optimization method, Optimization, 24, 269-284, (1992) · Zbl 0814.65063
[21] Lo, H.; Chen, A., Traffic equilibrium problem with route-specific costs: formulation and algorithms, Transportation research, 34B, 493-513, (2000)
[22] Facchinei, F.; Scares, J., A new merit function for nonlinear complementarity problems and a related algorithm, SIAM journal of optimization, 7, 1, 225-247, (1997) · Zbl 0873.90096
[23] Newell, G.F., A simplified theory of kinematic waves, () · Zbl 0258.60004
[24] Lo, H., A novel traffic control formulation, Transportation research, 33A, 433-448, (1999)
[25] Lo, H., A cell-based traffic control formulation: strategies and benefits of dynamic plans, Transportation science, 35, 2, 148-164, (2001) · Zbl 1069.90519
[26] Haupt, R.L.; Haupt, S.E., Practical genetic algorithms, (1998), Wiley New York · Zbl 0940.68107
[27] Lin, W.; Lo, H., Are the objectives and solutions of the dynamic user-equilibrium models always consistent?, Transportation research, 34A, 137-144, (2000)
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