A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations

Transportation Research Part B: Methodological

Volumn 42, Issue 9, 2008, Pages 823-842

  Liu, Henry X ^b   Ferris, Michael C ^c   Ran, Bin ^d  

^a Jeff)   (United States)

^b UNIVERSITY OF MINNESOTA   (United States)

^c University of Wisconsin Madison   (United States)

^d University of Wisconsin Madison   (United States)

Author keywords

Dynamic network loading; Dynamic traffic assignment; Dynamic user equilibrium; Nonlinear complementarity problem

Indexed keywords

CONTINUOUS TIME SYSTEMS; CRACK PROPAGATION; TRAFFIC CONTROL; TRAVEL TIME;

COMPLEMENTARITY MODELS; CONTINUOUS TIME MODELING; CONTINUOUS-TIME DYNAMICS; DYNAMIC NETWORK LOADING; DYNAMIC TRAFFIC ASSIGNMENTS; DYNAMIC USER EQUILIBRIUM; MIXED COMPLEMENTARITIES; NON-LINEAR COMPLEMENTARITY PROBLEMS;

ITERATIVE METHODS;

ALGORITHM; DISCRETE CHOICE ANALYSIS; GENERAL EQUILIBRIUM ANALYSIS; NUMERICAL METHOD; TRAFFIC MANAGEMENT; TRAVEL TIME;

EID: 49049121397     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2008.01.006     Document Type: Article

References (44)

1. Akamatsu T. An efficient algorithm for dynamic traffic equilibrium assignment with queues. Transportation Science 35 4 (2001) 389-404
2. Astarita V. A continuous time link model for dynamic network loading based on ravel time function. In: Lesort J.-B. (Ed). Transportation and Traffic Theory (1996), Pergamon, Oxford 79-102
3. Ban, X., 2005. Quasi-variational inequality formulations and solution approaches for dynamic user equilibria. Ph.D. Thesis, University of Wisconsin-Madison.
4. Ban, X., Liu, H., Ferris, M.C., 2006a. A link-node based complementarity model and its solution algorithm for asymmetric user equilibria. In: Proceedings of the 85th Transportation Research Board Annual Meeting (CD-ROM).
5. Ban, X., Liu, H., Ferris, M.C., Ran, B., 2006b. A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. In: Proceedings of DTA 2006: The First International Symposium on Dynamic Traffic Assignment, Leeds, UK.
6. Bar-Gera, H., 1999. Origin-based algorithm for transportation network modeling. Ph.D. Thesis, University of Illinois at Chicago, Chicago, IL.
7. Billups S.C., Dirkse S.P., and Ferris M.C. A comparison of large scale mixed complementarity problem solvers. Computational Optimization and Applications 7 1 (1997) 3-25
8. Bliemer, M.C.J., 2001. Analytical dynamic traffic assignment with interacting user-classes: Theoretical advances and applications using a variational inequality approach. Ph.D. Thesis, Delft University of Technology, The Netherlands.
9. Bliemer M.C.J., and Bovy P.H.L. Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem. Transportation Research Part B 37 6 (2003) 501-519
10. Brooke, A., Kendrick, D., Meeraus, A., et al., 1998. GAMS, A User's Guide. GAMS Development Corporation.
11. Cao M., and Ferris M.C. A pivotal method for affine variational inequalities. Mathematics of Operations Research 21 1 (1996) 44-64
12. Carey M. Optimal time-varying flows on congested networks. Operations Research 35 1 (1987) 58-69
13. Carey M., and Ge Y.E. Efficient discretisation for link travel time models. Networks and Spatial Economics 4 3 (2004) 269-290
14. Carey M., and McCartney M. Behavior of a whole-link travel time model used in dynamic traffic assignment. Transportation Research Part B 36 1 (2002) 83-95
15. Carey M., Ge Y.E., and McCartney M. A whole-travel time model with desirable properties. Transportation Science 37 1 (2003) 83-96
16. Chen H.K. Dynamic Travel Choice Models (1999), Springer-Verlag, New York
17. Chen H.K., and Hsuen C.F. A model and an algorithm for the dynamic user-optimal route choice problem. Transportation Research Part B 32 3 (1998) 219-234
18. Dafermos S.C. Traffic equilibrium and variational inequality. Transportation Science 14 1 (1980) 42-54
19. Daganzo C.F. The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B 28 4 (1994) 269-287
20. Daganzo C.F. The cell transmission model part II: Network traffic. Transportation Research Part B 29 2 (1995) 79-93
21. Daganzo C.F. Properties of link travel time functions under dynamic loads. Transportation Research Part B 29 2 (1995) 95-98
22. Dirkse S.P., and Ferris M.C. The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software 5 2 (1995) 123-156
23. Facchinei F., and Pang J.S. Finite-Dimensional Variational Inequalities and Complementarity Problems vols. I and II (2003), Springer-Verlag, New York
24. Ferris, M.C., Munson, T.S., 1998. PATH 4.6 User Manual. University of Wisconsin-Madison.
25. Ferris M.C., Fourer R., and Gay D.M. Expressing complementarity problems and communicating them to solvers. SIAM Journal on Optimization 9 4 (1999) 991-1009
26. Friesz T.L., and Mookherjee R. Solving the dynamic network user equilibrium problem with state-dependent time shifts. Transportation Research Part B 40 3 (2006) 207-229
27. Friesz T.L., Bernstein D., Smith T.E., et al. A variational inequality formulation of the dynamic network user equilibrium problem. Operations Research 41 1 (1993) 179-191
28. Friesz T.L., Bernstein D., Suo Z., and Tobin R.L. Dynamic network user equilibrium with time-dependent time lags. Networks and Spatial Economics 1 3-4 (2001) 319-347
29. Han, S., 2000. Dynamic traffic assignment techniques for general road networks. Ph.D. Thesis, University of College London.
30. Han S. Dynamic traffic modeling and dynamic stochastic user equilibrium assignment for general road networks. Transportation Research Part B 37 3 (2003) 225-249
31. Han S., and Heydecker B.G. Consistent objectives and solution of dynamic user equilibrium models. Transportation Research Part B 40 1 (2006) 16-34
32. Heydecker, B.G., Verlander, N., 1999. Calculation of dynamic traffic equilibrium assignments. In: Proceedings of the European Transport Conferences, Seminar F, pp. 79-91.
33. Lo H., and Szeto W.Y. A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transportation Research Part B 36 5 (2002) 421-443
34. Lo H.K., Ran B., and Hongola B. Multiclass dynamic traffic assignment model: formulation and computational experiences. Transportation Research Record 1537 (1996) 74-82
35. Nie X.J., and Zhang H.M. Delay-function-based link models: their properties and computational issues. Transportation Research Part B 39 8 (2005) 729-751
36. Peeta S., and Ziliaskopoulos A.K. Foundations of dynamic traffic assignment: the past, the present and the future. Networks and Spatial Economics 1 3-4 (2001) 233-265
37. Ran B., and Boyce D.E. Dynamic urban transportation network models: theory and implications for intelligent vehicle highway systems. Lecture Notes in Economics and Mathematical Systems vol. 417 (1994), Springer-Verlag, New York
38. Ran B., and Boyce D.E. Modeling Dynamic Transportation Networks: An Intelligent Transportation Systems Oriented Approach. second revised ed. (1996), Springer-Verlag, New York
39. Ran B., Lo H., and Boyce D.E. A formulation and solution algorithm for a multi-class dynamic traffic assignment problem. In: Lesort J.-B. (Ed). Transportation and Traffic Theory (1996), Pergamon, Oxford 195-216
40. Smith M.J. The existence, uniqueness and stability of traffic equilibria. Transportation Research Part B 13 4 (1979) 295-304
41. Ulbrich, M., 2002. Nonsmooth Newton-like methods for variational inequalities and constrained optimization problems in function spaces. Ph.D. Thesis, Technische Universitat Munchen, Germany.
42. Wardrop, J.G., 1952. Some theoretical aspects of road traffic research. In: Proceedings of the Institution of Civil Engineers Part II (1), pp. 325-378.
43. Wie B.W., Tobin R.L., and Carey M. The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation. Transportation Research Part B 36 10 (2002) 897-918
44. Xu Y.W., Wu J.H., Florian M., Marcotte P., and Zhu D.L. Advances in the continuous dynamic network loading problem. Transportation Science 33 4 (1999) 341-353