Complementarity formulations for the cell transmission model based dynamic user equilibrium with departure time choice, elastic demand and user heterogeneity

Transportation Research Part B: Methodological

Volumn 45, Issue 10, 2011, Pages 1749-1767

  Han, Lanshan ^a   Ukkusuri, Satish ^a   Doan, Kien ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Cell transmission model; Complementarity; Demand elasticity; Departure time; Heterogeneous users; User equilibrium

Indexed keywords

COMPUTATION THEORY; NUMERICAL ANALYSIS; TRANSPORTATION; TRAVEL TIME;

CELL TRANSMISSION MODEL; COMPLEMENTARITY; DEMAND ELASTICITIES; DEPARTURE TIME; HETEROGENEOUS USERS; USER EQUILIBRIUM;

TRAFFIC CONTROL;

DEMAND ELASTICITY; ESTIMATION METHOD; HETEROGENEITY; MODELING; TRANSPORTATION SYSTEM; TRAVEL TIME;

EID: 80455174682     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2011.07.007     Document Type: Article

References (30)

1. Arnott R., dePalma A., Lindsey R. A structural model of peak-period congestion: a traffic bottleneck with elastic demand. The American Economic Review 1993, 83(1):161-179.
2. Arnott R., dePalma A., Lindsey R. A welfare congestion tolls with heterogenous commuters. Journal of Transportation Economics and Policy 1994, 28(2):139-161.
3. Ban X.J., Liu H.X., Ferris M.C., Ran B. A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. Transportation Research Part B 2008, 42(9):823-842.
4. Carey M. Optimal time varying flows on congested network. Operation Research 1987, 35(1):58-69.
5. Carey M. Nonconvexity of the dynamic traffic assignment problem. Transportation Research Part B 1992, 26(2):127-133.
6. Carey M., Subrahmanian E. An approach to modeling time-varying flows on congested networks. Transportation Research Part B 2000, 34(3):157-183.
7. Cottle R.W., Pang J.S., Stone R.E. The linear complementarity problem 1992, Academic Press Inc, Boston, MA.
8. Daganzo C.F. The cell transmission model: a simple dynamic representation of highway traffic. Transportation Research Part B 1994, 28(4):269-287.
9. Daganzo C.F. The cell transmission model, part ii: network traffic. Transportation Research Part B 1995, 29(2):79-93.
10. Dirkse S.P., Ferris M.C. The path solver: a non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software 1995, 5(2):123-156.
11. Facchinei F., Pang JS. Finite-dimensional variational inequalities and complementarity problems 2003, Springer-Verlag, New York.
12. Filippov A.F. Differential Equations with Discontinuous Right-Hand Sides 1988, Kluwer Academic Publishers, Dordrecht.
13. Friesz T.L., Luque J., Tobin R.L., Wie B.W. Dynamic network traffic assignment considered as a continuous time optimal control problem. Operations Research 1989, 37(6):893-901.
14. Hendrickson C., Kocur G. Schedue delay and departure time decisions in a deterministic model. Transportation Science 1981, 15(1):62-77.
15. Lo H.K., Szeto W. A cell-based dynamic traffic assignment model-formulation and properties. Mathematical and Computer Modeling 2002, 35(7-8):849-865.
16. Lo H.K., Szeto W. A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transportation Research Part B 2002, 36(5):421-443.
17. Merchant D.K., Nemhauser G.L. A model and an algorithm for the dynamic traffic assignment problems. Transportation Science 1976, 12(3):183-199.
18. Newell G. The morning commute for nonidentical travellers. Transportation Science 1987, 21(2):74-88.
19. Peeta, S., 1994. System optimal dynamic traffic assignment in congested networks with advanced information system. PhD thesis, Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, Austin, TX.
20. Peeta S., Ziliaskopoulos A.K. Foundations of dynamic traffic assignment: the past, the present and the future. Network and Spatial Economics 2001, 1(3-4):233-265.
21. Ramadurai, G., 2009. Novel dynamic user equilibrium models: analytical formulations, multi-dimensional choice, and an efficient algorithm. PhD thesis, Department of Civil and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, NY.
22. Ramadurai, G., Ukkusuri, S.V., Han, L., Pang, J.S., 2009. Complementarity formulation for single link dynamic user equilibrium problem with cell transmission model of traffic flow. Manuscript.
23. Ramadurai G., Ukkusuri S.V., Zhao S., Pang J.S. Linear complementarity formulation for single bottleneck model with heterogeneous commuters. Transportation Research Part B 2010, 44(2):193-214.
24. Ran B., Boyce D.E., LeBlanc L.J. A new class of instantaneous dynamic user-optimal traffic assignment models. Operations Research 1993, 41(1):192-202.
25. Szeto W., Lo H.K. A cell-based simultaneous route and departure time choice model with elastic demand. Transportation Research Part B 2004, 38(7):593-612.
26. Ukkusuri S.V., Waller S.T. Linear programming models for the user optimal and system optimal network design problem: formulations, comparisons and extensions. Networks and Spatial Economics 2008, 8(4):383-406.
27. Verhoef E.T., Small K.A. Product differentiation on roads: constrained congestion pricing with heterogeneous users. Journal of Transport Economics and Policy 2004, 38(1):127-156.
28. Vickrey W.S. Congestion theory and transport investment. The American Economic Review 1969, 59(2):251-261.
29. Wu J.H., Chen Y., Florian M. The continuous dynamic network loading problem: a mathematical formulation and solution method. Transportation Research Part B 1998, 32(3):173-187.
30. Ziliaskopoulos A.K. A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transportation Science 2000, 34(1):37-49.