Flows over time with load-dependent transit times

SIAM Journal on Optimization

Volumn 15, Issue 4, 2005, Pages 1185-1202

  Köhler, Ekkehard ^a   Skutella, Martin ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Approximation algorithm; Congestion; Dynamic flow; Network flow; Traffic routing

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; POLYNOMIALS; ROUTERS; TELECOMMUNICATION TRAFFIC;

APPROXIMATION ALGORITHMS; CONGESTION; DYNAMIC FLOW; NETWORK FLOW; TRAFFIC ROUTING;

OPTIMIZATION;

EID: 27844611159     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623403432645     Document Type: Article

References (32)

1. R. K. AHUJA AND J. B. ORLIN, A capacity scaling algorithm for the constrained maximum flow problem, Networks, 25 (1995), pp. 89-98.
2. J. E. ARONSON, A survey of dynamic network flows, Ann. Oper. Res., 20 (1989), pp. 1-66.
3. M. BEN-AKIVA, H. KOUTSOPOULOS, R. MISHALANI, AND Q. YANG, Simulation laboratory for evaluating dynamic traffic management systems, ASCE Journal of Transportation Engineering, 123 (1997), pp. 283-289.
4. R. E. BURKARD, K. DLASKA, AND B. KLINZ, The quickest flow problem, Z. Oper. Res., 37 (1993), pp. 31-58.
5. M. CAREY, A constraint qualification for a dynamic traffic assignment model, Transportation Science, 20 (1986), pp. 55-58.
6. M. CAREY, Optimal time-varying flows on congested networks, Oper. Res., 35 (1987), pp. 58-69.
7. M. CAREY AND E. SUBRAHMANIAN, An approach to modelling time-varying flows on congested networks, Transportation Research B, 34 (2000), pp. 157-183.
8. H.-K. CHEN, Dynamic Travel Choice Models: A Variational Inequality Approach, Springer, Berlin, 1999.
9. H.-K. CHEN AND C.-F. HSUEH, A model and an algorithm for the dynamic user-optimal route choice problem, Transportation Research B, 32 (1998), pp. 219-234.
10. S. P. DIRKSE AND M. C. FERRIS, Traffic modeling and variational inequalities using GAMS, in Operations Research and Decision Aid Methodologies in Traffic and Transportation Management, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci. 166, P. L. Toint, M. Labbe, K. Tanczos, and G. Laporte, eds., Springer, Berlin, 1998, pp. 136-163.
11. L. FLEISCHER AND M. SKUTELLA, The quickest multicommodity flow problem, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 2337, W. J. Cook and A. S. Schulz, eds., Springer, Berlin, 2002, pp. 36-53.
12. L. FLEISCHER AND M. SKUTELLA, Minimum cost flows over time without intermediate storage, in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, 2003, pp. 66-75.
13. L. R. FORD AND D. R. FULKERSON, Constructing maximal dynamic flows from static flows, Oper. Res., 6 (1958), pp. 419-433.
14. L. R. FORD AND D. R. FULKERSON, Flows in Networks, Princeton University Press, Princeton, NJ, 1962.
15. T. L. FRIESZ, D. BERNSTEIN, T. E. SMITH, R. L. TOBIN, AND B. W. WIE, A variational inequality formulation of the dynamic network user equilibrium problem, Oper. Res., 41 (1993), pp. 179-191.
16. N. GARTNER, C. J. MESSER, AND A. K. RATHI, EDS., Traffic Flow Theory: A State of the Art Report, 1997, http://www.tfhrc.gov/its/tft/tft.htm.
17. A. HALL, S. HIPPLER, AND M. SKUTELLA, Multicommodity flows over time: Efficient algorithms and complexity, in Automata, Languages and Programming, Lecture Notes in Comput. Sci. 2719, J. C. M. Baeten, J. K. Lenstra, J. Parrow, and G. J. Woeginger, eds., Springer, Berlin, 2003, pp. 397-409.
18. A. HALL, K. LANGKAU, AND M. SKUTELLA, An FPTAS for quickest multicommodity flows with inflow-dependent transit times, in Approximation, Randomization, and Combinatorial Optimization, Lecture Notes in Comput. Sci. 2764, S. Arora, K. Jansen, J. D. P. Rolim, and A. Sahai, eds., Springer, Berlin, 2003, pp. 71-82.
19. H. W. HAMACHER AND S. A. TJANDRA, Mathematical modelling of evacuation problems: A state of the art, in Pedestrian and Evacuation Dynamics, M. Schreckenberg and S. D. Sharma, eds., Springer, Berlin, 2002, pp. 227-266.
20. B. HOPPE, Efficient Dynamic Network Flow Algorithms, Ph.D. thesis, Cornell University, Ithaca, NY, 1995.
21. B. HOPPE AND E. TARDOS, The quickest transshipment problem, Math. Oper. Res., 25 (2000), pp. 36-62.
22. B. KLINZ AND G. J. WOEGINGER, Minimum cost dynamic flows: The series-parallel case, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 920, E. Balas and J. Clausen, eds., Springer, Berlin, 1995, pp. 329-343.
23. E. KÖHLER, K. LANGKAU, AND M. SKUTELLA, Time-expanded graphs for flow-dependent transit times, in Algorithms - ESA '02, Lecture Notes in Comput. Sci. 2461, R. Möhring and R. Raman, eds., Springer, Berlin, 2002, pp. 599-611.
24. H. S. MAHMASSANI AND S. PEETA, System optimal dynamic assignment for electronic route guidance in a congested traffic network, in Urban Traffic Networks. Dynamic Flow Modelling and Control, N. H. Gartner and G. Improta, eds., Springer, Berlin, 1995, pp. 3-37.
25. N. MEGIDDO, Combinatorial optimization with rational objective functions, Math. Oper. Res., 4 (1979), pp. 414-424.
26. D. K. MERCHANT AND G. L. NEMHAUSER, A model and an algorithm for the dynamic traffic assignment problems, Transportation Science, 12 (1978), pp. 183-199.
27. D. K. MERCHANT AND G. L. NEMHAUSER, Optimality conditions for a dynamic traffic assignment model, Transportation Science, 12 (1978), pp. 200-207.
28. K. NAGEL, J. ESSER, AND M. RICKERT, Large-scale traffic simulations for transportation planning, in Annual Review of Computational Physics VII, D. Stauffer, ed., World Scientific, Singapore, 2000, pp. 151-202.
29. W. B. POWELL, P. JAILLET, AND A. ODONI, Stochastic and dynamic networks and routing, in Network Routing, Handbooks Oper. Res. Management Sci. 8, M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser, eds., North-Holland, Amsterdam, 1995, pp. 141-295.
30. I. PRIGOGINE AND R. HERMAN, Kinetic Theory of Vehicular Traffic, Elsevier Science B. V., Amsterdam, 1971.
31. B. RAN AND D. E. BOYCE, Modelling Dynamic Transportation Networks, Springer, Berlin, 1996.
32. Y. SHEFFI, Urban Transportation Networks, Prentice-Hall, Englewood Cliffs, NJ, 1985.