Simplified dynamics and optimization of large scale traffic networks

Mathematical Models and Methods in Applied Sciences

Volumn 14, Issue 4, 2004, Pages 579-601

  Herty, Michael ^a   Klar, Axel ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Macroscopic equations; Optimization; Traffic flow

Indexed keywords

EID: 3242705378     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202504003362     Document Type: Article

References (30)

1. A. Aw and M. Rascle, Resurrection of second order models of traffic flow, SIAM J. Appl. Math. 60 (2000) 916-938.
2. C. Bardos, A. LeRoux and J. Nedelec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations 4 (1979) 1017-1034.
3. N. Bellomo, M. Delitala and V. Coscia, On the mathematical theory of vehicular traffic flow ifluid dynamic and kinetic modelling, Math. Mod. Meth. Appl. Sci. 12 (2002) 1801-1843.
4. M. Blinkin, Problem of optimal control of traffic flow on highways, Automation Remote Control 37 (1976) 662-667.
5. A. Bressan, Hyperbolic Systems of Conservation Laws (Oxford Univ. Press, 2000).
6. R. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput. 16 (1995) 1190-1208.
7. R. Byrd, J. Nocedal and R. Schnabel, Representations of quasi-Newton matrices and their use in limited memory methods, Math. Program. 63 (1994) 129-156.
8. G. Coclite and B. Piccoli, Traffic flow on a road network, to appear in SIAM J. Math. Anal.
9. R. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math. 63 (2002) 708-721.
10. C. M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl. 38 (1972) 33-41.
11. C. Daganzo, A continuum theory of traffic dynamics for freeways with special lanes, Transp. Res. B31 (1997) 83-102.
12. J. Greenberg, Extension and amplification of the Aw-Rascle model, SIAM J. Appl. Math. 62 (2001) 729-745.
13. J. Greenberg, A. Klar and M. Rascle, Congestion on multilane highways, SIAM J. Appl. Math. 63 (2003) 818-833.
14. M. Gugat, M. Herty, A. Klar and G. Leugering, Optimal control for traffic flow networks, preprint.
15. M. Günther, A. Klar, T. Materne and R. Wegener, Multivalued fundamental diagrams and stop and go waves for continuum traffic flow equations, to appear in SIAM J. Appl. Math.
16. D. Helbing, Improved fluid dynamic model for vehicular traffic, Phys. Rev. E51 (1995) 3164.
17. D. Helbing, Traffic and related self-driven many-particle systems, Rev. Mod. Phys. 73 (2001) 1067-1141.
18. M. Herty and A. Klar, Modelling and optimization of traffic flow networks, to appear in SIAM Sci. Comput. (2003).
19. H. Holden and N. Risebro, A mathematical model of traffic flow on a network of unidirectional road, SIAM J. Math. Anal. 4 (1995) 999-1017.
20. _, Front-Tracking for Hyperbolic Conservation Laws (Springer, 2002).
21. A. Klar, R. Kuehne and R. Wegener, Mathematical models for vehicular traffic, Surv. Math. Ind. 6 (1996) 215.
22. A. Klar and R. Wegener, Kinetic derivation of macroscopic anticipation models for vehicular traffic, SIAM J. Appl. Math. 60 (2000) 1749-1766.
23. A. Kotsialos, M. Papageorgiou, M. Mangeas and H. Haj-Salem, Coordinated and integrated control of motorway networks via non-linear optimal control, Transp. Res. Part C10 (2002) 65-84.
24. R. Kühne, Macroscopic freeway model for dense traffic, in 9th Int. Symp. on Transportation and Traffic Theory, ed. N. Vollmuller (VNU Science Press, Utrecht, 1984), pp. 21-42.
25. J. Lebacque and M. Khoshyaran, First order macroscopic traffic flow models for networks in the contex of dynamic assignment, in Transportation Planning-State of the Art, eds. M. Patriksson and K. A. P. M. Labbe, 2002.
26. M. Lighthill and J. Whitham, On kinematic waves, Proc. Royal Soc. Edinburgh A229 (1983) 281-345.
27. P. Nelson, A kinetic model of vehicular traffic and its associated bimodal equilibrium solutions, Transp. Theory Statist. Phys. 24 (1995) 383-408.
28. H. Payne, FREFLO: A macroscopic simulation model of freeway traffic, Transp. Res. Rec. 722 (1979) 68-75.
29. G. Whitham, Linear and Nonlinear Waves (Wiley, 1974).
30. C. Zhu, R. Byrd, J. Lu and J. Nocedal, L-bfgs-b: Fortran subroutines for large scale bound constrained optimization, Tech. Report, NAM-11, EECS Department, Northwestern University (1994).