Minimising stop and go waves to optimise traffic flow

Applied Mathematics Letters

Volumn 17, Issue 6, 2004, Pages 697-701

  Colombo, R M ^a   Groli, A ^a  

^a UNIVERSITY OF BRESCIA   (Italy)

Author keywords

Conservation laws; Optimal control of PDE; Traffic flow

Indexed keywords

CALCULATIONS;

CALCULUS OF VARIATIONS; CONSERVATION LAW; EXISTENCE RESULTS; HYPERBOLIC CONSERVATION LAWS; NONSTANDARD PROBLEMS; OPTIMAL CONTROLS; STOP-AND-GO WAVES; TRAFFIC FLOW;

PHYSICAL PROPERTIES;

EID: 20744442189     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(04)90107-3     Document Type: Article

References (22)

1. M.J. Lighthill and G.B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Set. A. 229, 317-345, (1955).
2. P.I. Richards, Shock waves on the highway, Operations Res. 4, 42-51, (1956).
3. A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math. 60 (3), 916-938 (electronic), (2000).
4. S. Benzoni Garage and R.M. Colombo, An n-populations model for traffic flow, Europ. J. Appl. Math. (to appear).
5. R.M. Colombo, A 2 x 2 hyperbolic traffic flow model, Mathl. Comput. Modelling 35 (5/6), 683-688, (2002).
6. R.M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM Y. Appl. Math. 63 (2), 708-721, (2002).
7. A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford University Press, (2000).
8. D. Amadori and R.M. Colombo, Continuous dependence for 2 x 2 conservation laws with boundary, J. Differential Equations 138 (2), 229-266, (1997). (Pubitemid 127341163)
9. ∞ solutions for Temple class systems with boundary and properties of the attainable sets, SIAM J. Math. Anal. 34 (1), 28-63, (2002). (Pubitemid 36256579)
10. R.M. Colombo and A. Groli, On the initial boundary value problem for Temple systems, (Preprint), (2003).
11. A. Klar, Kinetic and Macroscopic Traffic Flow Models, School of Computational Mathematics: Computational Aspects in Kinetic Models, XX Edition, (2002).
12. B.S. Kerner and P. Konhäuser, Cluster effect in initially homogenous traffic flow, Physical Review E 48 (4), (1993).
13. E. Tomer, L. Safonov, N. Madar and S. Havlin, Optimization of congested traffic by controlling stop-and-go waves, Phys. Rev. E (3) 65 (6), 065101, 4, (2002).
14. W. Rudin, Real and Complex Analysis, Second Edition, McGraw-Hill, New York, (1974).
15. F. Ancona and G.M. Coclite, On the attainable set for Temple class systems with boundary, Technical Report 10/2002/M, SISSA, (February 2002).
16. F. Ancona and A. Marson, On the attainable set for scalar nonlinear conservation laws with boundary control, SIAM J. Control Optimization 36 (1), 290-312, (1998). (Pubitemid 128575642)
17. R.M. Colombo and A. Groli, On the optimization of a conservation law, Calc. Vat. Partial Differential Equations 19 (3), 269-280, (2004). (Pubitemid 38214276)
18. S. Bianchini, On the shift differentiability of the flow generated by a hyperbolic system of conservation laws, Discrete Contin. Dynam. Systems 6 (2), 329-350, (2000).
19. A. Bressan and G. Guerra, Shift-differentiability of the ftow generated by a conservation law, Discrete Contin. Dynam. Systems 3 (1), 35-58, (1997). (Pubitemid 127531874)
20. S. Bianchini, The semigroup generated by a Temple class system with non-convex flux function, Differential Integral Equations 13 (10-12), 1529-1550, (2000).
21. S. Bianchini and A. Bressan, Vanishing viscosity solutions of nonlinear hyperbolic systems, Annals of Mathematics (to appear).
22. R.M. Colombo and F.S. Priuli, Global well posedness of a traffic flow model with phase transitions, (Preprint), (2003).