The European Physical Journal B

, Volume 70, Issue 2, pp 257–274 | Cite as

Operation regimes and slower-is-faster effect in the controlof traffic intersections

  • D. HelbingEmail author
  • A. Mazloumian
Interdisciplinary Physics


The efficiency of traffic flows in urban areas is known to crucially depend on signal operation. Here, elements of signal control are discussed, based on the minimization of overall travel times or vehicle queues. Interestingly, we find different operation regimes, some of which involve a “slower-is-faster effect”, where a delayed switching reduces the average travel times. These operation regimes characterize different ways of organizing traffic flows in urban road networks. Besides the optimize-one-phase approach, we discuss the procedure and advantages of optimizing multiple phases as well. To improve the service of vehicle platoons and support the self-organization of “green waves”, it is proposed to consider the price of stopping newly arriving vehicles.


89.40.Bb Land transportation Control theory and feedback 47.85.L- Flow control 


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  1. O. Biham, A.A. Middleton, D. Levine, Phys. Rev. A 46, R6124 (1992)Google Scholar
  2. T. Nagatani, Phys. Rev. E 48, 3290 (1993)Google Scholar
  3. J. Esser, M. Schreckenberg, Int. J. Mod. Phys. B 8, 1025 (1997)Google Scholar
  4. P.M. Simon, K. Nagel, Phys. Rev. E 58, 1286 (1998)Google Scholar
  5. D. Chowdhury, A. Schadschneider, Phys. Rev. E 59, R1311 (1999)Google Scholar
  6. E. Brockfeld, R. Barlovic, A. Schadschneider, M. Schreckenberg, Phys. Rev. E 64, 056132 (2001)Google Scholar
  7. M. Fouladvand, M. Nematollahi, Eur. Phys. J. B 22, 395 (2001)Google Scholar
  8. M. Sasaki, T. Nagatani, Phys. Stat. Mech. Appl. 325, 531 (2003)Google Scholar
  9. B.A. Toledo, V. Munoz, J. Rogan, C. Tenreiro, J.A. Valdivia, Phys. Rev. E 70, 016107 (2004)Google Scholar
  10. T. Nagatani, Phys. Stat. Mech. Appl. 368, 560 (2006)Google Scholar
  11. M. Garavello, B. Piccoli, Discrete Contin. Dyn. Syst. B 5, 599 (2005)Google Scholar
  12. R. Barlovic, T. Huisinga, A. Schadschneider, M. Schreckenberg, Adaptive traffic light control in the ChSch model for city traffic, in Traffic and Granular Flow’03, edited by P.H.L. Bovy, S.P. Hoogendoorn, M. Schreckenberg, D.E. Wolf (Springer, Berlin, 2004)Google Scholar
  13. M.E. Fouladvand, Z. Sadjadi, M.R. Shaebani, J. Phys. A 37, 561 (2004)Google Scholar
  14. M.E. Fouladvand, M.R. Shaebani, Z. Sadjadi, J. Phys. Society Jpn 73, 3209 (2004)Google Scholar
  15. B. Faieta, B.A. Huberman, Firefly: A synchronization strategy for urban traffic control, Internal Report No. SSL-42 (Xerox PARC, Palo Alto, CA, 1993)Google Scholar
  16. D.-W. Huang, W.-N. Huang, Phys. Rev. E 67, 056124 (2003)Google Scholar
  17. S. Lämmer, H. Kori, K. Peters, D. Helbing, Physica A 363, 39 (2006)Google Scholar
  18. T. Nakatsuji, S. Seki, T. Kaku, Transport. Res. Rec. 1324, 137 (1995)Google Scholar
  19. K. Sekiyama, J. Nakanishi, I. Takagawa, T. Higashi, T. Fukuda, IEEE Int. Conf. Syst. Man. Cybern. 4, 2481 (2001)Google Scholar
  20. D. Helbing, R. Jiang, M. Treiber, Phys. Rev. E 72, 046130 (2005); R. Jiang, D. Helbing, P.K. Shukla, Q.-S. Wu, Physica A 368, 567 (2006)Google Scholar
  21. C. Gershenson, Complex Syst. 16, 29 (2005)Google Scholar
  22. S.-B. Cools, C. Gershenson, B. D’Hooghe, Self-organizing traffic lights: A realistic simulation, Advances in Applied Self-Organizing Systems, edited by M. Prokopenko (Springer, New York, 2007)Google Scholar
  23. D. Helbing, S. Lämmer, J.-P. Lebacque, Self-organized control of irregular or perturbed network traffic, in Optimal Control and Dynamic Games, edited by C. Deissenberg, R.F. Hartl (Springer, Dordrecht, 2005), pp. 239–274Google Scholar
  24. D. Helbing, J. Siegmeier, S. Lämmer, NHM 2, 193 (2007)Google Scholar
  25. S. Lämmer, D. Helbing, J. Stat. Mech. (JSTAT) P04019 (2008)Google Scholar
  26. S. Lämmer, Reglerentwurf zur dezentralen Online-Steuerung von Lichtsignalanlagen in Straßennetzwerken, Controller design for a decentralized control of traffic lights in urban road networks, Ph.D. thesis, Dresden University of Technology, 2007Google Scholar
  27. D. Schrank, T. Lomax, The 2005 Urban Mobility Report (Texas Transportation Institute, 2005)Google Scholar
  28. D. Helbing, Eur. Phys. J. B (2009),DOI: 10.1140/epjb/e2009-00093-7Google Scholar
  29. M. Schönhof, M. Treiber, A. Kesting, D. Helbing, Transp. Res. Rec. 1999, 3 (2007)Google Scholar
  30. A. Kesting, M. Treiber, M. Schönhof, D. Helbing, Transp. Res. Rec. 2000, 16 (2007)Google Scholar
  31. D. Braess, Unternehmensforsch. 12, 258 (1968)Google Scholar
  32. R. Steinberg, R.E. Stone, Transp. Sci. 22, 231 (1988)Google Scholar
  33. T. Roughgarden, Selfish Routing and the Price of Anarchy. (MIT Press, 2005)Google Scholar
  34. D. Helbing, I. Farkas, T. Vicsek, Nature 407, 487 (2000)Google Scholar
  35. R.J. Smeed, Transp. Sci. 1, 308 (1967)Google Scholar
  36. M. Ben-Akiva, A. de Palma, Transp. Sci. 20, 52 (1986)Google Scholar
  37. R.B. Cooper, S.-C. Niu, M.M. Srinivasan, Manag. Sci. 44, 1079 (2000)Google Scholar
  38. D. Helbing, S. Lämmer, Verfahren zur Koordination konkurrierender Prozesse oder zur Steuerung des Transports von mobilen Einheiten innerhalb eines Netzwerkes. Method for coordination of concurrent processes for control of the transport of mobile units within a network. Patent WO/2006/122528 (2006)Google Scholar
  39. D. Helbing, T. Seidel, S. Lämmer, K. Peters Self-organization principles in supply networks and production systems, in Econophysics and Sociophysics – Trends and Perspectives, edited by B.K. Chakrabarti, A. Chakraborti, A. Chatterjee (Wiley, Weinheim, 2006), pp. 535–558Google Scholar
  40. D. Helbing, R. Jiang, M. Treiber, Phys. Rev. E 72, 046130 (2005)Google Scholar
  41. D. Helbing, A. Johansson, J. Mathiesen, M.H. Jensen, A. Hansen, Phys. Rev. Lett. 97, 168001 (2006)Google Scholar
  42. H.-U. Stark, C.J. Tessone, F. Schweitzer, Adv. Complex Syst. 11, 551 (2008)Google Scholar
  43. S. Lämmer, R. Donner, D. Helbing, Eur. Phys. J. B 63, 341 (2008)Google Scholar
  44. D. Helbing, J. Phys. Math. Gen. 36, L593 (2003)Google Scholar
  45. D. Helbing, Production, supply, and traffic systems: A unified description, in Traffic and Granular Flow ’03 edited by S.P. Hoogendoorn, S. Luding, P.H.L. Bovy, M. Schreckenberg, D.E. Wolf (Springer, Berlin, 2005), pp. 173–188Google Scholar
  46. C.H. Papadimitriou, J.N. Tsitsiklis, Math. Oper. Res. 24, 293 (1999)Google Scholar
  47. G. Feichtinger, R.F. Hartl, Optimale Kontrolle ökonomischer Prozesse. Optimal Control of Economic Processes (de Gruyter, Berlin, 1986)Google Scholar
  48. C. Chase, P.J. Ramadge, IEEE Trans. Autom. Contr. 37, 491 (1992)Google Scholar
  49. J. Kennedy, R. Eberhart, Particle swarm optimization, in: Proceedings of the IEEE International Conference on Neural Networks (Perth, WA, Australia, 1995), Vol. 4, pp. 1942–1948Google Scholar
  50. G.B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.ETH Zurich, UNO D11, Universitätstr. 41ZurichSwitzerland

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