Mathematical Programming Methods for Urban Network Control

  • G. Improta
Conference paper
Part of the NATO ASI Series book series (volume 38)


The history of traffic light control (Webster and Cobbe 1966, Gazis 1974, Strobel 1982) began on December 1868 when the first traffic signal was installed in Westminster, London, in front of the Houses of Parliament.


Cycle Time Traffic Flow Traffic Control Traffic Signal Traffic Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allsop, R.E. (1968). Choice of Offsets in Linking Traffic Signals. Traff. Engng & Con., 9, 73–75.Google Scholar
  2. Allsop, R.E. (1969). An Analysis of Delays to Vehicle Platoons at Traffic Signals. Fourth Int. Symp. on Theory of Traffic Flow, Karlsruhe, June 1968. Strassenbau und Strassenverkehrstechnik, 86, 98–104.Google Scholar
  3. Allsop, R.E. (1971). Delay Minimizing Setting for Fixed Time Traffic Signals at a Single Road Junction. J. Inst. Maths Applics, 8, 164–185.MathSciNetCrossRefGoogle Scholar
  4. Allsop, R.E. (1972). Estimating the Traffic Capacity of a Signalized Road Junction. Transpn Res., 6, 345–355.CrossRefGoogle Scholar
  5. Allsop, R.E. (1974). Some Possibilities for Using Traffic Control to Influence Trip Destination and Route Choice. Transportation and Traffic Theory. Proc. Sixth Int. Symp. on Transportation and Traffic Theory, Elsevier, Amsterdam, 345–374.Google Scholar
  6. Allsop, R.E. (1983). Optimization of Timings of Traffic Signals. Proc. 1983 AIRO Conf. Guida Editori, Napoli, 103–120.Google Scholar
  7. Allsop, R.E. and Charlesworth, J.A. (1977). Traffic in a Signal Controlled Road Network: An Example of Different Signal Timings Inducing Different Routing. Traff. Engng & Con., 18, 262–264.Google Scholar
  8. Beckman, M.J., Mcguire, C.B. and Winsten, C.B. (1956). Studies in the Economics of Trasportation. Yale University Press, New Haven, CT.Google Scholar
  9. Boyce, D.E., Janson B.N. and Eash R.W. (1981). The Effect on Equilibrium Trip Assignment of Different Link Congestion Functions. Transpn Res., 15A, 223–232.Google Scholar
  10. Branston, D. (1976). Link Capacity Functions: A Review. Transpn Res., 10, 223–236.CrossRefGoogle Scholar
  11. Cantarella, G.E. and Improta, G. (1981). Una Metodologia per il Progetto Globale di Intersezioni Semaforizzate. Atti delle Giornate di lavoro AIRO 1981, Torino, 33–48.Google Scholar
  12. Cantarella, G.E. and Sforza, A. (1986). Methods for Equilibrium Network Traffic Signal Setting. To appear in Proc. of Advanced Workshop on: Flow Control of Congested Networks (A. Odoni, G. Szego eds.). Capri, October 12–18, 1986.Google Scholar
  13. Cantarella, G.E. and Improta, G. (1987). Capacity Factor and Cycle Time Optimization: A Graph Theory Approach, Transpn Res., B, (to appear).Google Scholar
  14. (1986).
    Cantarella, G.E., Cosentino, M., Improta, G., Sforza, A. . Equilibrium Network Control System Design. Preprints 5th IFAC — IFIP — IFORS Int. Conf. on Control in Transportation Systems,Uien, 8–11 July, 1986, 395–403.Google Scholar
  15. Cantarella, G.E., Improta, G., Sforza, A., Sorrentini, M.C. (1983). Flow Equilibrium for a Signalized Urban Network. An Application. Proc. 1983 AIRO Conf. Guida Editori Napoli, 821–845.Google Scholar
  16. Catling, I. (1977). Development of Junction Delay Formulae. LTR 1. Working Paper 2.Google Scholar
  17. Charlesworth, J.A. (1975). Relations between Travel-Time and Traffic Flow for the Links of Road Networks Controlled by Fixed-Time Signals. Univ. of Newcastle upon Tyne. Transport Oper. Res. Group, Research Report n. 13.Google Scholar
  18. Charlesworth, J.A. (1977). Mutually Consistent Traffic Assignment and Signal Timings for a Signal-Controlled Road Network. Univ. of Newcastle upon Tyne. Transport Oper. Res. Group, Working Paper n. 24.Google Scholar
  19. Dafermos, S.C. (1971). An Extended Traffic Assignment Model with Applications to Two-Way Traffic. Transpn Sci., 5, 366–389.CrossRefGoogle Scholar
  20. Dafermos, S.C. (1980). Traffic Equilibrium and Variational Inequalities Transpn Sci., 14, 42–54.MathSciNetGoogle Scholar
  21. Dickson, T.J. (1981). A Note on Traffic Assignment and Signal Timings in a Signal Controlled road network. Transpn Res., 15B, 267–271.Google Scholar
  22. Gallivan, S. (1984). Flow Profiles in Coordinated Networks. Advanced Course on Optimization for Traffic Engineering and Control. AIRO, P.F.T.-C.N.R., Capri October 18–25, 1984.Google Scholar
  23. Gallivan, S. and Heydecker, B.G. (1983). Optimising the Control Performance of Traffic Signals at a Single Junction. 15th Ann. Conf. Universities Transport Study Group, Imperial Coll. London (unpublished).Google Scholar
  24. Gartner, N.H. (1972a). Constraining Relations among Offsets in Synchronized Networks. Transpn Sci., 6, 88–93.CrossRefGoogle Scholar
  25. Gartner, N.H. (1972b). Optimal Synchronization of Traffic Signal Networks by Dynamic Programming. Proc. 5th. Int. Symp. on Theory of Traffic Flow and Transportation. (Ed. G.F. Newell). American Elsevier, New York, 281–295.Google Scholar
  26. Gartner, N.H. (1973). Microscopic Analysis of Traffic Flow Patterns for Minimizing Delay on Signal-Controlled Links. HRB Record, 445, 13–15.Google Scholar
  27. Gartner, N.H. (1976) in Area Traffic Control and Network Equilibrium. Traffic Equilibrium Methods (Ed. M. Florian). Springer-Verlag, Berlin, 274–297.Google Scholar
  28. Gartner, N.H. and Gershwin, S.B. (1983). Analitycal Models for Transportation System Management. Proc. 1983 AIRO Conf. Guida Editori Napoli, 793–804.Google Scholar
  29. Gartner, N.H. and Little, J.D.C. (1975). Generalized Combination Method for Area Traffic Control. Transpn Res. Rec., 531, 58–59.Google Scholar
  30. Gartner, N.H., Little, J.D.C., and Gabbay, H. (1975). Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming. Part I: The Network Coordination Problem; Part II: The Network Synchronization Problem, Transpn Sci., 9, 321–363.Google Scholar
  31. Gartner, N.H., Little, J.D.C. and Gabbay, H. (1976). Simultaneous Optimization of Offsets, Splits and Cycle Time. Transpn Res. Rec., 596, 6–15.Google Scholar
  32. Gartner, N.H., Gershwin, S.B., Little, J.D.C. and Ross, P. (1980). Pilot Study of Coraputer-Based Urban Traffic Management. Transpn Res., 14B, 203–217.Google Scholar
  33. Gazis, D.C. (1974). Traffic Science. Wiley., New York, USA.MATHGoogle Scholar
  34. Heydecker, B.G. (1983). Some Consequence of Detailed Junction Modeling in Road Traffic Assignment. Transpn Sci., 17, 263–281.CrossRefGoogle Scholar
  35. Heydecker, B.G. and Dudgeon, I.U. (1987). Calculation of Signal Settings to Minimize Delay at a Junction. To be published on Proc. Thenth Int. Symp. on Transportation and Traffic Theory. Cambridge Mass. July 8–10th 1987.Google Scholar
  36. HCM (1985). Highway Capacity Manual. Transportation Research Board., National Research Council Special Report 209.Google Scholar
  37. Hillier, J.A. (1966). Appendix to Glasgow’s Experiment in Area Traffic Control. Traff. Engng & Con., 7, 569–571.Google Scholar
  38. Hutchinson, T.P. (1972). Delay at a Fixed Time Traffic Signal -II: Numerical Comparisons of Some Theoretical Expressions. Transpn Sci., 6, 286–305.CrossRefGoogle Scholar
  39. Huddart, K.W. and Turner, E.D. (1969). Traffic Signal Progerssion G.L.C. Combination Method. Traff. Engng & Con., 11, 320–327Google Scholar
  40. Improta, G. (1978). Un Contributo sul Problema della Capacita’ per le Intersezioni a Raso Semaforizzate con Sistema Fixed-Time. Atti del XVIII Cong.Naz. Stradale, Taormina, Italy, 349–356.Google Scholar
  41. Improta, G. (1985). Traffic Engineering and Perspectives of Transportation Planning in the Region of Naples. The Practice of Trasportation Planning (Ed. M. Florian). Elsevier Science Publishers, Amsterdam, 161–209.Google Scholar
  42. Improta, G., Allsop, R.E. and Heydecker, B.G. (1986). Network Models for Traffic Management. To be published on Proc. of “The Management and Planning of Urban Transport Systems from Theory to Practice” on International Seminar Montreal, august 25–29, 1986, (Ed. M. Florian).Google Scholar
  43. Improta, G. and Cantarella, G.E. (1982). Signalized Junction Control System Design. EURO — TIMS XXV, Lausanne, july 1982 (unpublished).Google Scholar
  44. Improta, G. and Cantarella, G.E. (1984). Control System Design for an Individual Signalized Junction. Transpn Res., 18B, 147–167.MathSciNetGoogle Scholar
  45. Improta, G. and Sforza, A. (1982). Optimal Offsets for Traffic Signal Systems in Urban Networks. Transpn Res., 16B, 143–161.Google Scholar
  46. Little, J.D.C. (1966). The Synchronization of Traffic Signals by Mixed-Integer Linear Programming. Opns Res., 14, 568–594.MATHCrossRefGoogle Scholar
  47. Little, J.D.C., Martin, B.V., Morgan, J.T. (1966). Synchronizing Traffic Signals for Maximal Bandwidth. Highway Res. Rec. 118, 21–45.Google Scholar
  48. Little, J.D.C., Kelson, M.D., Gartner, N.H.(1981). MAXBAND: A Program for Setting Signals on Arteries and Triangular Networks. Transpn Res. Rec., 795, 40–46.Google Scholar
  49. Marcotte, P. (1983). Network Optimization with Continuous Control Parameters. Transpn Sci., 17, 181–197.CrossRefGoogle Scholar
  50. Moller, K. (1987). Calculation of Optimum Fixed-Time Signal Programs. To be published on Proc. Thenth Int. Symp. on Transportation and Traffic Theory. Cambridge Mass. July 8–10th 1987.Google Scholar
  51. Morton, G. (1985). The TRANSYT and SCOOT Methods of Traffic Control. Based on presentations given by D.I. Robertson. Advanced Course on Optimization for Traffic Engineering and Control. Capri, 18–25 October 1984.Google Scholar
  52. Nguyen S. (1976). A Unified Approach to Equilibrium Methods for Traffic Assignment. Traffic Equilibrium Methods (Ed. M. Florian), Springer-Verlag, Berlin, 148–182.Google Scholar
  53. Pacey, G.M. (1956). The Progress of a Bunch of Vehicles Released from a Traffic Signal. Road Res. Note No. RN/2665/GMP.Google Scholar
  54. Robertson, D.I. (1969). TRANSYT Method for Area Traffic Control. Traff. Egng & Con., 11, 276–281.Google Scholar
  55. Robertson, D.I. (1982). Research on Strategies for Traffic Control and Management. ARRB Proc., vol. 11, part. 1, 83–89.Google Scholar
  56. Seddon, P.A. (1972). The Prediction of Platoon Dispersion in the Combination Methods of Linking Traffic Signals. Transpn Res., 6, 125–130CrossRefGoogle Scholar
  57. Smith, M.J. (1979a). Traffic Control and Route-Choice: a simple example. Transpn Res., 13B, 289–294.Google Scholar
  58. Smith, M.J. (1979b). The Existence, Uniqueness and Stability of Traffic Equilibria. Transpn Res., 13B. 295–304.Google Scholar
  59. Smith, M.J.(1981a). The Existence of an Equilibrium Solution of the Traffic Assignment Problem when there are Junction Interactions. Transpn Res., 15B, 443–451.Google Scholar
  60. Smith, M.J.(1981b). Properties of a Traffic Control Policy which Ensure the Existence of a Traffic Equilibrium Consistent with the Policy. Transpn Res., 15B, 453–462.Google Scholar
  61. Smith, M.J. (1982). Junction Interaction and Monotonicity in Traffic Assignment. Transpn Res., 18B, 1–3.Google Scholar
  62. Smith, M.J. (1983). The Existence and Calculation of Traffic Equilibria. Transpn Res., 17B, 291–303.Google Scholar
  63. Smith, M.J. (1985). Traffic Signals in Assignment. Transpn Res., B, 19B, 155–160.Google Scholar
  64. Stoffers, K.E. (1968). Scheduling of Traffic Lights — A New Approach. Transpn Res., 2, 199–234.CrossRefGoogle Scholar
  65. Strobel, H. (1982). Computer Controlled Urban Transportation -A Survey of Concepts, Methods and International Experiences. IIASA.Google Scholar
  66. Tan, H., Gershwin, S.B. and Athans, M. (1979). Hybrid Optimization in Urban Traffic Networks. Report No. DOT-TSC-RSP- 79–7, MIT Cambridge, MA.Google Scholar
  67. Taylor, M.A.P. (1984). A Note on Using Davidson’s Function in Equilibrium Assignment. Traspn Res., 18B, 181–199.CrossRefGoogle Scholar
  68. Vincent, R.A., Mitchell, A.I. and Robertson, D.I. (1980). TRANSYT Version 8. Road Res. Lab. Report, LR 80, Crothorne, Berkshire.Google Scholar
  69. Wagner, F.A., Gerlough, D.L. and Barnes, F.C. (1969). Improved Criteria for Traffic Signal System on Urban Arterials. N.C.H.R.P. Report 73, Highway Research Board.Google Scholar
  70. Wardrop, J.G. (1952). Some Theoretical Aspects of Road Traffic Research. Proc. Instn Civil Engnrs, Part. II, 1, 325–378.Google Scholar
  71. Webster, F.V. (1958). Traffic Signal Setting. Road Research Technical Paper, 39, HMSO, London.Google Scholar
  72. Webster, F.V. and Cobbe, B.M. (1966). Traffic Signals. Road Research Technical Paper, 56, HMSO, London.Google Scholar
  73. Wormleighton, R. (1965). Queues at a Fixed Time Traffic Signal with Periodic Random Input. C.O.R.S. Journal, 3, 129–141.Google Scholar
  74. Yagar, S. (1974). Capacity of a Signalized Road Junction. Transpn Res., B6, 137–147.CrossRefGoogle Scholar
  75. Zuzarte Tully, I.M. (1977). Syntesis of Sequences for Traffic Signal Controllers Using Techniques of the Theory of Graphs,Ph.D. Thesis, University of Oxford Engineering Laboratory Report QUEL, 1189/77.Google Scholar
  76. Zuzarte Tully, I.M. and Murchland, J.D. (1978). Calculation and Use of the Critical Cycle Time for a Single Traffic Controller. PTRC Summer Annual Meet, Proc., PTRC-P152, 96–112.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • G. Improta
    • 1
  1. 1.Dipartimento di Informatica e Sistemistica, Cattedra di Ricerca OperativaUniversita’ di NapoliNapoliItaly

Personalised recommendations