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Development of a Combined Traffic Signal Control-Traffic Assignment Model

  • Mohammed Al-Malik
  • Nathan H. Gartner
Part of the Transportation Analysis book series (TRANSANALY)

Abstract

Having recognized the mutual interaction that exists between traffic signal control and route choice behavior, this paper considers the traffic assignment problem for a traffic signal controlled network. The interaction is characterized by (1) the effects of delay, due to traffic signals, on route choice, and (2) the influence of the resulting traffic assignment, due to the changes in route selection, on the timing of traffic signals. In this paper Webster’s method for calculating green splits and the HCM delay model are used to develop a link performance function that implicitly produces optimal signal settings for the arriving traffic volumes. This link-performance function is then used in an assignment procedure to develop a combined traffic signal control/traffic assignment model. The model provides simultaneous solution of the traffic signal control problem and the traffic assignment problem. The result is a set of signal settings that optimally matches the assigned traffic flows. The combined model results in a non-convex problem which produces multiple equilibria. A modification of Wardrop’s two principles is proposed to produce an assignment which converges to a single solution.

Keywords

Traffic Signal Route Choice Delay Function Traffic Assignment Arrival Flow Rate 
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.

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References

  1. [1]
    Al-Malik, M.S. (1991). “An Investigation and Development of a Combined Traffic Signal Control - Traffic Assignment Model.” Ph.D. Thesis, Georgia Institute of Technology.Google Scholar
  2. [2]
    Allsop R.E.(1974). “Some Possibilities for Using Traffic Control to Influence Trip Distribution and Route Choice.” Proceedings 6th International Symposium on Transportation and Traffic Theory, Sydney.Google Scholar
  3. [3]
    Allsop R.E. and J.A. Charlesworth (1977). “Traffic in a Signal-Controlled Road Network: An example of Different Signal Timings Inducing Different Routing.” Traffic Engineering and Control, 18(5), 262–264.Google Scholar
  4. [4]
    Cantarella G.E. and A. Sforza (1987). “Methods for Equilibrium Network Traffic Signal Setting.” Flow Control of Congested Networks, Springer-Verlag, Berlin.Google Scholar
  5. [5]
    Cantarella G.E., G. Improta and A. Sforza (1991). “An Iterative Procedure for Equilibrium Network Traffic Signal Settings.” Transportation Research 25B(4).Google Scholar
  6. [6]
    Dafermos S. (1972). “The Traffic Assignment Problem for Multiclass-User Transportation Networks.” Transportation Science 6, 73–87.CrossRefGoogle Scholar
  7. [7]
    Dickson, T.J. (1981) “A Note on Traffic Assignment and Signal Timings in a Signal Controlled Road Network.” Transportation Research 15B, 267–271. 186Google Scholar
  8. [8]
    Gartner N.H. (1976). “Area Traffic Control and Network Equilibrium.” Proceedings International Symposium on Traffic Equilibrium Methods (Edited by Florian, M. A. ), Springer Verlag.Google Scholar
  9. [9]
    Gartner N.H. (1977a). “Influencing Traffic Equilibrium in a Network by Control Measures.” Transportation Research Record 644, 125–129.Google Scholar
  10. [10]
    Gartner N.H. (1977b). “Analysis and Control of Transportation Networks by Frank-Wolfe Decomposition.” Proceedings 7th International Symposium in Transportation and Traffic Theory (Edited by T. Sasaki and T.Y. Yamaoka) Tokyo, Japan.Google Scholar
  11. [11]
    Highway Capacity Manual. “Special Report 209”, TRB, National Research Council, Washington, D.C.Google Scholar
  12. [12]
    Improta G. (1987). “Mathematical Programming Methods for Urban Network Control.” Flow Control of Congested Networks, Springer-Verlag, Berlin.Google Scholar
  13. [13]
    Miller A.J. (1963). “Settings for fixed-cycle traffic signals.” Oper. Res. Q., 14: 373–386.CrossRefGoogle Scholar
  14. [14]
    Newell G.F. (1965). “Approximation methods for queues with applications to the fixed-cycle traffic light.” SIAM Rev.,7(2):223–240.Google Scholar
  15. [15]
    Sheffi Y. (1979). “Urban Transportation Networks.” Prentice Hall, Englewood Cliffs, N.J.Google Scholar
  16. [16]
    Smith M.J. (1981). “Properties of a Traffic Control Policy which Ensure the Existence of a Traffic Equilibrium Consistent with the Policy.” Transportation Research 18B(1), 63–65.Google Scholar
  17. [17]
    Smith M.J. (1985). “Traffic Signals in Assignments.” Transportation Research 19B(2), 155–160.Google Scholar
  18. [18]
    Tan H., S.B. Gershwin and M. Athans (1979). “Hybrid Optimization in Urban Traffic Networks”. Report No. DOT-TSCRSP-79–7, MIT Cambridge, MA.Google Scholar
  19. [19]
    Wardrop J.G. (1952). “Some Theoretical Aspects of Road Traffic Research.” Proceedings, Institution of Civil Engineers 11(1),325–378.Google Scholar
  20. [20]
    Webster F.V. “Traffic Signal Settings.” Road Research Laboratory Report 39, Crowthorne, Berkshire, England.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1995

Authors and Affiliations

  • Mohammed Al-Malik
    • 1
  • Nathan H. Gartner
    • 2
  1. 1.Department of Civil EngineeringKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Department of Civil EngineeringUniversity of MassachusettsLowellUSA

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