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Design of optimal traffic flow control at intersection with regard for queue length constraints

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Abstract

Consideration was given to a well-known problem of traffic control at an individual intersection with minimal total delay. The constraints on control (duration of green light in the main direction) and phase variables (queue lengths along each direction) were taken into account. A continuous traffic model and the methods of the optimal control theory were used. An analytical solution was established in the form of feedback control design. The solutions obtained were compared with the results acquired in the 1960s and 1970s.

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References

  1. Webster, F., Traffic Signal Settings, in Road Research Technical Paper, London: Great Britain Road Research Laboratory, 1958, no. 39, p. 58.

    Google Scholar 

  2. Allsop, R., SIGCAP: A Computer Program for Assessing the Traffic Capacity of Signal-Controlled Road Junctions, Traffic Eng. Control, 1976, vol. 17, pp. 338–341.

    Google Scholar 

  3. Gazis, D. and Potts, R., The Oversaturated Intersection, Proc. 2nd Int. Symp. Theory Traffic Flow, 1963, pp. 221–237.

  4. Gazis, D., Optimum Control of a System of Oversaturated Intersections, Oper. Res., 1964, vol. 12, no. 6, pp. 815–831.

    Article  MATH  Google Scholar 

  5. Gazis, D., Control Problems in Automobile Traffic, in Proc. IBM Scientific Comput. Symp. Control Theory Appl., New York: IBM, 1966.

    Google Scholar 

  6. Traffic Science, Gazis, D., Ed., New York: Wiley, 1974.

    MATH  Google Scholar 

  7. D’And, G. and Gazis, D., Optimal Control of Oversaturated Store-and-Forward Transportation Networks, Transportat. Sci., 1976, vol. 10, pp. 1–19.

    Article  Google Scholar 

  8. Michalopoulos, P.G. and Stephanopoulos, G., Oversaturated Signal Systems with Queue Length Constraints. I, Transportat. Res., 1977, vol. 1, no. 11, pp. 413–421.

    Article  Google Scholar 

  9. Michalopoulos, P.G. and Stephanopoulos, G., Oversaturated Signal Systems with Queue Length Constraints. II, Transportat. Res., 1977, vol. 1, no. 11, pp. 423–428.

    Article  Google Scholar 

  10. Michalopoulos P.G. and Stephanopoulos, G., Optimal Control of Oversaturated Intersections: Theoretical and Practical Considerations, Traffic Eng. Control, 1978, vol. 19, no. 5, pp. 216–221.

    Google Scholar 

  11. Guardabassi, G., Locatelli, A., and Papageorgiou, M., A Note on the Optimal Control of an Oversaturated Intersection, Transportat. Res., Part B, 1984, vol. 18, no. 2, pp. 111–113.

    Article  Google Scholar 

  12. Stotsky, A., Stability of Traffic Flow: Lyapunov Analysis, Transportat. Syst., 1997, vol. 2, pp. 759–764.

    Google Scholar 

  13. De Schutter, B. and De Moor, B., Optimal Traffic Light Control for a Single Intersection, Eur. J. Control, 1998, vol. 4, pp. 260–276.

    MATH  Google Scholar 

  14. De Schutter, B., Optimizing Acyclic Traffic Signal Switching Sequences through an Extended Linear Complementarity Problem Formulation, Eur. J. Oper. Res., 2002, vol. 139, pp. 400–415.

    Article  MATH  Google Scholar 

  15. Gazis, D., Traffic Theory, New York: Kluwer, 2002.

    MATH  Google Scholar 

  16. Haddad, J., De Schutter, B., Mahalel, D., and Gutman, P.-O., Steady-State and N-Stages Control for Isolated Controlled Intersections, Proc. 2009 Am. Control Conf., St. Louis, 2009, pp. 2843–2848.

  17. Haddad, J., Mahalel, D., De Schutter, B., Ioslovich, I., and Gutman, P.-O., Optimal Steady-State Traffic Control for Isolated Intersections, Proc. 6th IFAC Sympos. Robust Control Design (ROCOND’09), Haifa, 2009, pp. 96–101.

  18. Haddad, J., De Schutter, B., Mahalel, D., Ioslovich, I., and Gutman, P.-O., Optimal Steady-State Control for Isolated Traffic Intersections, IEEE Trans. Autom. Control, 2010, vol. 55, pp. 2612–2617.

    Article  Google Scholar 

  19. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Fizmatlit, 1961.

    Google Scholar 

  20. Denn, M.M., Optimization by Variational Methods, New York: McGraw-Hill, 1969.

    Google Scholar 

  21. Khrustalev, M.M., Necessary and Sufficient Dynamic Programming Conditions for Optimal Control Problem with State Constraints, in Lecture Notes in Control and Inform. Sci., System Modelling and Optimization, Wien: Springer, 1989, vol. 143, pp. 311–320.

    Google Scholar 

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Original Russian Text © I. Ioslovich, P.-O. Gutman, D. Mahalel, J. Haddad, 2011, published in Avtomatika i Telemekhanika, 2011, No. 9, pp. 39–48.

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Ioslovich, I., Gutman, P.O., Mahalel, D. et al. Design of optimal traffic flow control at intersection with regard for queue length constraints. Autom Remote Control 72, 1833–1840 (2011). https://doi.org/10.1134/S0005117911090050

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  • DOI: https://doi.org/10.1134/S0005117911090050

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