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
Webster, F., Traffic Signal Settings, in Road Research Technical Paper, London: Great Britain Road Research Laboratory, 1958, no. 39, p. 58.
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.
Gazis, D. and Potts, R., The Oversaturated Intersection, Proc. 2nd Int. Symp. Theory Traffic Flow, 1963, pp. 221–237.
Gazis, D., Optimum Control of a System of Oversaturated Intersections, Oper. Res., 1964, vol. 12, no. 6, pp. 815–831.
Gazis, D., Control Problems in Automobile Traffic, in Proc. IBM Scientific Comput. Symp. Control Theory Appl., New York: IBM, 1966.
Traffic Science, Gazis, D., Ed., New York: Wiley, 1974.
D’And, G. and Gazis, D., Optimal Control of Oversaturated Store-and-Forward Transportation Networks, Transportat. Sci., 1976, vol. 10, pp. 1–19.
Michalopoulos, P.G. and Stephanopoulos, G., Oversaturated Signal Systems with Queue Length Constraints. I, Transportat. Res., 1977, vol. 1, no. 11, pp. 413–421.
Michalopoulos, P.G. and Stephanopoulos, G., Oversaturated Signal Systems with Queue Length Constraints. II, Transportat. Res., 1977, vol. 1, no. 11, pp. 423–428.
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.
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.
Stotsky, A., Stability of Traffic Flow: Lyapunov Analysis, Transportat. Syst., 1997, vol. 2, pp. 759–764.
De Schutter, B. and De Moor, B., Optimal Traffic Light Control for a Single Intersection, Eur. J. Control, 1998, vol. 4, pp. 260–276.
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.
Gazis, D., Traffic Theory, New York: Kluwer, 2002.
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.
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.
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.
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.
Denn, M.M., Optimization by Variational Methods, New York: McGraw-Hill, 1969.
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.
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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