J. Haddad, B. De Schutter, D. Mahalel, and P.-O. Gutman, "Steady-state and N-stages control for isolated controlled intersections," Proceedings of the 2009 American Control Conference, St. Louis, Missouri, pp. 2843-2848, June 2009.
In this paper a simplified isolated controlled intersection is introduced. Discrete-event piecewise affine (PWA) and discrete-event max-plus models are proposed to formulate the optimization problem for the switching sequences. Two control problems are considered: steady-state control and N-stages control. The formulated discrete-event PWA and max-plus problems are converted to be solved by linear programming (LP), mixed-integer programming (MIP), and mixed-integer linear programming (MILP). In the special case when the criterion is a strictly monotonous and linear function of the queue lengths, the steady-state control problem is solved analytically.