Steady-state and N-stages control for isolated controlled intersections

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 maxplus 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.