J. Haddad, D. Mahalel, B. De Schutter, I. Ioslovich, and P.-O. Gutman, "Optimal steady-state traffic control for isolated intersections," Proceedings of the 6th IFAC Symposium on Robust Control Design (ROCOND'09), Haifa, Israel, pp. 96-101, June 2009.
In this paper a simplified isolated controlled intersection is introduced. A discrete-event max-plus model is proposed to formulate the optimization problem for the switching sequences. The formulated max-plus problem is converted to be solved by linear programming (LP). In the special case when the criterion is a strictly increasing and linear function of the queue lengths, the steady-state control problem can be solved analytically. In addition, necessary condition for the steady-state control is derived.