State-space equations and the first-phase algorithm for signal control of single intersections

State-space equations were applied to formulate the queuing and delay of traffic at a single intersection in this paper. The signal control of a single intersection was then modeled as a discrete-time optimal control problem, with consideration of the constraints of stream conflicts, saturation flow rate, minimum green time, and maximum green time. The problem cannot be solved directly due to the nonlinear constraints. However, the results of qualitative analysis were used to develop a first-phase signal control algorithm. Simulation results show that the algorithm substantially reduces the total delay compared to fixed-time control.