Dynamic User Optimal Signal Design at Isolated Intersections

This paper presents a proposal of novel signal design problem at isolated intersections, which assumes that the effective green times assigned to each signal phase follow dynamic user optimal (DUO) principle. At the DUO state, the average delays of vehicles using the signal phases with positive additional green times (the assigned effective green times minus the minimum effective green times) are equal and maximum. The proposed signal design problem is formulated as a variational inequality (VI) problem. The point queue (PQ) model is applied to represent traffic dynamics and to generate the cumulative traffic flows, which is further used to estimate the average delay of each signal phase. The existence of the solution of the proposed VI problem is proved and a solution algorithm based on the method of successive averages (MSA) is developed to solve the proposed signal design problem. Finally, a sample intersection is used to illustrate the application of the proposed model and the solution algorithm.