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Design of Optimal Phase Plans for Isolated Intersections Using Vertex Coloring and Binary Integer Linear Programming

In this paper, a novel optimization technique is proposed to minimize the total number of phases in a traffic signal cycle at isolated intersections for safer and efficient traffic signal allocation. Each phase consists of traffic movements with no conflicts and includes all pedestrian crosswalks once in the signal cycle. The traffic movements and associated conflicting relations are converted to an incompatibility graph. Two vertices in the graph are assigned the same color if they are not connected by an edge. A vertex coloring algorithm has been employed to find the minimum number of colors that can identify and group the nonconflicting vertices. We formulate it as a Linear programming problem with appropriate constraints to obtain the minimum possible colors. The color class sets obtained constitutes the optimal phases which ensure safety at an isolated intersection.