This paper presents a model of the core logic of a traffic signal controller. The model is formulated on the basis of the traditional North American ring, phase, and barrier construct and includes phase intervals such as minimum and maximum times, pedestrian service, alternative minimum times, and a priority service extension. The mathematical model is based on precedence graphs that are familiar to engineers involved with project management techniques such as Gantt charts, the critical path method, and the program evaluation and review technique. The model presents an analytical framework for the analysis of complex controller behaviors and is demonstrated for the case of multiple priority requests. An example shows that a first-come, first-served policy for serving priority requests can result in more delay than will a multiple-priority-request policy generated by the model developed in this paper. Additional controller behaviors, such as preemption, coordination, and offset transition, can be analyzed with this model.