Determining interphase transition programs using various objective functions

Abstract: The article describes the principles of creating interphase transition programs for adaptive traffic control algorithms. The article characterizes the formal requirements that interphase transition programs must meet. These requirements serve as a starting point for the formal notation of programs and for defining constraints imposed on the control function. The need to use different methods for determining transitions depending on the type of control and the adopted control principles is also justified. The following methods for creating interphase transitions are described: maximization of intergreen times, implementation of equal start for signal groups, minimization of interphase transition length, and a method based on minimizing intergreen times between critical groups. The article also presents an evaluation and potential applications of individual methods, as well as examples of solutions used in the practice of designing signaling programs.1. INTERPHASE TRANSITION PROGRAMS IN THE THEORY
AND PRACTICE OF DESIGNING TRAFFIC SIGNAL PROGRAMS
Nowadays, the design of traffic signals largely requires the creation of adaptive control algorithms, the most popular variety of which is actuated control. In such control, the state of signal groups determined by the control function depends on information transmitted from detectors, and decisions regarding the values of the control function are made in real-time, based on the designed algorithm. In adaptive control, we can distinguish periods in which only permissive or restrictive signals are displayed, called phases, and periods in which signal changes occur, called interphase
transitions. A formal definition of a phase in a signaling program is given in [9] and is defined as a period in which the control function takes values such that the subset of signal groups displaying permissive signals is not a subset of any other set displaying permissive signals in another period. Sometimes phases are called variable intervals, because their length, while maintaining certain constraints resulting from formal requirements and the nature of the traffic process, can be changed. (…)

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