Euclidean Approach to Green-Wave Theory Applied to Traffic Signal Networks

A recent paper (Friedman et al., 2024) introduced a traffic signal control procedure that allows motorists who travel at a recommended speed on suburban arterial two-way roads to make every traffic signal. Arterial roads on which vehicles traveling at the recommended speed make every traffic signal are termed Ride-the-Green-Wave (RGW) roads. Building on the RGW concept, this paper presents a Euclidean-inspired mathematical framework for uninterrupted flow and maximum throughput in networks of arterial roads. Travel on long arterials with signalized intersections is often inefficient without proper coordination. Long progressions save travel time and fuel and reduce pollution and traffic accidents by enabling smoother traffic. As the number of signals increases, coordination becomes more challenging, and traditional progression schemes tend to break down. This paper shows that green-wave theory can be applied to a network of intersecting arterial roads. It enables uninterrupted flow on arbitrarily long signalized arterials using a Road-to-Traveler-Feedback Device. The theory is modeled after Euclid’s geometric reasoning. We define concepts such as RGW roads (roads where vehicles traveling at recommended speed make all traffic signals), green-arrows (representing vehicle platoons), real nodes (representing signalized intersections where RGW roads intersect) and virtual nodes, green-wave speed, and Blocks—the analog of Euclid’s points, lines, and parallel lines. We postulate green-arrow laws of motion—the analog of Euclid’s postulates. We then use geometric reasoning to deduce results: green-arrow lengths have a maximum value, are restricted to discrete values, and show that select existing arterial roads can be converted to RGW roads. Traditional methods of coordinating traffic signals rely on computer algorithms that calculate offsets, signal durations, and cycle times to optimize an objective function. Here, deductive reasoning provides insight into the necessary and sufficient conditions for achieving uninterrupted flow with maximum throughput. The signal timings and offsets that are produced have been shown to be effective in Friedman et al., (2024) using a simulation model called RGW-SIM.