Arterial traffic signal coordination makes traffic flow more efficient and safer. This paper presents a partition-enabled multi-mode band (PM-BAND) model that is designed to solve the signal coordination problem for arterials with multiple modes, i.e., passenger cars and transit vehicles. The proposed method permits the progression bands to be broken if necessary and optimizes system partition and signal coordination in one unified framework. The impacts of traffic demand of passenger cars and transit vehicles as well as the geometry characteristics of the arterials are taken into account. Signal timings and waiting time of transit vehicles at stations are optimized simultaneously. The PM-BAND model is formulated as a mixed-integer linear program, which can be solved by the standard branch-and-bound technique. Numerical example results have demonstrated that the PM-BAND model can significantly reduce the average number of stops and delay compared with the other models, i.e., MAXBAND and MULTIBAND. Moreover, the progression bands generated by the PM-BAND model have a higher reliability and effectiveness.

Link performance functions (LPFs) are essential components of macroscopic models for signal optimization, traffic assignment, or combined control-assignment models. Numerous studies have developed a variety of performance functions for signal optimization. Most of these studies attempted to use simplified LPFs that did not capture the important relationships and dependencies among the variables. Dependent LPFs are introduced; in these LPFs the performance on any link depends on the flow pattern not only on that link alone but also on the feeder links. Such functions represent with greater fidelity the performance characteristics of the link and can lead to better control and assignment. An optimization model explicitly considers flow interactions among successive links and applies it in a dynamic programming procedure to determine optimal signal settings. The procedure, which is an offshoot of the combination method for offset optimization, is illustrated for an arterial street and demonstrates its efficacy in comparison with existing optimization models.

This paper describes a traffic signal control strategy that allows motorists who travel at a recommended speed on suburban arterial two‐way roads with a common cycle time to make every traffic signal. A road‐to‐traveler‐feedback‐device (RTFD) advises motorists how fast they should travel to do this. Signalized arterial roads where vehicles that travel at the recommended speed make every traffic signal are termed Ride‐the‐Green‐Wave (RGW) roads. Left‐turn‐arounds enable vehicles to turn left from two‐way RGW roads to intersecting/orthogonal two‐way RGW‐road while allowing maximum flow at the intersection. The traffic signal control technique that enables vehicles that travel at the recommended speed to make every traffic signal has been verified using a simulation program (RGW‐SIM). In addition to introducing novel traffic signal control strategies, the methods presented in this paper have implications for road network design, public transport control, connected and automated vehicles, and environmental impacts.

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.