ITE Journal - March 2020 - 34

An Explanation of Mats Järlström's

Extended Kinematic Equation

S

By Jay Beeber (M)

ince the yellow indication was first added to traffic signals in 1920, the proper interval
duration has been robustly debated.1 Seemingly, the timing of the yellow indication

appears straightforward. However, determining the illumination interval is quite
intricate since it is part of a complex system of physical and human-made laws,

technology, and human behavior that all must operate compatibly.
In 1960, Denos Gazis, Robert Herman, and Alexei A. Maradudin
(GHM) provided a scientific solution to the yellow change interval
question in their paper, "The Problem of the Amber Signal Light
in Traffic Flow."2 GHM presented a kinematic solution to a binary
STOP or GO dilemma when a driver is faced with the onset of a
yellow signal indication. The problem GHM solved and eliminated
was an area in the roadway known as the "dilemma zone", where a
driver-vehicle complex could neither STOP safely and comfortably
nor GO without the need to violate the red or accelerate unsafely
into the intersection.
34

Ma rch 2020

ite j o u rn al

GHM's solution to regulate a yellow change interval first
appeared in the 1965 ITE Traffic Engineering Handbook, and it
has become known as the kinematic equation.3 However, GHM's
solution is limited to vehicles traveling through level intersections
at constant velocity, which does not include vehicle deceleration to
execute safe turning maneuvers. This article presents a brief review
covering GHM's original solution and Mats Järlström's extended
kinematic equation which allows for vehicle deceleration and
turning maneuvers.4

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ITE Journal - March 2020

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