# ITE Journal - March 2020 - 36

a "reasonable" driver closer to the intersection than their critical
distance proceeds into the intersection when presented with a
yellow indication. Figure 2 illustrates this concept.
The logic behind the methodology for determining the duration
of the yellow change interval is that the interval should provide
a reasonable driver who is too close to the intersection to stop
safely and comfortably (i.e., closer than the critical distance) with
adequate time to traverse the minimum stopping distance and
legally enter the intersection before the signal turns red.
A reasonable driver is defined as one who is not violating the law
(i.e., acting legally), and whose chosen actions are rational, prudent,
and feasible. Safety and equity requires that the motion of any roadway
user who exhibits reasonable behavior must be accommodated within
the signal timing protocol, even if their chosen actions are not the
"average" or most common to be encountered upon the roadway.
In conformance with the standard for through lane movements,
the calculation of the minimum yellow change interval for turning
movements must also provide a reasonable driver adequate time
to traverse the minimum stopping distance and legally enter the
intersection before the onset of the red indication. This calculation
must allow for the extra time necessary for a vehicle to traverse

the stopping distance while decelerating from the initial approach
velocity (v0) to the intersection entry velocity (vE) to safely and
comfortably negotiate a turning maneuver.
In contrast to the condition where a driver approaches a
signalized intersection in a through lane, scenarios where a driver
approaches a signalized intersection in a turning lane are significantly more complicated. Although there is a range of possibilities as
model of driver-vehicle motion which encompasses the "worst-case
scenario" or "boundary condition" for a decelerating vehicle. A full
explanation of this concept and examination of other models of
driver-vehicle motion is presented in "Yellow Change Intervals for
Turning Movements Using Basic Kinematic Principles," available
on the ITE website at www.ite.org/technical-resources/topics/
traffic-engineering/traffic-signal-change-and-clearance-intervals.

Järlström's Extended Kinematic Equation
For the extended solution, conceive that the driver begins their
deceleration at the Critical Braking Point, decelerating at their
maximum safe and comfortable deceleration (amax) to their target
entry velocity (vE) and then traverses the remainder of the braking
distance at this velocity into the intersection.
Under this "boundary condition" model for a decelerating vehicle,
the minimum stopping distance (xC) is divided into three distinct
areas of vehicle movement: 1) the Perception-Reaction zone (xPR), 2)
a Deceleration Zone (xDec) where the driver decelerates to their target
entry velocity (vE) beginning at the Critical Braking Point, and 3) a
Non-Deceleration "Go Zone" (xGo) starting at the end of the Deceleration Zone where the driver continues at their target entry speed to the
limit line and into the intersection. Figure 3 illustrates these concepts.
The minimum time to traverse the minimum stopping distance
is, therefore, the combination of 1) the time to traverse the
perception-reaction distance (tPR), plus 2) the time to traverse the
Deceleration Zone (tDec), plus 3) the time to traverse the Go Zone
(tGo). This combination is the minimum yellow change interval
(Ymin) necessary to eliminate the dilemma zone for this model of
driver-vehicle motion, expressed as:
Ymin = tPR + tDec + tGo	(5)
The time to traverse the Deceleration Zone is given by:
tDec =

Figure 2. Illustration of the STOP or GO scenario encountered when
approaching a signalized intersection.
36

Ma rch 2020

ite j o u rn al

(v - v )
amax

0
E
_______

(6)

The time to traverse the Go Zone (tGo) is determined as follows:
First, calculate the length of the Go Zone (xGo) by subtracting
the length of the Deceleration Zone (xDec) from the full braking
distance (xBr).

http://www.ite.org/technical-resources/topics/traffic-engineering/traffic-signal-change-and-clearance-intervals http://www.ite.org/technical-resources/topics/traffic-engineering/traffic-signal-change-and-clearance-intervals

# ITE Journal - March 2020

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