Minimum Yellow Change Interval and Vehicle Motion Graph
By
Mats Järlström • Beaverton, Oregon, USA • March 3, 2016 • Rev. A

The below universal graph is a direct extension to Gazis, Herman and Maradudin’s (GHM) original work presented in the 1960 paper, "The Problem
of the Amber Signal Light in Traffic Flow". The graph combines a wide range of vehicle motion with a boundary condition in time and space, set
forth by the current state-of-the-art defined input values calculating a minimum yellow change interval referenced an intersection’s geometry.

Comparing to GHM’s paper, figure 3 or 4, the "Common Asymptote" is the analytical reference, the intersection’s entry point at zero distance (d)
(the linear red line referenced to the origin is the plot of -VE/2a + d/VE when d = 0 feet and gradients plotted at d = ±10 feet increments). The "Locus
of Minima" represents the defined maximum safe and comfortable constant deceleration rate (a) (the linear blue line referenced to the origin is the
plot of the VL/a kinematic deceleration term which is also the boundary condition between the “stop” or “go” areas). The linear green line is time
shifted -1.0 seconds from the VL/a term to allocate a defined maximum time (t) for the driver-vehicle complex to perceive and react to the onset of
a yellow traffic signal. The green line yields both the minimum stopping times and distances, i.e. GHM’s "critical distance". The shaded grey area
defines where a vehicle and its driver, passengers, cargo etc. are able to decelerate safely and comfortably to a stop before entering the intersection
if the roadway conditions allow. The shaded area also defines where the vehicle’s constant approach limit velocity variable (VL) is applicable. Hence,
the vehicle’s constant intersection entry velocity variable (VE) is valid beyond the blue defined boundary line or the VL/a kinematic term.

35
30
25
20
15
10

5
0

t
0f
10

40

t
0f

45

ft
-100

50

80

t
-200 f

55

ft/s

-300 ft

mph

-400 ft

Velocity, V

70

20
0f
t

Direction of Motion

GRAPH INPUT VALUES (Level Grade):
Maximum Deceleration Rate, a = 10.0 ft/s²
Complex Perception Reaction Time, t = 1.0 s
"𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃", 𝑌𝑌𝑃𝑃 ≥ 𝒕𝒕 +

60

"𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅", 𝑌𝑌𝑅𝑅 ≥ 𝒕𝒕 +

50
30
20
-10.0

𝑽𝑽𝑳𝑳 𝑽𝑽𝑬𝑬 𝑑𝑑𝐶𝐶𝐶𝐶
−
+
𝒂𝒂 𝟐𝟐𝟐𝟐 𝑉𝑉𝐸𝐸

Where VL ≥ VE > 0 and:
dE = Legal definition of vehicle entry
distance
dCE = Legal definition of vehicle
clearance and exit distance

40

10

𝑽𝑽𝑳𝑳 𝑽𝑽𝑬𝑬 𝑑𝑑𝐸𝐸
−
+
𝒂𝒂 𝟐𝟐𝟐𝟐 𝑉𝑉𝐸𝐸

(VE = VL yields GHM’s original solution)

Time, t

-9.0

-8.0

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0 seconds

Change Interval - Main
Change Interval - Cross

This graph is dedicated in loving memory to Marianne Järlström, David and Lois Hodge and Gordon Long.