Chapter 21: Fundamentals of Signal Timing and
Design: Pretimed Signals
Chapter objectives: By the end of this chapter the
student will be able to:







Explain the basics of signal timing
Know how to handle left-turn vehicles by various phase
plans
Define terms related to phasing
Explain how change and clearance intervals are determined
Explain how pedestrians are dealt with in signal timing
State a few more ways to deal with left turns
Get familiar with typical steps for simple signal timing
Chapter 21
1
Key Steps of signal timing development, p.489
1. Development of a
phase plan and sequence
2. Determination of vehicular
signal needs:
(a) Timing of change interval (y)
and clearance interval (ar)
3. Determination of
pedestrian signal
needs:
(a) Determine min.
pedestrian green
(b) Check if vehicular
greens meet min
pedestrian needs
(c) Check the need for
pedestrian actuators
or for adjusting
timing
(b) Determination of critical lane
volume (Vc)
(c) Determination of lost time per
phase (tL) and per cycle (L)
(d) Determination of desired cycle
length (C)
(e) Allocation of effective green
time
The process is not exact, nor is there often a single
“right” design and timing for a traffic signal.
Chapter 21
2
21.1 Development of signal phase plans
The most critical aspect of signal design and timing is
the development of an appropriate phase plan.
21.1.1 Treatment of left turns (the single most important
feature that drives the development of a phase plan)
vo/No
Two general guidelines (not absolute criteria):
• vLT ≥ 200 veh/h, or
• vLT*(vo/No) ≥ 50,000 (Cross product rule)
2 left turn vehicles/cycle may be
able to turn left as “sneakers”
during the yellow interval (about
120 LTs per hour).
Chapter 21
vLT
3
LT treatment (continue), p.490
Permitted LT phasing should be provided when the following
conditions exist:
1.
The LT demand flow within the peak hour falls within the “permitted”
portion of the figure below.
2.
The sight distance for LT vehicles not restricted.
3.
Fewer than 8 LT accidents have occurred within the last 3 years at any one
approach with permitted-only phasing. (Permitted LT phase must exist to
apply this criterion.)
Figure 21.1
Chapter 21
4
LT treatment (continue), p.491
Fully protected phasing is recommended when any TWO of
the following criteria are met:
1. LT flow rate is greater than 320 veh/h
2.
Opposing flow rate is greater than 1,100 veh/h
3.
Opposing speed limit is greater than or equal to 45 mph
4.
There are two or more LT lanes (in this case, only protected LT
phase is used.)
Chapter 21
5
LT treatment (continue), p.491
Fully protected phasing is also recommended when any ONE of the
following criteria are met:
1. There are 3 opposing lanes, and the opposing speed is 45 mph or greater
2.
LT flow rate is greater than 320 veh/h, and the percent of heavy vehicles
exceeds 2.5%
3.
The opposing flow rate exceeds 1,100 veh/h, and the percent of LT exceeds
2.5%
4.
Seven or more LT accidents have occurred within 3 years under compound
phasing.
5.
The average stopped delay to LT traffic is acceptable for fully protected
phasing, and the engineer judges that additional LT accidents would occur
under the compound phasing option.
Compound phasing (protected-permitted) may be considered when LT
protection is needed but none of these criteria are met. – Use compound
phasing at less critical areas because it is a confusing phasing.
Chapter 21
6
21.1.2 General considerations in signal phasing
Phasing can be used to
minimize conflicting movements
and associated hazards. But the
higher number of phases means
decreased efficiency and
increased delay.  Each phase
add about 3 to 4 seconds of
effective red (lost time).
A phase plan must be implemented in
accordance with the standards and
criteria of the MUTCD, and must be
accompanied by the necessary signs,
markings, and signal hardware needed to
identify appropriate lane usage.  See
MUTCD about signal heads, associated
signs, etc.
The more phases you have
more delay you create. But,
saturation flow rate increases
because of less conflicts. Hence,
look for balance between them.
 The LT saturation flow rate
is at the mercy of on-coming
vehicles for permitted left turns.
The phase plan must be consistent
with the intersection geometry, lane use
assignments, volumes and speeds, and
pedestrian crossing requirements. 
e.g. If there is no LT-bay or exclusive
LT-lane, do not provide a protected LT
phase. It’s useless!
Chapter 21
7
21.1.3 Phase and ring diagrams
Fig 21.2
Selected signal
phase arrows
illustrated
Chapter 21
8
21.1.3 Phase and ring diagrams (continued)
Phase diagram: Shows
all movements being
made in a given phase
within a single block of
the diagram.
Ring diagram: Shows
which movements are
controlled by which
“ring” on a signal
controller.
A “ring” of a controller generally controls one set of signal faces. Thus, while a
phase involving two opposing through movements would be shown in one block of
a phase diagram, each movement would be
separately
shown in a ring diagram. 9
Chapter
21
21.1.4 Common phase plans and their use
Basic two-phase signalization
This works for either case of having a left-turn bay or not having a left-turn bay.
If a left-turn bay is available, performance and safety increases.
Chapter 21
10
With a
protected
left-turn
phase
This LT phase may be
inefficient if only one
direction has a lot of LTs.
General guidelines to deal with left-turn vehicles:
 LT protection is rarely used for LT volumes of less than 100 vph. But even
under 100 vph, it may be used if sight distance is a problem.
 LT protection is almost always used for LT volumes of more than 250-300 vph
 Between these bounds, the provision of LT protection must consider opposing
volumes and number of lanes, accident experience, system signal constraints, etc.
Chapter 21
11
Exclusive LT phase with leading green phase
Chapter 21
Note how LTs are
treated One
direction (WB in
this case) has a
short LT phase.
12
Eight-phase actuated control (NEMA), p.497
The term “phase” is loosely used
sometimes. “Eight-phase” here is
that it is possible to have 8
phases, but usually 4 phases as
you see in the ring diagram.
NEMA no longer
includes lead-lag
option and this 8phase scheme
replaced it.
Chapter 21
13
Safety
Lead vs Lag (with Protected/permitted)


“No significant Difference.”
Except for with protected/permitted
timing:
“Yellow Trapping”
or
“Left-Turn Trapping”
Overlapping “phases”
Possible Collision
Chapter 21
14
Safety
Yellow Trapping
Chapter 21
Lead vs. Lag
15
Protected-permitted left-turns (1)
This order may have a problem.
This one, too.
LTs may be trapped in the intersection
because there is no clearance time for
LTs beyond the yellow interval.
(sometimes there is AR – then possibility
for rear-end collision)
Possible rear-end collisions for LTs because
the LT driver might hesitate for an instant.
Chapter 21
16
Protectedpermitted leftturns with
parallel through
traffic
LTs are
permitted, but
dangerous.
Chapter 21
(Source, pages 61-65, “Manual of Traffic Signal Design” by Kell & Fullerton, ITE)
17
Simultaneous
lead-left turns
with parallel
through traffic
stopped
Chapter 21
18
Lag-left turn with no opposing left turn
Chapter 21
19
Lag-left turns moving simultaneously
Chapter 21
20
The exclusive pedestrian phase
An exclusive pedestrian phase is added. This was
started in New York City by then Traffic
commissioner Henry Barnes, hence called “Barnes
Dance.” Not any more in NYC but you see right next
to Clyde Building. Visit 900N & East Campus Dr.
Chapter 21
21
T-intersection & 5-leg intersection
If this street is a one-way street heading
south, then it is not that bad (3 phases).
But disallow “U-turn from the south
approach
into the diagonal link.
Chapter 21
22
Right-turn phasing and RT lane
This was created
by a data set
collected in Salem,
Oregon. It may not
apply to other
cities, but it is
useful to make
initial plans.
This figure shows a
case of one-lane
approach.
Note that this
figure was
eliminated in the
3rd and 4th edition
of the text. But, I
thought it would be
useful.
Chapter 21
23
21.2 Determining vehicular signal requirements
21.2.1 Change and clearance intervals
All red = clearance interval
Yellow = change interval
Yellow change intervals should have
a normal range of approximately 3 to 6
seconds. Generally the longer intervals
are appropriate to higher approach
speeds.
The MUTCD carries no
requirement for an all red or
clearance interval.
But, ITE recommends use of
both a yellow change interval
and an all-red clearance interval.
p.441 2nd edition: If there is no all-red interval, it is the driver’s responsibility
to check if the intersection was cleared of traffic. “…over 60% is not aware of
this legal responsibility. Also, 60% indicated that they did not bother to look
for traffic from the conflicting street when given the GREEN indication.” -Note that this statement was eliminated in the 3rd edition. So, this is not in the
4th edition, either.
Chapter 21
24
Safely stop at or before the stop bar or clear
the intersection & dilemma zone (using SSD
formula)
To safely stop:
2
X c  D  votr 
vo
2g( f  G)
To safely clear: X o  D  v o t Y  (W  L )
Chapter 21
Cannot stop or cannot
clear (Xc>Xo)
25
Eliminating the dilemma zone
When Xc = Xo, there is no dilemma zone - at least theoretically.
2
v o t Y  (W  L )  v o t r 
vo
2g( f  G)
2
v o tY  v o t r 
tY  t r 
ITE took this
part as the
length of the
yellow
interval.
vo
2g( f  G)
vo
2g( f  G)
vo
tY  t r 
2g(


 (W  L )
(W  L )
vo

(W  L )
vo
 G)
g
 tr 
vo
2  2 gG

This part as the
length of the allred interval.
(W  L )
vo
Chapter 21
26
ITE-recommended practice on change (yellow)
interval, eq. 21-2, p.503
yt
1 . 47 S 85
2 a  2 gG
t
1 . 47 S 85
2  a  gG 
a = deceleration rate (e.g., 10 ft/s2)
g = gravity (32.2 ft/s2)
G = grade of approach (in decimals)
t = perception-reaction time (1.0 sec)
S85 = 85th percentile speed or the speed limit, mph
S15 = S – 5
S85 = S + 5
Chapter 21
This part shows the
effect of gravity on
deceleration vector.
Note that where
approach speeds are
not measured and the
speed limit is used,
both the y and ar
intervals will be
determined using the
same speed. (p.504
Left col.) Not
desirable, though.
See next page for
Why?
27
21.2.1ITE-recommended practice on clearance (AR)
intervals: (3 cases to evaluate and use the longest)
Case 1: Practically no (or low)
pedestrian (w = street width)
w
W
ar 
wL
(S15 in mph)
1 . 47 S 15
Case 3: Some pedestrian traffic:
 W L
P

ar  max 
,
 1 . 47 S 15 1 . 47 S 15
Typical




Case 2: Significant number of
pedestrians OR where the crosswalk is
protected by pedestrian signals
ar 
PL
1 . 47 S 15
S15 = S – 5
W
S85 = S + 5
S = average approach speed
Chapter 21
If LTs are
more critical28
Chapter 21
29
21.2.2 Determining lost times
A
B
G
y
l1
e
ar
R
l2
R
C
tL
g
R
D
r
g
r
A. Actual signal indications
B. Actual use of green and yellow; e is extended green, i.e. part
of the yellow used as green
C. Lost times l1 and l2 are added and placed at the beginning of
the green for modeling purposes
l2  Y  e
D. Effective green and effective red
l1 = 2 sec/phase
Y  y  ar
t L  l1  l 2
e = 2 sec/phase
(by HCM 2010)
n
L 
Chapter 21
t
i 1
Li
i = Number of
phases
30
21.2.3 Determining the sum of critical-lane volume
Two factors require special attention:


Approach demand volumes cannot be simply compared:
heavy vehicles, left turns and right turns affect traffic flow
differently.
Where phase plans involve overlapping elements, the ring
diagram must be carefully examined to determine which
flows constitute critical-lane volumes.
Convert all turning demand volumes to equivalent through
vehicle units (TVUs) first. Please note that adjustments for
heavy vehicles are not done for initial signal timing
because it gets too complex (see p.505, right column, 2nd
paragraph).
Chapter 21
31
Permitted LTs
The effect of turning vehicles are included in Vc by multiplying ELT and
ERT as shown in Table 21.1 and 21.2 (Note these are different from the
ones we use for computing fHV in capacity analysis.)
Interpolation not recommended
V LTE  V LT * E LT
V RTE  V RT * E RT
Can be interpolated.
V EQ  V LTE  V TH  V RTE
Chapter 21
V EQL 
V EQ
N
32
Determining critical lane volume
Use Example 21-2
Chapter 21
33
Figure 21.11 Determining critical lane volumes
(more complex case)
Chapter 21
34
21.2.4 Determining the desired cycle length
This simple method gives you the direction for detailed signal timing.
This method using the formula for the “time budgeting” method as the
basis.
Assumptions:
S = 1900 pcphgpl, but use 85% of it. Hence, s = 0.85x1900 = 1615
pcphgpl (h = 3600/1615 = 2.23 sec/veh)
12-ft lane width, no parking or local buses, 5% heavy vehicles, +1% grade,
a CBD location, and a lost-time/phase of 3 seconds
Nt L
C des 
1
3N

Vc
1
PHF ( v / c )( 3600 / h )
Chapter 21
Vc
1615 PHF ( v / c )
35
21.2.5 Splitting the green
Once the cycle length is determined, the available effective
green time in the cycle must be divided (split) among the
various signal phases in proportion to Vci/Vc.
g TOT  C  L
g i  g TOT
 V ci
* 
 Vc




Finding actual green interval values (Gi):
Gi = gi – Yi + tLI
Do the sample timing in page 507.
Chapter 21
36
Chapter 21
37
21.3 Determining pedestrian signal requirements
HCM 2000 (& 2010) requirements:
G P  3 .2  ( 2 .7 *
N ped
WE
G P  3 . 2  ( 0 . 27 * N ped
 L 

)
S 
 p 
 L 

)
S 
 p 
For WE > 10 ft
(width of crosswalk in ft)
For WE ≤ 10 ft
Nped = No. of peds crossing
per phase (cycle).
The sum total of 1st and 2nd term is WALKmin. The third term is
FLASHING DON’T WALK.
If Gp > G + Y, (a) change the signal timing to satisfy this requirement, or (b) install
pedestrian detectors (buttons) at the intersection. When the button is pressed, the
controller will provide a G + Y equal to Gp during the next available green phase.
When Gp controls, make changes in green times to maintain the original ratio of
vehicular green time. See pages 509 and 510.
Chapter 21
38
Chapter 21
39
Relationship between vehicular signal
indications and pedestrian signal indications,
Figure 21.12
Note that in this case Gp = G + y + ar
Chapter 21
40
21.4 Compound signal timing
• Treat the protected and permitted portions of the phase as if
they were separate phases.
• In converting volumes to tvu’s, use different equivalents
(Table 21.1) as appropriate for each portion of the phase.
• Estimate the cycle length (C) and green time splits (g)
treating the protected and permitted portions of the phase
separately.
•Remember that there will be “yellow” between the green
arrow and the green ball as the phase transitions from
protected to permitted (or vice versa). This yellow counts as
green time for left turns.
Chapter 21
41
21.5 Simple signal timing applications
for
1.
Develop a reasonable signal phase plan. Decide how to deal
with left-turning vehicles.
2.
Convert all left-turning and right-turning volumes to through
car equivalents (tvu’s) using Tabs 21-1 and 21-2.
3.
Establish a reasonable phase plan and draw a ring diagram.
4.
Determine yellow and all-red intervals for each signal phase.
5.
Determine lost times per cycle using Eq. 21-5 through 21-7.
6.
Determine the actual sum of critical lane volumes, Vc, using
this plan. Check the sum of critical lane volumes in tvu’s for
reasonableness. Using Equation 21-11, determine the desirable
cycle length based on a desired v/c ratio (0.85-0.90), and the
PHF
7.
Allocate the available effective green time within the cycle in
proportion to the critical lane volumes (in tvu’s) for each
signal phase.
8.
Check pedestrian requirements and adjust signal timing as
needed.
Chapter 21
42