# Chapter 18

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```					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
Components of signal timing development, p.489
2. Determination of vehicular
1. Development of a                         signal needs:
phase plan and sequence                 (a) Timing of change interval (y)
and clearance interval (ar)
3. Determination of                        (b) Determination of critical lane
pedestrian signal                           volume (Vc)
needs:
(c) Determination of lost time per
(a) Determine min.                              phase (tL) and per cycle (L)
peds green
(d) Determination of cycle length
(b) Check if vehicular                          (C)
greens meet min
(e) Allocation of effective green
peds needs
time
(c) Check the need of
peds actuators or of   The process is not exact, nor is there often a single
adjusting timing       “right” design and timing for a traffic control 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)

Two general guidelines (not absolute criteria):
• vLT ≥ 200 veh/h
• 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.

Chapter 21                      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 (must have a compound phasing now)
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. (must have a compound
phasing now)
Compound phasing (protected-permitted) may be considered when LT
protection is needed but none of these criteria are met. – Use compound
Chapter 21                              6
phasing at less critical areas because it is a confusing phasing.
21.1.2 General considerations in signal phasing

Phasing can be used to              A phase plan must be implemented in
minimize conflicting movements       accordance with the standards and
and associated hazards. But the      criteria of the MUTCD, and must be
higher number of phases means        accompanied by the necessary signs,
decreased efficiency and             markings, and signal hardware needed to
increased delay.  Each phase        identify appropriate lane usage.  See
effective red (lost time).           signs, etc.

The more phases you have            The phase plan must be consistent
more delay you create. But,          with the intersection geometry, lane use
saturation flow rate increases       assignments, volumes and speeds, and
because of less conflicts. Hence,    pedestrian crossing requirements. 
look for balance between them.       e.g. If there is no LT-bay or exclusive
 The LT saturation flow rate        LT-lane, do not provide a protected LT
is at the mercy of on-coming         phase. It’s useless!
vehicles for permitted left turns.
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
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
This LT phase may be
With a                        inefficient if only one
direction has a lot of LTs.
protected
left-turn
phase

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
splitting the exclusive left-turn phase
Count the number of                                           How many
phases in one ring to                                         phases are there?
find how many lost
times exist.

Overlapping phase

Lagging green for WB LT

A2 is a compound
phase if LTs are
We do not have to have both leading and lagging            permitted.
phases. We may have only a leading or lagging
phase depending on the prevailing conditions.
Chapter 21                             12
Exclusive LT phase with leading green phase

Note how LTs are
treated. One
direction (WB in
this case) has a
short LT phase.
Chapter 21                  13
Eight-phase actuated control (NEMA)

The term “phase” is loosely used
sometimes. “Eight-phase” here is
that it is possible to have 8
phases, but usually 4 phases as           NEMA no longer includes lead-lag
Chapteroption and this 8-phase scheme
21                                14
you see in the ring diagram.              replaced it.
Safety
 “No significant Difference.”
 Except for:
“Yellow Trapping”
or
“Left-Turn Trapping”

Possible Collision
Chapter 21   15
Yellow Trapping

Chapter 21             16
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.              Possible rear-end collisions for LTs because
(sometimes there is AR – then possibility    the LT driver might hesitate for an instant.
for rear-end collision)                     Chapter 21                                 17
Protected-
permitted left-
turns with
parallel through
traffic

LTs are
permitted, but
dangerous.

Chapter 21                          18
(Source, pages 61-65, “Manual of Traffic Signal Design” by Kell & Fullerton, ITE)
Simultaneous
with parallel
through traffic
stopped

Chapter 21   19
Lag-left turn with no opposing left turn

Chapter 21            20
Lag-left turns moving simultaneously

Chapter 21         21
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 & Campus Dr.
Chapter 21                  22
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
Chapter 21                                23
Right-turn phasing
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 is useful.
Chapter 21                       24
21.2 Determining vehicular signal requirements
21.2.1 Change and clearance intervals

All red = clearance interval
The MUTCD carries no
requirement for an all red or
clearance interval.
Yellow = change interval
But, ITE recommends use of
Yellow change intervals should have                both a yellow change interval
a normal range of approximately 3 to 6               and an all-red clearance interval.
seconds. Generally the longer intervals
are appropriate to higher approach
speeds.
p.441 2nd edition: If there is no all-read 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                                    25
Safety stop at or before the stop bar or clear
the intersection & dilemma zone (using SSD
formula)

To safely stop:                           2
vo
X c  D  vot r 
2 g ( f  G)
To safely clear: X o  D  votY  (W  L)                Cannot stop or cannot
finish crossing (Xc>Xo)
Chapter 21                             26
Eliminating the dilemma zone
When Xc = Xo, there is no dilemma zone - at least theoretically.

2
vo
votY  (W  L)  vot r 
2 g ( f  G)
2
vo
votY  vot r                 (W  L)
2 g ( f  G)
vo        (W  L)
tY  t r                
ITE took this                   2 g ( f  G)       vo
vo         (W  L)         This part as the
part as the          tY  t r             
          vo            length of the all-
length of the                   2 g (  G)                    red interval.
g
yellow
interval.                         vo      (W  L)
 tr              
2  2 gG       vo

Chapter 21                             27
ITE-recommended practice on change (yellow)
interval, eq. 21-2, p.503
This part shows the
1.47 S85      1.47 S85
y t           t                                   effect of gravity on
2a  2 gG     2a  gG                         deceleration vector.

Note that where
approach speeds are
not measured and the
speed limit is used,
a = deceleration rate (e.g., 10 ft/s2)
both the y and ar
g = gravity (32.3 ft/s2)                                 intervals will be
determined using the
G = grade of approach (in decimals)                      same value of speed.
(p.504 Left col.) Not
t = perception-reaction time (1.0 sec)
desirable, though.
S85 = 85th percentile speed or the speed limit, mph
Chapter 21                                  28
21.2.1ITE-recommended practice on clearance (AR)
intervals: (3 cases to evaluate and use the longest)
Case 1: Practically no pedestrian (low
pedestrian demand
w L
ar                     (S15 in mph)
1.47 S15
Case 3: Some pedestrian traffic:
 W L       P 

ar  max        ,        

Typical
 1.47S15 1.47S15 
Case 2: Significant number of
pedestrians OR where the crosswalk is
protected by pedestrian signals
PL          S15 = S – 5
ar 
1.47 S15      S85 = S + 5                                  If LTs are
S = average approach speed              Chapter 21               more critical29
21.2.2 Determining lost times
A
G                       y         ar               R
B       l1                             e            l2                R

C            tL                    g                                  R

r                     g                                  r
D

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             Y  y  ar
l1 = 2 sec/phase                                t L  l1  l2
e = 2 sec/phase                                        n
L   t Li
i = Number of
(by HCM 2000)                                                    phases
i 1
Chapter 21                                    30
21.2.3 Determining the sum of critical-lane volume

Two factors require special attention:
   Simple 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 demand volumes to equivalent through vehicle
units (TVUs) first.

Chapter 21                     31
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.)

VLTE  VLT * ELT
VRTE  VRT * ERT
VEQ  VLTE  VTH  VRTE
VEQ
VEQL 
Chapter 21            N                32
Figure 21.11 Determining critical lane volumes

Chapter 21                 33
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                     3N
Cdes                             
Vc                     Vc
1                         1
PHF (v / c)(3600 / h)      1615PHF (v / c)
34
Chapter 21
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.

gTOT  C  L
 Vci 
g i  gTOT    * 
V 
 c

Finding actual green interval values (Gi):

Gi = gi – Yi + tLI

Do the sample timing in page 507.

Chapter 21                                 35
21.3 Determining pedestrian signal requirements
HCM 2000 requirements:

 L 
N ped
GP  3.2  (2.7 *    )                     For WE > 10 ft
WE   S 
 p                   (width of crosswalk in ft)
 L 
GP  3.2  (0.27 * N ped )                     For WE ≤ 10 ft
S 
 p

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                                      36
Relationship between vehicular signal
indications and pedestrian signal indications,
Figure 21.12

Chapter 21                  37
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 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                          38
21.5 Simple signal timing applications
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.

for     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), 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                                  39

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