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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

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Chapter 21: Fundamentals of Signal Timing and Design: Pretimed Signals

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chapter 21 fundamentals of signal timing and design pretimed signals
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

key steps of signal timing development p 489
Key Steps of signal timing development, p.489
  • 2. Determination of vehicular signal needs:
  • Timing of change interval (y) and clearance interval (ar)
  • (b) Determination of critical lane volume (Vc)
  • (c) Determination of lost time per phase (tL) and per cycle (L)
  • (d) Determination of cycle length (C)
  • (e) Allocation of effective green time

1. Development of a phase plan and sequence

  • 3. Determination of pedestrian signal needs:
  • Determine min. pedestrian green
  • Check if vehicular greens meet min pedestrian needs
  • Check the need for pedestrian actuators or for adjusting timing

The process is not exact, nor is there often a single “right” design and timing for a traffic control signal.

Chapter 21

21 1 development of signal phase plans
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, 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

lt treatment continue p 490
LT treatment (continue), p.490
  • Permitted LT phasing should be provided when the following conditions exist:
  • The LT demand flow within the peak hour falls within the “permitted” portion of the figure below.
  • The sight distance for LT vehicles not restricted.
  • 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

lt treatment continue p 491
LT treatment (continue), p.491
  • Fully protected phasing is recommended when any TWO of the following criteria are met:
  • LT flow rate is greater than 320 veh/h
  • Opposing flow rate is greater than 1,100 veh/h
  • Opposing speed limit is greater than or equal to 45 mph
  • There are two or more LT lanes (in this case, only protected LT phase is used.)

Chapter 21

lt treatment continue p 4916

Fully protected phasing is also recommended when any ONE of the following criteria are met:

  • There are 3 opposing lanes, and the opposing speed is 45 mph or greater
  • LT flow rate is greater than 320 veh/h, and the percent of heavy vehicles exceeds 2.5%
  • The opposing flow rate exceeds 1,100 veh/h, and the percent of LT exceeds 2.5%
  • Seven or more LT accidents have occurred within 3 years under compound phasing.
  • 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.
LT treatment (continue), p.491

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


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 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!
  • 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.

Chapter 21

21 1 3 phase and ring diagrams continued
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.

Chapter 21

21 1 4 common phase plans and their use
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

with a protected left turn phase

This LT phase may be inefficient if only one direction has a lot of LTs.

With a 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

exclusive lt phase with leading green phase
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

eight phase actuated control nema
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 you see in the ring diagram.

NEMA no longer includes lead-lag option and this 8-phase scheme replaced it.

Chapter 21

lead vs lag


Lead vs. Lag
  • “No significant Difference.”
  • Except for:

“Yellow Trapping”


“Left-Turn Trapping”

Possible Collision

Chapter 21

yellow trapping


Lead vs. Lag

Yellow Trapping

Chapter 21

protected permitted left turns 1
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

protected permitted left turns with parallel through traffic
Protected-permitted left-turns with parallel through traffic

LTs are permitted, but dangerous.

Chapter 21

(Source, pages 61-65, “Manual of Traffic Signal Design” by Kell & Fullerton, ITE)

the exclusive pedestrian phase
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

t intersection 5 leg intersection
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

right turn phasing and rt lane
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 is useful.

Chapter 21

21 2 determining vehicular signal requirements
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.
  • But, ITE recommends use of both a yellow change interval and an 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.

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

safely stop at or before the stop bar or clear the intersection dilemma zone using ssd formula
Safely stop at or before the stop bar or clear the intersection & dilemma zone (using SSD formula)

To safely stop:

To safely clear:

Cannot stop or cannot clear (Xc>Xo)

Chapter 21

eliminating the dilemma zone
Eliminating the dilemma zone

When Xc = Xo, there is no dilemma zone - at least theoretically.

ITE took this part as the length of the yellow interval.

This part as the length of the all-red interval.

Chapter 21

ite recommended practice on change yellow interval eq 21 2 p 503
ITE-recommended practice on change (yellow) interval, eq. 21-2, p.503

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 value of speed. (p.504 Left col.) Not desirable, though. See next page for Why?

a = deceleration rate (e.g., 10 ft/s2)

g = gravity (32.3 ft/s2)

G = grade of approach (in decimals)

t = perception-reaction time (1.0 sec)

S85 = 85th percentile speed or the speed limit, mph

Chapter 21

21 2 1ite recommended practice on clearance ar intervals 3 cases to evaluate and use the longest
21.2.1ITE-recommended practice on clearance (AR) intervals: (3 cases to evaluate and use the longest)

Case 1: Practically no pedestrian (w = street width)

(S15 in mph)

Case 3: Some pedestrian traffic:


Case 2: Significant number of pedestrians OR where the crosswalk is protected by pedestrian signals

S15 = S – 5

S85 = S + 5

If LTs are more critical

Chapter 21

S = average approach speed

21 2 2 determining lost times





21.2.2 Determining lost times
  • Actual signal indications
  • Actual use of green and yellow; e is extended green, i.e. part of the yellow used as green
  • Lost times l1 and l2 are added and placed at the beginning of the green for modeling purposes
  • Effective green and effective red

l1 = 2 sec/phase

e = 2 sec/phase

i = Number of phases

(by HCM 2010)

Chapter 21


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 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


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.)

Permitted LTs

Interpolation not recommended

Can be interpolated.

Chapter 21


Determining critical lane volume

Use Example 21-2

Chapter 21

21 2 4 determining the desired cycle length
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

Chapter 21

21 2 5 splitting the green
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.

Finding actual green interval values (Gi):

Gi = gi – Yi + tLI

Do the sample timing in page 507.

Chapter 21

21 3 determining pedestrian signal requirements
21.3 Determining pedestrian signal requirements

HCM 2000 (& 2010) requirements:

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

relationship between vehicular signal indications and pedestrian signal indications figure 21 12
Relationship between vehicular signal indications and pedestrian signal indications, Figure 21.12

Note that in this case Gp = G + y + ar

Chapter 21

21 4 compound signal timing
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

21 5 simple signal timing applications
21.5 Simple signal timing applications
  • Develop a reasonable signal phase plan. Decide how to deal with left-turning vehicles.
  • Convert all left-turning and right-turning volumes to through car equivalents (tvu’s) using Tabs 21-1 and 21-2.
  • Establish a reasonable phase plan and draw a ring diagram.
  • Determine yellow and all-red intervals for each signal phase.
  • Determine lost times per cycle using Eq. 21-5 through 21-7.
  • Determine the actual sum of critical lane volumes, Vc, using this plan. Check the sum of critical lane volumes in tvu’sfor reasonableness. Using Equation 21-11, determine the desirable cycle length based on a desired v/c ratio (0.85-0.90), and the PHF
  • Allocate the available effective green time within the cycle in proportion to the critical lane volumes (in tvu’s) for each signal phase.
  • Check pedestrian requirements and adjust signal timing as needed.


Chapter 21