8.1 Traffic Signal Timing and Phasing

Traffic Signal Timing and Phasing

1. Introduction to Signal Phasing and Terminology

Traffic signals are the primary operational control mechanism used at high-volume at-grade intersections. Their fundamental objectives are to minimize vehicular delay, maximize intersection capacity, and mitigate conflict points between intersecting movements to enhance safety. To analyze signal timing, several terms must be precisely understood:

• Cycle Length ($C$): The total time required for one complete sequence of signal phases (i.e., from the start of green for one phase to the next start of green for that same phase).
• Phase: A controller timing unit associated with the control of one or more movements. A phase includes green, yellow change, and red clearance intervals.
• Interval: A discrete portion of the signal cycle during which signal indications do not change (e.g., green interval, yellow change interval, red clearance interval).
• Movement: The physical direction of travel (e.g., northbound through, eastbound left turn) that vehicles or pedestrians take through an intersection.
• Clearance Interval: The combined yellow change and red clearance intervals designed to allow vehicles to safely stop or clear the intersection before conflicting traffic is released.

2. NEMA Phase Sequencing and Dual-Ring Controllers

The National Electrical Manufacturers Association (NEMA) standardizes phase numbering to ensure uniformity across controller manufacturers. A standard NEMA dual-ring controller manages up to eight vehicular phases. The phases are assigned as follows:

• Odd Phases (1, 3, 5, 7): Left-turn movements.
• Even Phases (2, 4, 6, 8): Through and right-turn movements.
• Phases 1, 2, 5, and 6: Major street movements.
• Phases 3, 4, 7, and 8: Minor (cross) street movements.

3. Ring-and-Barrier Diagrams

A Ring-and-Barrier Diagram represents the sequencing of phases and illustrates which phases can run concurrently.

• Ring: A sequence of phases that must run in order and cannot run concurrently. Dual-ring controllers have two parallel rings running at the same time (Ring 1 on top, Ring 2 on bottom).
• Barrier: A conceptual separator that divides conflicting approaches (typically separating the major street from the minor street). Phases on the left of the barrier (Phases 1, 2, 5, 6) cannot run concurrently with phases on the right of the barrier (Phases 3, 4, 7, 8). The controller must cross the barrier in both rings simultaneously.

Phases within the same ring cannot run together (e.g., Phase 1 and Phase 2 cannot be green at the same time). However, phases in Ring 1 can run concurrently with phases in Ring 2 if they are on the same side of the barrier. For example, Phase 1 (EB Left) and Phase 5 (WB Left) typically run concurrently. When Phase 1 terminates, the controller transitions Ring 1 to Phase 2 (WB Through) while Ring 2 continues in Phase 5 or transitions to Phase 6 (EB Through).

4. Vehicle Change (Yellow) and Clearance (Red) Intervals

The change period consists of the yellow change interval and the red clearance (all-red) interval. This transition period is designed to eliminate the dilemma zone. The dilemma zone is the spatial region upstream of the intersection where a driver, at the onset of the yellow indication, can neither stop comfortably before the stop line nor clear the intersection before the conflicting green begins.

Yellow Change Interval ($Y$)

The yellow change interval alerts drivers that the green interval has ended and a red indication is imminent. It is calculated using the following ITE/NCEES formula:

$Y = t + \frac{V}{2a \pm 64.4G}$

Where:

• $Y$ = Yellow change interval (seconds)
• $t$ = Perception-reaction time, standardized at 1.0 second
• $V$ = Approach design speed or 85th percentile speed (ft/s) [Note: $1\text{ mph} = 1.467\text{ ft/s}$]
• $a$ = Deceleration rate, standardized by AASHTO/ITE at 10 ft/s²
• $G$ = Approach grade (decimal percent, e.g., $+3% = +0.03$, $-3% = -0.03$)
• Note: Use $+64.4G$ for uphill grades and $-64.4G$ for downhill grades.

Red Clearance Interval ($R_c$)

The red clearance interval provides additional time after the yellow change interval to allow vehicles that entered the intersection on yellow to clear the conflict area before conflicting movements are released. It is calculated using the following formula:

$R_c = \frac{W + L}{V}$

Where:

• $R_c$ = Red clearance interval (seconds)
• $W$ = Width of the intersection (feet) from the near-side stop line to the far edge of the conflicting traffic lane.
• $L$ = Length of the vehicle, standardized at 20 feet
• $V$ = Approach speed (ft/s)

5. Pedestrian Timing and Phasing

Pedestrian safety requires dedicated timing analysis whenever pedestrian facilities are present. Pedestrian signal indications consist of a Walk interval and a Pedestrian Clearance Interval (represented by the flashing Upraised Hand / Flashing Don't Walk indication).

Walk Interval

The Walk interval provides time for pedestrians to react to the signal and step off the curb into the crosswalk. Under the MUTCD, the minimum Walk interval is 7.0 seconds. In areas with very low pedestrian volumes, this may be reduced to 4.0 seconds if cycle lengths are highly constrained.

Pedestrian Clearance Interval ($PCI$)

The Pedestrian Clearance Interval allows a pedestrian who stepped into the crosswalk during the Walk interval to safely cross to the opposite curb or a pedestrian refuge. The PCI is calculated as:

$PCI = \frac{D_p}{S_p}$

Where:

• $PCI$ = Pedestrian clearance interval (seconds)
• $D_p$ = Pedestrian walking distance (feet) from the curb to the far edge of the traveled way or to a refuge island.
• $S_p$ = Pedestrian walking speed. The MUTCD standard walking speed is 3.5 ft/s. In areas with a high concentration of elderly pedestrians or individuals with disabilities, a walking speed of 3.0 ft/s must be used.

Minimum Vehicular Green for Pedestrians ($G_{min}$)

To ensure pedestrian safety, the green interval of the concurrent vehicular phase must be long enough to accommodate the pedestrian Walk and Clearance intervals. The minimum green time ($G_{min}$) is computed in one of two ways based on local operational guidelines:

1. Standard MUTCD Clearance Overlap (Flashing Don't Walk continues through yellow and red clearance): $G_{min} = Walk + PCI - Y - R_c$
2. Conservative Clearance (Flashing Don't Walk must complete before yellow begins): $G_{min} = Walk + PCI$

6. Example Timing Calculation

Scenario: A flat ($G = 0%$) intersection has an approach speed of 40 mph, an intersection width of 85 ft, and a pedestrian crossing distance of 50 ft. Calculate the yellow change, red clearance, pedestrian clearance, and minimum vehicular green time using standard values.

Step 1: Convert Approach Speed to ft/s

$V = 40\text{ mph} \times 1.467 = 58.68\text{ ft/s}$

Step 2: Calculate Yellow Change Interval ($Y$)

$Y = 1.0 + \frac{58.68}{2(10) + 64.4(0)} = 1.0 + \frac{58.68}{20} = 1.0 + 2.93 = 3.93\text{ seconds} \approx 4.0\text{ s}$

Step 3: Calculate Red Clearance Interval ($R_c$)

$R_c = \frac{W + L}{V} = \frac{85 + 20}{58.68} = \frac{105}{58.68} = 1.79\text{ seconds} \approx 1.8\text{ s}$

Step 4: Calculate Pedestrian Clearance Interval ($PCI$)

Using standard walking speed $S_p = 3.5\text{ ft/s}$: $PCI = \frac{D_p}{S_p} = \frac{50}{3.5} = 14.29\text{ seconds} \approx 14.3\text{ s}$

Step 5: Calculate Minimum Vehicular Green ($G_{min}$)

Assuming standard MUTCD clearance overlap (pedestrian clearance can overlap with yellow and red clearance): $G_{min} = Walk + PCI - Y - R_c = 7.0 + 14.3 - 4.0 - 1.8 = 15.5\text{ seconds}$

7. Practical PE Exam Design Tips

• Unit Conversion: Always convert speed from mph to ft/s by multiplying by 1.467. Forgetting this conversion is the most common mathematical trap on the exam.
• Vehicle Length: In the red clearance formula, always add the standard vehicle length ($L = 20\text{ ft}$) to the intersection width ($W$) unless the problem explicitly states otherwise.
• Grade Sign: Watch the sign of the grade. Downhill grades (negative $G$) increase the stopping distance and yield longer yellow change intervals. Uphill grades (positive $G$) decrease the stopping distance and yield shorter yellow change intervals.
• Pedestrian Walking Speed: Use $3.5\text{ ft/s}$ as the default. Only use $3.0\text{ ft/s}$ if the problem text specifically mentions school children, seniors, or disabled pedestrians.