9.2 Traffic Safety and Operations

Traffic Safety and Operations

Traffic Signal Timing Design

Traffic signals are critical operational controls that allocate right-of-way to conflicting movements at an intersection. Designing a signal timing plan involves balancing the need for safe vehicle clearance with the desire to minimize delay. A signal cycle consists of multiple phases, which in turn contain specific intervals: green, yellow change, and all-red clearance.

Yellow Change Interval ($Y$)

The yellow change interval warning is designed to alert approaching drivers that the green interval has ended and a red interval will follow immediately. It must be long enough to allow a vehicle to safely stop before the stop line, or if the vehicle is too close to stop, to safely cross the stop line. The Institute of Transportation Engineers (ITE) formula for the yellow change interval is: $Y = t_r + \frac{V}{2a + 2gG}$ Where:

• $t_r$ = perception-reaction time of the driver (standard value is 1.0 second).
• $V$ = approach speed (ft/s). Note that speed is often given in mph on exams and must be converted to ft/s by multiplying by 1.467.
• $a$ = deceleration rate of the vehicle (typically $10\text{ ft/s}^2$ or $11.2\text{ ft/s}^2$ depending on local standards; ITE recommends 10 $ft/s^2$).
• $g$ = acceleration due to gravity ($32.2\text{ ft/s}^2$).
• $G$ = roadway grade (expressed as a decimal; e.g., +0.03 for a 3% upgrade, -0.02 for a 2% downgrade).

All-Red Clearance Interval ($R_c$)

The all-red clearance interval is a short period where all approaches display a red signal. This allows vehicles that entered the intersection at the very end of the yellow interval to completely clear the conflict zone before cross-street traffic receives a green light. The ITE formula is: $R_c = \frac{W + L}{V}$ Where:

• $W$ = width of the intersection, measured from the approach stop line to the far edge of the conflicting traffic lane (ft).
• $L$ = length of the design vehicle (typically 20 ft for passenger cars).
• $V$ = approach speed (ft/s).

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The Dilemma Zone

The dilemma zone is an area upstream of the intersection where a driver approaching a yellow signal can neither stop safely before the stop line nor clear the intersection before the signal turns red. This occurs when the required stopping distance is greater than the distance the vehicle can travel during the yellow change interval.

Mathematical Definition of the Dilemma Zone

• Safe stopping distance ($X_{stop}$): The minimum distance from the stop line at which a vehicle can come to a complete stop before reaching the stop line: $X_{stop} = V \cdot t_r + \frac{V^2}{2a + 2gG}$
• Clearing distance ($X_{clear}$): The maximum distance from the stop line from which a vehicle can enter and completely clear the intersection during the yellow change interval: $X_{clear} = V \cdot Y - (W + L)$

A dilemma zone exists if: $X_{stop} > X_{clear}$ In this case, if the yellow light appears when a vehicle is between $X_{clear}$ and $X_{stop}$, the driver is in a "dilemma": if they try to stop, they will slide into the intersection; if they try to clear, they will run a red light. To eliminate the dilemma zone, the total change and clearance interval ($Y + R_c$) must be designed to satisfy: $Y + R_c \ge t_r + \frac{V}{2a + 2gG} + \frac{W + L}{V}$

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Webster's Optimum Cycle Length Method

For pre-timed signal controllers, Webster's method is a widely accepted formula for determining the cycle length ($C$) that minimizes total vehicle delay at the intersection: $C_{opt} = \frac{1.5L + 5}{1 - \sum_{i=1}^n Y_i}$ Where:

• $C_{opt}$ = optimum cycle length (seconds).
• $L$ = total lost time per cycle (seconds). Lost time represents time when the intersection is not being fully utilized by any movement. It includes start-up lost time ($l_1$, typically 2.0 s per phase) and clearance lost time ($l_2$, yellow + all-red minus the portion used for clearing). On exams, if not specified, assume a total lost time of 4.0 to 5.0 seconds per phase. $L = \sum_{i=1}^n t_{Li}$
• $Y_i$ = critical volume-to-saturation flow ratio for phase $i$ ($Y_i = \frac{v_i}{s_i}$).
  • $v_i$ = design flow rate for critical lane group $i$ (veh/h).
  • $s_i$ = saturation flow rate for critical lane group $i$ (typically 1,900 passenger cars per hour of green per lane, adjusted for lane width, heavy vehicles, turning movements, and local factors).
• $\sum Y_i$ = sum of critical flow ratios for all phases in the cycle. For the signal to operate stably under pre-timed control, the sum of the critical flow ratios must be strictly less than 1.0 (typically $\le 0.85$ to avoid severe congestion).

Effective Green Time Allocation

Once the optimum cycle length is calculated, the total lost time ($L$) is subtracted to find the total effective green time ($G_e = C - L$). This time is then allocated to each phase proportional to its critical flow ratio: $g_i = \left( \frac{Y_i}{\sum Y_i} \right) \cdot (C - L)$ Where $g_i$ is the effective green time for phase $i$.

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Signal Phasing and NEMA Standards

Signal phasing organizes the order in which movements receive right-of-way. Modern traffic signal controllers use a ring-barrier diagram to organize these movements and prevent conflicting movements from occurring simultaneously.

Ring-Barrier Concepts

• Ring: A sequence of phases that run in order.
• Barrier: A physical divider separating major street movements from minor street movements. Phases in Ring 1 and Ring 2 that are on the same side of the barrier can run concurrently, but rings cannot cross the barrier independently.
• Standard NEMA phasing designates 8 movements:
  • Phases 2 & 6: Major street through movements.
  • Phases 1 & 5: Major street left-turn movements.
  • Phases 4 & 8: Minor street through movements.
  • Phases 3 & 7: Minor street left-turn movements.

Left-Turn Treatments

Left-turning vehicles conflict with opposing through traffic. Traffic engineers choose left-turn phasing based on volume, speed, and safety records:

1. Permissive left-turn phasing: Left-turning vehicles must yield to opposing through traffic and turn during the circular green phase. This is suitable for low volumes and low-speed streets.
2. Protected left-turn phasing: Left-turning vehicles have an exclusive green arrow phase while opposing through traffic is stopped. This is required for high left-turn volumes, high approach speeds, or when crossing three or more lanes.
3. Protected-permissive left-turn phasing: Left-turning vehicles have a protected green arrow phase followed by a permissive circular green phase.
4. Split phasing: One entire approach moves (through and left turns) while the opposing approach is stopped, then the opposing approach moves. Used when geometric constraints prevent simultaneous left turns.

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Traffic Signal Warrants

The Manual on Uniform Traffic Control Devices (MUTCD) governs the installation of traffic control devices. A traffic signal should only be installed if an engineering study shows that safety or operational conditions will improve, and at least one of the nine signal warrants is met:

1. Warrant 1: Eight-Hour Vehicular Volume: Met if minimum volumes are exceeded on both the major and minor streets for any 8 hours of a typical day.
2. Warrant 2: Four-Hour Vehicular Volume: Met if traffic volumes exceed a threshold curve for any 4 hours of a typical day.
3. Warrant 3: Peak Hour: Designed for locations with high peak hour traffic (e.g., manufacturing plants, office parks).
4. Warrant 4: Pedestrian Volume: Met if pedestrian volume crossing a major street is high and gaps are insufficient.
5. Warrant 5: School Crossing: Met if there are insufficient gaps at a school crossing location.
6. Warrant 6: Coordinated Signal System: Installed to maintain vehicle platooning and progression.
7. Warrant 7: Crash Experience: Met if five or more correctable crashes have occurred within a 12-month period, and volume thresholds of Warrants 1 or 2 are met at a 56% level.
8. Warrant 8: Roadway Network: Installed to encourage concentration of traffic on major routes.
9. Warrant 9: Grade Crossing: Installed near highway-rail grade crossings to manage queue lengths.

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Traffic Signs and Markings

The MUTCD defines standard shapes, colors, and retroreflectivity requirements to ensure that signs are easily recognized by drivers day and night.

Retroreflectivity

All traffic signs and pavement markings must maintain minimum retroreflectivity levels. Retroreflectivity is the property of a material to reflect light back toward its source (headlights back to driver's eyes), which is critical for night visibility.

Colors and Shapes

• Red: Regulatory prohibition (Stop, Yield, Wrong Way).
• Yellow: Warning (e.g., curves, pedestrian crossings).
• Orange: Temporary traffic control (construction zones).
• Black/White: Regulatory speed and lane commands (Speed Limit, One Way).
• Green: Destination guide and distance information.
• Blue: Roadside services (e.g., hospital, food, lodging).
• Brown: Cultural, historical, or recreational parks.
• Octagon: Exclusively reserved for Stop signs.
• Equilateral Triangle: Exclusively reserved for Yield signs.
• Pennant (sideways triangle): Exclusively reserved for No Passing Zone warning signs (placed on the left side of the roadway).
• Diamond: Warning of hazards ahead.

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Crash Analysis and Safety Metrics

Evaluating historical crash records allows engineers to identify safety hazards and measure the effectiveness of safety improvements.

Crash Rates

Simply counting crashes does not account for differences in traffic exposure. Crash rates normalize crash frequencies by exposure:

• Intersection Crash Rate ($R_{MEV}$): Expressed in crashes per million entering vehicles (MEV): $R_{MEV} = \frac{A \cdot 1,000,000}{EV \cdot 365}$ Where:
  • $A$ = number of crashes in a given period (usually 1 or 3 years).
  • $EV$ = Average Daily Entering Volume (veh/day), which is the sum of entering volumes on all approaches.
• Segment Crash Rate ($R_{HMVM}$): Expressed in crashes per hundred million vehicle miles traveled (HMVM): $R_{HMVM} = \frac{A \cdot 100,000,000}{365 \cdot ADT \cdot L \cdot N}$ Where:
  • $ADT$ = Average Daily Traffic on the segment (veh/day).
  • $L$ = length of the roadway segment (miles).
  • $N$ = number of years of data analyzed.

Crash Modification Factors (CMFs)

A crash modification factor (CMF) is a multiplicative factor used to compute the expected number of crashes after implementing a countermeasure: $N_{expected} = N_{observed} \cdot CMF$

• A CMF of 1.0 indicates that the countermeasure has no effect on safety.
• A CMF < 1.0 indicates a reduction in crashes (e.g., CMF = 0.85 means a 15% reduction in crashes).
• A CMF > 1.0 indicates an increase in crashes.
• Combined CMFs: If multiple independent countermeasures are applied to a site, their CMFs can be multiplied: $CMF_{combined} = CMF_1 \cdot CMF_2$.