7.3 Actuated Phase Parameters, Minimum Green, Passage Time & Termination

7.3 Actuated Phase Parameters, Minimum Green, Passage Time & Termination

[!NOTE] IMSA Level III Examination Focus: Senior Traffic Signal Field Technicians are expected to configure, calibrate, and troubleshoot complex actuated controller timing databases. Understanding the interaction between vehicle detection geometry, passage time, maximum green limits, termination states (gap-out vs. max-out), recall modes, and volume-density algorithms is fundamental to maximizing intersection capacity, minimizing vehicular delay, and maintaining dilemma zone safety.

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1. Fundamental Actuated Phase Parameters & Operational States

Traffic signal actuation adapts signal timings dynamically to fluctuating vehicular demand. Actuated control falls into two primary categories:

1. Semi-Actuated Control: Vehicles on the major street receive continuous green without actuation; detectors are installed solely on minor cross-street approaches and left-turn bays. The controller dwells in major-street green until a side-street vehicle or pedestrian call interrupts.
2. Fully Actuated Control: Every approach (through lanes, left turns, and crosswalks) features dedicated detection. Phase green durations, cycle lengths, and sequence selections vary continuously in response to real-time traffic pulses.

The Actuated Phase Timing Cycle

An actuated green interval consists of three successive functional stages:

+-----------------------------------------------------------------------------+
|                        ANATOMY OF AN ACTUATED GREEN INTERVAL                |
+-----------------------------------------------------------------------------+
|                                                                             |
|   |<--- Minimum Green --->|<---------- Extensible Green --------->|         |
|   +-----------------------+---------------------------------------+-------+ |
|   |    Initial Interval   |     Passage Time (Unit Extension)     |Yellow | |
|   |   Guaranteed Display  | Resets with each vehicle actuation    |Change | |
|   +-----------------------+---------------------------------------+-------+ |
|                           ^                                       ^         |
|                           |                                       |         |
|                   Phase becomes                   Phase Terminates via:     |
|                     extensible                    - Gap-Out (Headway > PT)  |
|                                                   - Max-Out (Max Timer = 0) |
+-----------------------------------------------------------------------------+

Detector Memory Modes: Locking vs. Non-Locking

The controller's channel detector input can be programmed in one of two memory modes:

• Locking Memory (Memory ON): An actuation registered during yellow or red is remembered (latched) by the controller until that phase is serviced, even if the vehicle turns right on red or drives away. Locking mode is mandatory for point/pulse detectors (such as small 6 ft x 6 ft advance loops located 300 feet upstream) where a vehicle briefly trips the sensor and then vacates it.
• Non-Locking Memory (Memory OFF): The controller drops the call if the vehicle leaves the detection zone before green is displayed. Non-locking mode is standard industry practice for stop bar presence loops (e.g., 6 ft x 40 ft or 6 ft x 50 ft loops in turn lanes). If a right-turning vehicle arrives on red, stops, finds an acceptable gap, and executes a legal Right-Turn-On-Red (RTOR), the call automatically drops, eliminating an unnecessary green phase for an empty lane.

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2. Minimum Green ($G_{\min}$) Calibration & Detector Setback Dynamics

Minimum Green ($G_{\min}$) is the shortest duration for which a green signal indication can be displayed once initiated. It is an absolute controller constraint that cannot be truncated by gap-out or preemption.

Engineering Objectives of Minimum Green

1. Driver Expectancy & Perception: Prevents "green flashes" or abrupt signal changes that startle motorists and cause rear-end collisions.
2. Queue Dissipation: Allows standing vehicles queued between the stop line and the advance detector to accelerate and enter the intersection.
3. Pedestrian Safety in Absence of Pushbuttons: If pedestrian signal heads and pushbuttons are not present on an actuated approach, the vehicular Minimum Green must be programmed to provide adequate pedestrian crossing clearance ($G_{\min} \ge \text{Walk} + \text{FDW}$).

Typical Minimum Green Ranges

• Protected Left Turns: 4.0 to 7.0 seconds (short queues, high driver vigilance).
• Minor Cross-Street Through: 7.0 to 10.0 seconds.
• Major Arterial Through: 10.0 to 15.0 seconds (higher driver expectancy, higher approach speeds).

Mathematical Calculation for Advance Point Detection

When detection relies on an advance point detector located at distance $d$ from the stop line: $G_{\min} = t_{\text{startup}} + h_s \cdot \left(\frac{d}{s_v}\right)$ Where:

• $t_{\text{startup}}$ = Driver startup perception-reaction lost time = $2.0\text{ to } 3.0\text{ seconds}$.
• $h_s$ = Saturated queue discharge headway = $2.0\text{ seconds/vehicle}$.
• $d$ = Distance from stop line to advance detector (feet).
• $s_v$ = Average vehicle queue storage space = $25.0\text{ feet/vehicle}$.

Field Example: On a 45 mph approach with an advance loop at $d = 200\text{ feet}$: $\text{Queued Vehicles } N = \frac{200\text{ ft}}{25\text{ ft/veh}} = 8\text{ vehicles}$ $G_{\min} = 2.5 + (2.0 \times 8) = 18.5\text{ seconds}$ (Note: As analyzed under volume-density control in the next section, providing an 18.5-second fixed minimum green every cycle causes excessive delay during off-peak periods; volume-density variable initial timing resolves this issue).

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3. Passage Time (Unit Extension) & Dilemma Zone Protection

Passage Time ($PT$), also referred to as Unit Extension or Vehicle Extension, is the time allocated to a vehicle to travel from the detector to the stop line. In addition, it defines the maximum allowable headway (MAH) between consecutive vehicles required to maintain the phase in green: $\text{MAH} = PT$

Reset Timing Logic

During the extensible portion of green (after Minimum Green has elapsed):

1. The Passage Timer starts at $PT$ and counts down toward zero.
2. Every time a new vehicle actuation occurs, the Passage Timer instantly resets back to the programmed $PT$ value and resumes counting down.
3. If a subsequent vehicle arrives before the timer reaches zero, the green is successfully extended.

Determination of Passage Time

For an advance detector located at setback distance $d$ on an approach with operating speed $v$ (in $\text{ft/s}$): $PT = \frac{d}{v}$

• Example: Approach speed $= 40\text{ mph} = 58.7\text{ ft/s}$, advance detector at $d = 180\text{ ft}$: $PT = \frac{180}{58.7} = 3.06\text{ s} \approx 3.1\text{ s}$
• Stop Bar Presence Detection: With a long $50\text{-foot}$ loop at the stop line, vehicles occupy the loop continuously as they enter. Consequently, Passage Time is set very low—typically $0.0\text{ to } 2.0\text{ seconds}$—to ensure the phase terminates immediately once the last queued vehicle clears the zone.

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4. Phase Termination Mechanics: Gap-Out vs. Max-Out

The fundamental operational conflict in actuated control is balancing the efficiency of the active phase against the waiting delay of conflicting movements.

+-----------------------------------------------------------------------------+
|                        GAP-OUT vs. MAX-OUT MECHANICS                        |
+-----------------------------------------------------------------------------+
| SCENARIO A: GAP-OUT (EFFICIENT PLATOON TERMINATION)                         |
|   Active Phase Green                                                        |
|   Veh 1 ---> [Detector] ---> Veh 2 ---> [Detector]                          |
|              (Timer Reset)              (Timer Reset)                       |
|                                                        ... [No Vehicle] ... |
|                                                        Passage Timer -> 0.0s|
|   RESULT: Green terminates cleanly. Phase transitions to Yellow.             |
|   Safety: Trailing vehicles are far back and can stop comfortably.          |
|                                                                             |
| SCENARIO B: MAX-OUT (SATURATED CONFLICTING DEMAND)                          |
|   Conflicting call arrives on side street ---> Max Green Timer begins: 45s  |
|   Veh 1 -> Veh 2 -> Veh 3 -> Veh 4 -> Veh 5 (Passage Timer keeps resetting)|
|   Continuous traffic maintains green ... until Max Timer counts to 0.0s!    |
|   RESULT: Green is FORCEFULLY TRUNCATED while vehicles are moving.          |
|   Safety: High risk! Trailing vehicle caught in dilemma zone.               |
+-----------------------------------------------------------------------------+

Gap-Out Dynamics

• Definition: The passage timer reaches $0.0\text{ seconds}$ because the time headway between successive vehicles exceeds the programmed Passage Time.
• Operational Status: Represents an orderly, efficient transfer of right-of-way. The platoon has passed; the queue has discharged.
• Safety Profile: High. Because the headway between the last vehicle and any approaching vehicle exceeds the passage time, approaching drivers are upstream of the dilemma zone and can execute a smooth, comfortable stop.

Max-Out Dynamics

• Definition: The continuous arrival of vehicles repeatedly resets the passage timer, holding the phase in green until the Maximum Green Timer ($G_{\max}$) expires in the presence of a waiting conflicting actuation.
• The Conflict Requirement: The Maximum Green timer DOES NOT run unless a call exists on a conflicting phase. In the absence of conflicting calls, a phase can extend indefinitely without maxing out.
• Safety Hazard: Severe. Involuntary truncation occurs while vehicles are traveling at full speed through the dilemma zone. Drivers who expected the signal to remain green are suddenly confronted with a yellow change, dramatically elevating the incidence of red-light running, emergency skid stops, and rear-end collisions.
• Field Diagnostic Rule: If an actuated phase consistently maxes out during off-peak or light-traffic hours, the technician must inspect for:
  1. A defective, shorted, or chattering loop detector generating continuous false actuations.
  2. Excessive passage time programming (e.g., $PT = 5.0\text{ s}$ on a stop-bar presence loop).
  3. An unintended controller recall mode (e.g., phase locked in Maximum Recall).