**Principles of Intersection Signalization**

**Component of a Signal Cycle**

**Types of Signal Operation**

**Right and Left Turns**

**Critical Movement Analysis**

**Measuring Delay**

**Introduction**

Assuming that traffic signal is warranted...

Credit: 2009 MUTCD

Example of a signal phasing plan

Credit: GDOT Signal Design Guidelines, Example plan set

The intersection signal design process interacts with geometric design, placement of detectors and signal hardware

Signal Design Policy and User Groups

Credit: Signal Design Handbook

(http://ops.fhwa.dot.gov/publications/fhwahop08024/fhwa_hop_08_024.pdf

Methodologies to plan, design and operate traffic signals

Credit: STM

Field data is collected on existing traffic signal phasing, timing and traffic volumes in preparation for a signal timing plan.

Image credit: STM

Traffic volume data is collected in order to prepare (weekday and weekend) signal timing plans. Note the relationship between volume peaking and cycle length.

Image credit: STM

Example of signalization analysis using Highway Capacity Software (HCS)

Credit: Alexandra Frackelton

Signal timing projects can be evaluated using a before-after study (Example of speed and delay before and after signal timing change)

Credit: STM

Signal Interval

Signal Phase

Signal Cycle

One complete rotation through all of the indications provided

The cycle length is the time (in seconds) to complete one full cycle, represented as

C

A period of time during which no signal indication changes

Change ("yellow") interval

Clearance ("all red") interval

Green interval

Red interval

Pedestrians and Bicyclists

Transit Riders

Automobile and Freight Drivers

Adapted from STM

Pedestrian/Bicyclist Focused Signal Policy

Shorter cycle lengths

Extended crossing time

Bicycle/pedestrian detection

Exclusive pedestrian phasing

Leading pedestrian interval

A non-motorized signal timing policy may be appropriate in areas with high pedestrian traffic (i.e. downtowns)

Image credit: Flickr

Transit Focused Signal Policy

Signal preemption for high importance modes

Signal priority for strategic transit routes

Extended pedestrian crossing time

Exclusive pedestrian phasing

Leading pedestrian interval

A transit focused signal timing policy may be appropriate in areas along transit corridors or near transit stations

Image credit: Wikimedia (Chinatown, Toronto)

Automobile/Freight Focused Signal Policy

Avoid cycle failure

Maintain progression on coordinated systems

Use appropriate cycle lengths

Ensure appropriate pedestrian signal timing

A non-motorized signal timing policy may be appropriate in areas with high automobile/freight traffic or facilities of regional importance.

Image credit: http://aug-cdn.com/sites/default/files/imagecache/superphoto/editorial/images/spotted/73/732821.jpg

Credit: 2009 MUTCD

Example of the relationship between vehicular phase intervals and pedestrian intervals

Set of intervals that allows a movement to flow and be halted before conflicting movements are released

Green interval

Change interval

Clearance interval

Pretimed Operation

Cycle length, phase sequence and timing are constant

Signal controller establishes pretimed settings for different time periods (i.e. AM peak, PM peak, off-peak)

Semi-Actuated Operation

Detectors placed on minor approaches

Light is green on major street unless an actuation is noted on minor approaches

Often used where reason for signalization is "interruption of continuous traffic"

Fully Actuated Operation

All approaches monitored by detectors

Cycle length and phase sequence may vary from cycle to cycle

Credit: STM

Permitted Left Turn

Left-turning traffic must yield to vehicle and pedestrian through movements

Protected Left Turn

Left turning movement is made without an opposing vehicular flow on a green arrow display

Protected-Permissive

Left-turning drivers have the right-of-way during the protected left-turn phase.

They can also complete the turn "permissively" when the adjacent through movement receives its circular green indication

Example of a permitted left turn phase

Image credit: http://safety.fhwa.dot.gov/intersection/resources/casestudies/fhwasa09015/.

Credit: STM

Example of a protected left turn phase

Image credit: http://safety.fhwa.dot.gov/intersection/resources/casestudies/fhwasa09015/

Credit: STM

Credit: 2009 MUTCD

Credit: STM

http://www.cdeep.iitb.ac.in/nptel/Civil%20Engineering/Transportation%20Engg%20I/41-Ltexhtml/p6/

The traffic stream at a signalized intersection

is conceptualized as a queueing system

When the light turns GREEN, there is a queue of stored vehicles waiting to be discharged (i.e. the traffic signal functions as the queue restriction in this conceptual diagram).

Image credit: Wikimedia (http://commons.wikimedia.org/wiki/File:Queue_System.PNG)

The first headway is the time between the initiation of the GREEN indication and when the front wheels of the first vehicle cross the stop line.

By the fourth or fifth headway, headways level out and a stable moving queue is established (this constant headway achieved is the saturation headway h).

Signalized Intersection

Capacity Concepts

Discharge and

Saturation Headways

Lost Time and Effective GREEN Time

Start-Up Lost Time

Clearance Lost Time

Concept of Effective GREEN Time

Intersection Lane Capacity Analysis

Intersection lane capacity is measured as the proportion of the cycle length that is effective green time (the "green ratio")

Saturation Flow Rate

Capacity of the approach lanes if the signal were always GREEN

Flow Departing a Queue at a Signalized Intersection

Total Lost Time

Image credit: STM

*The HCM defines a default value of 4 s/phase for total lost time

Effective GREEN Time

Where g is the effective green time, G is the actual green interval, Y is the actual yellow interval, and R is the actual red interval.

Intersection Lane Capacity Equation

Where c is the capacity, s is the saturation flow rate (vph), g is the effective green time (s), and C is the cycle length (s).

Illustration of volume and capacity

Image credit: STM

An Example Problem

C = 60 s

G = 27 s

Y = 4 s

h = 2.4 s/v

l(1) = 2 s

l(2) = 2 s

**Measuring Traffic Flow**

Critical-Lane and Time-Budget Concepts

The Time Budget

Signal control allocates time to different vehicular and pedestrian movements

The Critical Lane

Identify the movements with the most intense traffic demand, which will control the timing of a given phase

One and only one critical lane per phase

Maximum Sum of Critical-Lane Volumes

The maximum sum of critical-lane volumes is a "general measure" of intersection capacity

May be derived using the total lost time and saturation flow rate

Finding an Appropriate Cycle Length

Example Problem

Determine the number of lanes required for each critical movement

Determine minimum desirable cycle length

Total Lost Time and Effective Green Time

Lost Time per Signal Cycle

Lost Time per Hour

Effective Green Time per Hour

Maximum Sum of Critical-Lane Volume

Lost Time per Cycle

Effective Green Time for Critical Lane Movement per Hour

Lost Time per Hour

Critical-Lane Volume, Cycle Length

and Number of Phases

Plot of maximum sum of critical lane volumes:

relationship between "capacity," cycle length and number of phases.

Minimum Acceptable Cycle Length

If demand is known and critical lanes are identified, the minimum cycle length is calculated by solving the previous equation for C.*

*This equation assumes that demand is uniformly distributed throughout the hour.

The minimum cycle length equation is modified to account for peaks in demand

Estimate the flow rate in the peak 15-minute period using a known Peak Hour Factor

Accommodate need for excess capacity due to variation in demand using a v/c ratio

Desirable Signal Cycle Length

Relationship between desirable cycle length

and maximum sum of critical-lane volume

Sample Problem Given Data

C = 60 s

Lost time = 4 s/phase

2 phases

PHF = 0.95

target v/c = 0.90

h = 2.3 s/veh

SB volume = 1,200 veh/h

EB volume = 1,800 veh/h

Modeling Left Turns

Left-turning vehicles use more effective green time than through vehicles

Models account for this by expressing left turning traffic in "through vehicle equivalents" for the same amount of time passing through the intersection

Left Turn Equivalency, Opposing Flow & Number of Lanes

Consider a two-lane intersection with 10% left-turning vehicles, a LTE of 5.0 and a saturation headway (h) of 2 s/veh. What is the average saturation flow rate?

Adjusting for Left-Turn in Saturation Flow Rate

HCM Approach to Left-Turn Adjustment

The Highway Capacity Manual utilizes a left-turn adjustment factor that converts an ideal saturation flow rate to a saturation flow rate for prevailing conditions (i.e. adjusting for left-turn volumes)

**Left Turn Equivalency**

Example of Left-Turn Equivalency Concept

Consider a situation where 11 through vehicles are equal to 5 through vehicles plus 2 left-turning vehicles

Therefore, for these prevailing conditions, the left-turn equivalent is 3.0

Each left turn consumes 3 X the effective green time

LTE increases as opposing flow increases

LTE decreases as the number of opposing lanes increases, but non-linearly

Example Calculations

10% of the traffic stream has a saturation headway of 10 s/veh (2 X 5)

90% of the traffic stream has a saturation headway of

2 s/veh

A Note

The left-turn equivalency concept is also used to model

Right turns

Heavy-vehicle traffic

Local-bus traffic

Delay as a Measure of Effectiveness

Delay is used to characterize the operational quality of a signalized intersection

The amount of time consumed in traversing the intersection

Departure Time - Arrival Time

Types of Delay

Basic Theoretical Models of Delay

Inconsistencies in Random and Overflow Delay

Delay Models in the 2000 HCM

Stopped-time delay

Stopped in queue waiting to pass through intersection

Approach delay

Includes approach speed and acceleration to desired speed

Time-in-queue delay

Until discharge across the STOP bar

Travel time delay

Difference between expected and actual travel time

Control delay

Delay caused by a traffic control device

Illustration of Delay Measures

Figure 20.10

A uniform vehicle arrival rate (v) is assumed

W(i): Total time that any vehicle (i) spends waiting in the queue

Q(t): Total number of vehicles queued at any time (t)

The aggregate delay is the area between the arrival and departure curves (vehicles X time)

Three Types of Intersection Operation

Stable flow

No signal cycle failure

Uniform delay

Credit: Pearson Higher Education, 2011

Credit: Pearson Higher Education, 2011

Overall period of analysis is stable (demand does not exceed capacity)

Some signal cycle failure but capacity "catches up" to demand

Overflow delay

Credit: Pearson Higher Education, 2011

Majority signal cycle failure

Demand (arrival) outpaces capacity (departure)

Overflow delay component > uniform delay component

When demand exceeds capacity (v/c > 1.00), delay depends on the length of time that the condition exists

Components of Delay

Uniform Delay

Uniform arrivals

Stable flow

No cycle failure

Random Delay

Additional delay due to random distribution of flow at isolated intersections

Overflow Delay

Image credit: Pearson Higher Education, 2011

Additional delay due to greater demand than capacity

Adjustment to uniform or random delay needed due to the existence of platooned arrivals due to signalization

Webster's Uniform Delay Model

Modeling Random Delay

Modeling Overflow Delay

Credit: Pearson Higher Education, 2011

Illustration of Webster's Uniform Delay Model

Formula for the area of the aggregate delay triangle

Webster's equivalence for length of the RED phase:

Determining the time it takes for the queue to clear by setting arrivals equal to departures:

Substituting for t:

Substituting for R:

Formula for aggregate delay:

Average uniform delay per vehicle:

A form using capacity rather than saturation flow rate:

Note: the maximum value of X (v/c) is 1.00

Uniform delay model assumes uniform arrivals and no signal cycle failure, but vehicle arrivals are likely to be random

Random delay models assume a Poisson distribution of arrivals

Webster's random delay model:

Formulation for total delay (sum of uniform and random delay) which corrects for slight overestimation of delay:

Oversaturation

For a period where v/c > 1.00, delay consists of uniform and overflow delay

Uniform delay formula, substituting 1.00 for X given the oversaturated condition:

Derivation of the Overflow Delay Formula

Image credit: Pearson Higher Education, 2011

Image credit: Pearson Higher Education, 2011

Credit: Pearson Higher Education, 2011

Observed equivalency between left-turning and through vehicles

Credit: Pearson Higher Education, 2011

Credit: Pearson Higher Education, 2011

Credit: Pearson Higher Education, 2011

Credit: Pearson Higher Education, 2011

Average overflow delay is calculated by dividing the aggregate delay by the number of vehicles discharged within time T:

The resulting model for average delay per vehicle:

Credit: Pearson Higher Education, 2011

Both the random delay model and the overflow delay models are inconsistent when the v/c ratio reaches 1.00

The uniform delay model is sufficient when v/c is 0.85 or less

The overflow delay model is sufficient when v/c is 1.15 or greater

A commonly used model for bridging the gap between the uniform and overflow delay models:

The delay model in the 2000 HCM incorporates:

uniform delay model

overflow delay model

Factor incorporating delay from the existing queue

A progression factor adjusting for the effect of platooned arrivals

Note: the 2010 HCM replaces this traditional delay model with Incremental Queue Analysis (IQA).