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Principles of Intersection Signalization

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on 7 April 2014

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Transcript of Principles of Intersection Signalization

Principles of Intersection Signalization
Component of a Signal Cycle
Types of Signal Operation
Right and Left Turns
Critical Movement Analysis
Measuring Delay
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
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
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
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
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:
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).
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