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CE 2710: Transportation Engineering. Traffic Signals April 3, 2009 Nicholas Lownes, Ph.D. Traffic Signals – Why?. Increase throughput Reduce delay Improve safety Provide progression through network Help low volume roads. Source: www.flickr.com/photos/meckleychina/926962569/.

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CE 2710: Transportation Engineering

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Ce 2710 transportation engineering

CE 2710: Transportation Engineering

Traffic Signals

April 3, 2009

Nicholas Lownes, Ph.D.

Traffic signals why

Traffic Signals – Why?

  • Increase throughput

  • Reduce delay

  • Improve safety

  • Provide progression through network

  • Help low volume roads

Source: www.flickr.com/photos/meckleychina/926962569/

Current system

Current System

  • “It is estimated that improper traffic signal timing accounts for 5 to 10 percent of all traffic delay, or 295 million vehicle-hours of delay, on major roadways alone.”

What do they cost

What do they Cost?

  • Installation Cost: $75,000 - $500,000

    • Signal heads

    • Support structure (cable or cantilever)

    • Sensors

    • Wiring

    • Controllers

    • Labor

What do they cost1

What do they Cost?

  • Annual Maintenance: $3,000 - $8,000

    • Labor

    • Bulb replacement

  • Electricity: ≈$1,400/yr (Arizona DOT)

  • Update Signal timing: $2,500 - $3,100 per intersection per update

    • Should be done often – cheap way of improving operations

    • Labor-intensive

What do they cost2

What do they Cost?

  • Upgrade signal: $10,000 per intersection

    • Should be done every 10 years (National Traffic Signal Report Card)

  • Major Investment… not to be taken lightly.

  • Always consider alternatives.



  • Improve markings, signage, other (less expensive) control devices

  • If safety is concern:

    • use speed mitigation measures

    • Roadway lighting (if nighttime is major issue)

  • Restrict turning movements

  • Add turning lanes

When is a traffic signal warranted

When is a Traffic Signal Warranted?

  • Manual on Uniform Traffic Control Devices (MUTCD)

    • Available free online: http://mutcd.fhwa.dot.gov

  • National Minimum Standard for all traffic control devices on streets, highways and bicycle trails.


Signal warrants volume

Signal Warrants – Volume

  • #3 Peak hour (1 hour on average day)




  • How do you determine an average day?

    • Which day of the week?

    • What month of the year?

    • What type of weather?

Signal lingo

Signal Lingo

  • Phase: allotted time to a movement

  • Ring: Sequence of phases

    • Green phase (G)

    • Red phase (R)

    • Amber (yellow) phase (Y)

    • All-red phase (AR)

  • Cycle length (C) – time from start of green phase to green phase on an approach (typically 45-180 s)

    C = G + R + Y + AR

Nema ring barrier structure

NEMA Ring & Barrier Structure


Permissive lefts only 2 phase

Permissive Lefts Only (2 phase)


Split lefts 6 phase

Split Lefts (6 phase)

  • Split timing not usually the most efficient

Protected Left and Right

Permissive turns

Split phases

Dual lefts

Dual Lefts

Pedestrian Movements

LeadingDualProtected Left Turns

Papacostas & Prevedouros, 1993

Common question




For Show

Note: Oval size approximates the frequency of each type in practice

Pedestrian Volume

Common Question

  • How do pedestrian push-buttons work?

Goals of signal timing

Goals of Signal Timing

  • Minimize the # of Green phases

  • Maximize the # of vehicles moving through the intersection during all green phases

    • Keep as many traffic streams flowing at all times as possible

  • Minimize delay (shorter cycle lengths)

  • Maximize throughput (longer cycle lengths)

Types of signals

Types of Signals

  • Pretimed

  • Semi-actuated

  • Fully Actuated

  • Adaptive



  • Lengths of Phases predetermined and statically set

  • Strengths

    • Simplest

    • Less infrastructure (read: maintenance)

  • Weakness

    • Can not account for cycle-to-cycle variation of traffic

    • Will remain fixed until updated (which costs $)

Critical movements

Critical Movements

  • Left turns and right turns take longer

    • Protected left turns take a factor of roughly 1.6 times as long as a through movement

    • Unprotected lefts can take up to ten times as long (depending on opposing traffic)

    • Right turns take roughly 1.4 times as long

  • Critical movements are approach-by-approach

    • The maximum converted lane volume



For SB approach, critical volume is max{820, 640} = 820

820 vph (T)

640 vph (T)

For EB approach, critical volume is max{460, 340+120*1.4} = 508

460 vph (T)

340 vph (T) 120 vph (R)

Cycle length

Cycle Length

Lost Time = yellow + all-red

  • Rule of Thumb ≈ 45 – 180 s

  • Webster’s Method (min delay)

Critical volume for phase i

Saturation flow

Optimal Cycle Length

Saturation flow

Saturation flow

  • The Highway Capacity Manual (HCM) 2000 suggests 1900 vphpl as the base saturation flow rate

  • This baseline can be increased or decreased depending upon the situation Factors such as:

    • Lane width

    • Grade

    • Pedestrians

    • On-street parking



Assume: 2 phases, 3s Yellow for each

C1 = 820

C2 = 508

Allocating green time

Allocating Green Time

  • Minimum Pedestrian crossing phase

12’ lanes

4 ft/s peds

  • Need to make sure our green phases are at least 10 s

  • 7 second baseline from MUTCD – min walk interval

Green allocation

Green Allocation

  • Allocate Green time proportional to critical movement

  • Total Green time = Co – L = 41 s



  • Moving through a series of signals without stopping

  • Certain assumptions generally apply

    • You drive the speed limit (or the design speed)

    • Uncongested traffic

Source: http://www.minagarinc.com/red.jpg



  • Assumptions can be released, but it gets much more complex

  • Offset = time increment from appearance of base intersection green to green at intersection of interest

    • Offset should be multiple of ½ cycle length (for manual method at least)



  • Bandwidth = length of time in which one could arrive at intersection and achieve progression

    • Increases with cycle length

    • Decreases with increase in progression speed

    • Decreases with queue clearance

Ce 2710 transportation engineering

For Intersections, choose offset of 0 or ½ cycle placing beginning of green as close to sloping line as possible

Draw initial sloping line with slope ½ cycle per 1000 ft

Time (Cycles)



Distance (ft)


Ce 2710 transportation engineering

Then adjust line as needed

Time (Cycles)


Distance (ft)

Ce 2710 transportation engineering


Time (Cycles)


Distance (ft)

Ce 2710 transportation engineering


Time (Cycles)


Distance (ft)

Ce 2710 transportation engineering


Time (Cycles)


Distance (ft)

Ce 2710 transportation engineering

We’ve now determined offsets for each intersection

Time (Cycles)


Distance (ft)

Actuated signals

Actuated Signals

  • Most use Inductive-Loop Detectors in pavement

Source: FHWA

Source: www.richmond.ca/__shared/printpages/page2080.htm

Fully actuated

Fully actuated

  • Sensors/detectors on all legs of intersection

  • There is a pretimed framework that underlies an actuated intersection

  • Green Phase on an approach is requested (or extended) if presence of vehicle is detected.

  • Can enter the next phase in one of two ways:

    • Max out: the phase reaches its predetermined maximum

    • Gap out: no vehicle detected for a movement within some predetermined amount of time

Max out example green phase

Max Out –Example Green Phase

Not to scale

Max Green = 20s

Minimum Green = 10s

Green time remaining (s)




Green Extension = 4s

Time, t (s)


Vehicle arrives at t = 4, 5, 7, 16, 18 s

Gap out example green phase

Gap Out –Example Green Phase

Not to scale

Actual Green Phase = 14s

Max Green = 20s

Green time remaining (s)

Minimum Green = 10s




Green Extension = 4s

Time, t (s)


Vehicle arrives at t = 4 s



  • Signals are a major investment and their installation requires careful thought

  • We want to maximize throughput and minimize delay

  • We want to provide progression for signalized corridors

  • Pre-timed signals are simple & cheaper

  • Actuated can account for cycle-to-cycle variation



  • Pre-timed

    • Lower maintenance resources

    • Consistent demand

    • Simpler

  • Actuated

    • Significant variation in demand

    • High volume meets low volume road

    • Greater control

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