6. signalized Intersections 1 Traffic Management and Control (ENGC - - PDF document

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

• 6. signalized

Intersections

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

1. HCM 2000, chapter 16 2. safety.fhwa.dot.gov/intersection/signalized/sig_int_pps051508

References

/short/sigint_short.ppt 3. mason.gmu.edu/~aflaner/CEIE_360/Signalized%20Intersectio n_ch7_part_1_student.ppt 4. Sarraj, Y. and Almasri , E. 2007, Advanced traffic engineering, lecture notes. Note:

• some slides are quoted from given references.
• text is from HCM.

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4-way Intersection Conflicts

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conflict points

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Objectives of Signal Timing

• Minimize delay
• Minimize delay
• Minimize conflicts
• Maximize capacity
• Reduce crashes

Each objective leads to a different solution We must find an appropriate compromise

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Warrants for the use of traffic signals

A decision on the installation of traffic signals may A decision on the installation of traffic signals may be made on the basis of:

Traffic flow Pedestrian safety Accident experience And the elimination of traffic conflict.

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Warrants for the use of traffic signals

Quick guide:

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Quick guide: For traffic flow:

Traffic signals are justified if the following traffic flow exists for eight hours on an average day.

1 2 4

Flow on the major road (1+2) ≥ 900 vehicles/hour and Flow on the minor road (3) or (4) ≥ 100 vehicles/hour.

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Warrants for the use of traffic signals

For Pedestrian safety: For Pedestrian safety:

Signal control offers considerable assistance to pedestrian movements. The Department of Transport in the UK advises that a pedestrian stage is required:

• 1. if pedestrians across any arm of the junction is ≥ 300

ped./hour ped./hour

• 2. or if turning traffic flow into any arm has an average

headway of < 5 seconds and conflicting with a pedestrian flow of ≥ 50 pedestrian/hour

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Signal aspects

The indication given by a signal is known as the signal aspect. g y g g p The usual sequence of signal aspects or indications in the UK and USA is:

In UK

• Red
• Red/Amber

In USA

• Red
• Green and
• Green and
• Amber
• Amber

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Meaning of traffic signal indications

Color

Red Red-Amber Green Amber Signal indication

Meaning

Stop & keep stopping Prepare to go but do not move Go Clear the intersection but do not cross the stop line

Duration (s)

2 3

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Cycle: a complete rotation through all the indications provided. Every legal movement

Terms

p y g receives a “green” Cycle Length (C): time (seconds) for the signal to complete one full cycle. Interval: an interval of time during which none

• f the lights at a signalized intersection changes

Ch i t l ll i di ti f i Change interval: yellow indication for a given movement

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Terms

Clearance interval: all red, after yellow Green interval: green indication for a Green interval: green indication for a particular movement Red interval: red indication for a particular movement All-Red: red indication for all approaches Phase: the aspect of a cycle allocated to one the aspect of a cycle allocated to one

• r more streams of traffic
• r more streams of traffic

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Example: “T” intersection of two

• ne-way streets

Cycle: a complete rotation through all the indications g

• provided. Every legal

movement receives a “green” Cycle length: 20 + 3 + 30 sec = 53 sec

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Permitted Left Turns: a permitted left turn receives a

Terms

p “green” ball but must yield right of way to opposing movements, used when left turn movements are reasonable and gaps in

• pposing traffic flow are

adequate

http://www.drivingschool.ca/drivereducation/page16.html

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Protected Left Turns:

Terms

provided separate phase, left turn movements are protected by arrow, left turns

• n one-way or T-intersection

are considered “protected” within that phase

http://www.drivingschool.ca/drivereducation/page16.html

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Protected/Permitted : left turns are given

Terms

left turns are given permitted for part of the cycle and then protected for another part of the cycle or protected and then permitted

Image source: http://www.fhwa.dot.gov/aard/signals.gif

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Types of Signal Timing

• Isolated Signals:
• Fixed / Pretimed
• Fixed / Pretimed

Signals which have a designated cycle which does not change regardless of flow or time of day

• Semi-actuated

Signals in which a major flow sees green unless: a detector on a minor approach is triggered AND a preset, minimum green time is exceeded on the major approach

F ll t t d

• Fully actuated

Signals in which current flow sees green unless: a detector is triggered AND the preset, minimum green time is exceeded on the current approach OR the preset, maximum green time is exceeded

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Design Process (Webster’s Method)

• Collect Traffic Variables:
• Hourly volume
• Peak hour volumes for all movements
• Peak 15-min volumes for all movements
• Design
• Design

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Isolated Intersections

• Basic Timing Elements:
• Green: Green time

Green: Green time

• Yellow: Yellow time
• Effective Green: Green + Yellow – time vehicles are

discharging

• All-Red: All movements have red
• Intergreen time: Yellow + All-Red
• Pedestrian WALK: 4-7 seconds when sign says WALK
• Pedestrian crossing time (PCT): time required for a

pedestrian to cross the intersection

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General Approach for Signal Timing (step1)

Select phasing plan

• Select phasing plan
• Calculate design flow rate using peak hour

volume and PHF

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Peak Hour Factor (PHF)

• Design Hourly Volume (DHV):

DHV = (Peak-Hour Volume / PHF) Design Hour Volume is the one hour traffic volume used as the basis of design volume used as the basis of design (usually as a prediction of a future condition)

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Design Hour Volume

PHF Adjusts volume to match peak 15 minutes j p PHF = 0.85 Calculated Volume = 1200 v/hr DHV=1,200 vph = 1,411 vph 0.85

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General Approach for Signal Timing (Step2)

• Find the critical movements or lanes and

calculate the critical flow ratios

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Lane Group

• Separates traffic into consecutive movements
• Lane group

g p

– set of movements that has same green phase and move together – Can be one or more lanes

• Guidelines for deciding lane groups:

– use separate lane groups for exclusive left-turn lane(s) unless a shared left-through also exists for the unless a shared left-through also exists for the approach – use separate lane groups for exclusive right-turn lane(s) unless a shared right-through also exists for the approach

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Lane Group

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Saturation Flow Rate

service rate: maximum vehicles that can service rate: maximum vehicles that can be served in 1 hour assuming continuous green and a continuous queue of vehicles

• Represents capacity for the lane group

h i l t ti d

• when signal turns green – reaction and

delay time as vehicles start up, then flow becomes uniform – headway becomes uniform

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Saturation Flow Rate

• sat. flow can be determined directly in

the field or calculated

• ideal so = 1,900 pcphgpl (passenger

cars per hour of green per lane) cars per hour of green per lane)

• adjust so to reflect non-ideal conditions

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Saturation Flow Rate

Number of vehicles that could enter the intersection after initial startup if constant queue p q existed and constant green s = _3600_(sec/hour) h where: s = saturation flow rate in vehicles per hour of green per lane(vphgpl) green per lane(vphgpl) h = saturation headway (seconds)

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prevailing saturation flow for a specific lane group: s = so * N * fw * fHV * fg * fp * fbb * fa * fLU * fLT * fRT * fLbp * fRbp N = number of lanes in lane group fw = lane width adjustment factor fHV = heavy vehicle adjustment factor fg = grade adjustment factor fp = parking adjustment fbb = bus blockage factor ffa = area type Ideal saturation flow rate is adjusted to represent all the factors for the lane group which decrease capacity (non-ideal conditions)

LU = lane utilization factor

fLT = left turn adjustment factor fRT = right turn adjustment factor fLbp = pedestrian and bike adjustment factor for left turn movement fRbp = pedestrian and bike adjustment factor for right turn movement )

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See Appendix D in Chapter 16 of HCM of more details for pedestrian and bicycle blockage

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Example of pedestrian blockage

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Critical Lane Group

• For a given phase: several lanes of traffic on one or

For a given phase: several lanes of traffic on one or more approaches move simultaneously

• One of those movements has the most intense traffic
• One lane (movement) requires the most time, all
• thers require less
• Becomes the “design” lane
• If sufficient time is given to the critical lane, all other

If sufficient time is given to the critical lane, all other lanes moving within the phase will be accommodated

• Only one critical lane (movement) per phase

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Critical Movement or Lane

• Movement that requires the most time to

execute execute

• If phase is long enough for the most

critical movement, other movements in phase will be serviced as well

• Can be determined using flow ratios
• Movement with highest flow ratio is critical

movement (ratio of flow to saturation flow)

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Flow Ratio

• Flow ratio =

actual flow

• Flow ratio = ___actual flow___

saturation flow rate

Flow = 1,200 vph Saturation flow = 1500 vph Flow ratio = ____1,200 vph_____ = 0.80 1,500 vph Same as volume/capacity

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Critical Lane Example Critical Lane Example

• Find critical lanes for each phase

(v/s)north = 250/1700 = 0.15

Phase 1 Phase 2

(v/s)

t = 750/1700 = 0 44

( / ) 600/1700 0 35 (v/s)west 750/1700 0.44 (v/s)south = 300/1700 = 0.18 (v/s)east = 600/1700 = 0.35

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Critical Lane Example Critical Lane Example

• v/s for critical lane group

(v/s) = 0 44 (v/s)west 0.44 (v/s)south = 0.18

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Example

For a NB/SB phase the following flows and saturation flow rates are available Movement Design Flow Rate (pcu/hr) Sat Flow Rate (pcu/hr) Movement Design Flow Rate (pcu/hr) Sat Flow Rate (pcu/hr) NB L,T 600 1200 NB R,T 500 1700 SB L,T 450 1330 SB R,T 720 1600 Which is the critical lane movement? What is the critical flow ratio? Solution: for NB L,T flow ratio = 600/1200 = 0.5 Movement Flow Ratio NB L,T 0.50 NB R,T 0.29 SB L,T 0.34 SB R,T 0.45

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General Approach for Signal Timing (step 3)

• Calculate intergreen time

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Intergreen Time

Determined based on

The intergreen period of a phase consists of both the yellow (amber) indication and the all-red indication

Determined based on:

Stopping Sight Distance Intersection clearance time Pedestrian crossing time – if there are no

pedestrian signals (will discuss under minimum green) g ee )

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Examples of inter-green periods at a two-phase traffic signal

Intergreen Time

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Examples of inter-green periods at a two-phase traffic signal

Intergreen Time

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First we calculate the minimum safe stopping

Calculation of Intergreen Time

First, we calculate the minimum safe stopping

• distance. The equation for this distance is given below .

Minimum Safe Stopping Distance:

SD = 1.47*Vo*tr + (1.47*Vo)2/(30*[f ± G])

Where: SD = Min safe stopping dist (ft) SD = Min. safe stopping dist. (ft) Vo = Initial velocity (mph) tr = Perception/Reaction time (sec) f = Coefficient of friction G = Grade, as a percentage

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Next, we calculate the time required for a vehicle to

Calculation of Intergreen Time

Next, we calculate the time required for a vehicle to

travel the minimum safe stopping distance and to clear the intersection. This is simple kinematics as well. Intersection Clearance Time:

T = (SD + L + W)/(1.47*Vo)

Where: Where: T = Intersection clearance time (sec) Vo = Initial velocity (mph) L = Length of the vehicle (ft) SD = Min. safe stopping dist. (ft) W = Width of the intersection (ft)

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Calculation of Intergreen Time

Now that you’ve determined the first two elements of the

intergreen period length

• stopping distance and
• intersection clearance time

you need to consider the pedestrians. The intergreen time for intersections that have signalized pedestrian movements is the same as the intersection clearance time.

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Calculation of Intergreen Time

If you have an intersection where the pedestrian movements y p are not regulated by a separate pedestrian signal, you need to protect these movements by providing enough intergreen time for a pedestrian to cross the intersection. In other words, if a pedestrian begins to cross the street just as the signal turns yellow for the vehicular traffic, he/she must be able to cross the street safely before the next phase y p

• f the cycle begins.

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Calculation of Intergreen Time

The formula for this calculation is shown below. Pedestrian Crossing Time:

PCT = W/V

Where: PCT = Pedestrian crossing time (sec) W = Width of the intersection (feet) V = Velocity of the pedestrian (usually 4 ft/sec)

The intergreen time is equal to whichever is larger, the pedestrian crossing time or the intersection clearance time.

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General Approach for Signal Timing (step 4)

• Calculate the optimum cycle length

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Cycle Length

• Cycle should be long enough to serve

critical movements but no longer

• If cycle is too short

inefficient because of

• If cycle is too short -- inefficient because of

time lost to too many changes high compared to usable green time

• If too long, delays will be lengthened as

vehicles wait

• Several ways to calculate optimum cycle

y p y length

• Webster's:

– most common – minimizes intersection delay – Gives optimum cycle length as a function of lost time and critical flow ratio

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Cycle Length

Co = 1.5L + 5 1 - Σ(Yi)

where: Co = optimum cycle length L = sum of the lost time for all phases Yi = ratio of the design flow rate to the saturation flow rate for the critical approach or lane in each phase cycle length should be increased to the nearest multiple of 5 seconds

• nce have cycle length subtract intergreen time allocate

green based on critical movements

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Lost Time

• Some time is “lost” as vehicles start up

Some time is lost as vehicles start up from a stop until vehicles are progressing at the saturation flow rate through the intersection

• Vehicles utilize some the yellow interval

so this adds to the actual time available to vehicles

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Start up lost time

• Average headway
• Average headway

is greater than h

• First 3 or 4

vehicles at signal require more time q to react and accelerate than subsequent

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Start up lost time

• h = saturation headway (seconds)
• Average headway for first few vehicles in

queue > h

• Start up lost time
• l1 = ∑∆i

h – where – l1 = start-up lost time (sec/phase) – ∆i = incremental headway (time > h) for vehicle i

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Time to discharge Queue

• Green time to discharge queue of vehicles
• T = l1 + nh

Tn l1 + nh

• Where
• Tn = GREEN time to move queue of n

vehicles through signalized intersection for phase

• l1 =start-up lost time
• n = number of vehicles in queue
• n = number of vehicles in queue
• h = saturation headway (s/veh)

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Clearance Lost time

• Lost time associated with stopping queue

t d f GREEN i l (l2) at end of GREEN signal (l2)

• Difficult to observe in field
• Time between last vehicle’s front wheels

crossing stop line and initiation of GREEN for next phase for next phase

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Total lost time

• Lost time due to vehicles starting up at

beginning of green and vehicles stopping at end beginning of green and vehicles stopping at end

• f green
• tL = l1 + l2
• Where:
• tL = total lost time (sec/phase)

tL total lost time (sec/phase)

• l1 = start-up lost time (sec/phase)
• l2 = clearance lost time (sec/phase)

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Lost Time for Phase i

li = G i + y – G i li = Gai + y Gei Where: li = lost time for phase i Gai = actual green time for phase i y = yellow interval for phase I Gei = effective green time for phase i

ei

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Lost time includes start-up delay plus any portion

• f yellow not used for vehicle movement

Image source: http://hcmdev.kittelson.com/Case1/popup_terms/effgreen_popup.htm

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Effective green time

• Amount of time during cycle that vehicles are moving for

a particular movement p – g1 = Gi + Yi – tLi – Where: – g1 = effective green time (sec) for movement i – Gi = actual green time (sec) for movement i – Yi = sum of yellow interval for movement i

• tLi = total lost time for movement i
• Yi = yi + ari
• Where:
• yi = yellow interval for movement i
• ari = all red interval for movement i

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Effective Red time

• Amount of time vehicles for a particular

t t i movement are not moving

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Total Lost Time

• Total lost time for a cycle is given by:

L = Σli + R Where L = lost time per cycle li = lost time for phase i

i

p R = total all red during cycle

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Example

Given: 3 phases, Calculate the optimum cycle length based on the following information Phase Critical Flow Ratio Lost Time (sec) 1 0.23 6 2 0.13 4 3 0.26 7 Solution: Co = 1.5L + 5 = __1.5(6+4+7) +5___ = 1.5(17) + 5 1 - Σ (V/s) 1 - (0.23+0.13+0.26) 1 - 0.62 Co = 80.3 sec, use 80 sec

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General Approach for Signal Timing(step5)

• Allocate available green based on critical

flow ratios

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Green Split Calculations

• With Co, allocate available green to phases

All t d b iti l fl ti

• Allocated by critical flow ratios
• Each phase receives green consistent with

it's ratio of critical flow compared to that for

• ther phases

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Green Split Calculations

• For phase I:

gi = (V/s)i * Gte Σ (V/s) where: gi = length of green interval for phase i (sec) (V/s)i = critical flow ratio for phase i Gte = available green for the cycle (sec)

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Total Available Green

• Gte = C – L

Where: Gte = total effective green time per cycle C = actual cycle length L = total lost time

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Example

Given: Given: 2 phase cycle s = same for both phases= 900 pcu/hr available green time = 60 sec Phase 1: critical flow rate = 500 pcu/hr Phase 2: critical flow rate = 250 pcu/hr

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Example

Given: 2 phase cycle s = same for both cycles = 900 pcu/hr il bl ti 60 available green time = 60 sec Phase 1: critical flow rate = 500 pcu/hr, flow ratio = 0.56 Phase 2: critical flow rate = 250 pcu/hr, flow ratio = 0.28

Solution for phase I:

g (V/s) * G 0 56 * 60 40 40 sec sec g1 = __(V/s)1_* GTE___ = __0.56 * 60____ = 40 40 sec sec Σ (V/s) (0.56+0.28)

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General Approach for Signal Timing (Step 6)

• Calculate length of minimum green time

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Minimum Green Interval

• Pedestrian crossing time is the minimum green

that can be given that can be given

• Pedestrians can only cross intersection as long

as no conflicting movements are present (with the exception of permitted left and right turns)

• Sum of green and intergreen must provide time

for ped. to cross approach

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Minimum Green Interval

• With pedestrian signal Assumptions:
• With pedestrian signal Assumptions:

– pedestrian walk signal will be on for approx. 7 sec – a pedestrian may begin crossing the street as DON'T WALK begins to flash – pedestrians walk about 4 ft/sec p – WALK interval is contained in the green interval of the corresponding approach

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Minimum Green Interval

Pt = 3.2 + _L_ + 2.7(Nped) for WE > 10 ft Sp WE

p E

Pt = 3.2 + _L_ + 2.7(Nped) for WE <= 10 ft Sp

where: Pt = pedestrian crossing time (sec) for pedestrian signal L = width of intersection (feet) Sp = velocity of the pedestrian (usually 4 ft/sec) --depends on ped. Nped = number of pedestrians crossing during an interval

ped

p g g 3.2 = pedestrian start-up time WE = effective crosswalk width (feet)

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Minimum Green Interval

gmin = Pt - I gmin

t where: gmin = minimum green time (sec) Pt = pedestrian crossing time (sec) I = clearance interval (sec) I clearance interval (sec)

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Example

Given: Intersection width = 60 feet 12 peds/interval Sp = 4 feet/sec 9 ft crosswalk Clearance time is 6 sec.

Gt = 3.2 + _L_ + 0.27(Nped) for WE <= 10 ft Sp WE G = 3 2 + 60 ft + 0 27(12) = 18 6 sec Gt 3.2 + _60 ft__ + 0.27(12) 18.6 sec 4 ft/sec 9

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Example

Given: Intersection width = 60 feet 12 peds/interval Sp = 4 feet/sec 9 ft crosswalk Clearance time is 6 sec.

gmin = Pt - I = 18.6 sec - 6 sec = 12.6 sec

Pt = 18.6 sec

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General Approach for Signal Timing

• Allocate available green based on critical

Allocate available green based on critical flow ratios

• Calculate the capacity
• Check design flow rates /capacity and

green intervals/minimum green intervals g g

• Adjust cycle timing if necessary

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Adjustments

• Once done need to see if results work

M k t i t dj t

• Make sure green meets requirements or adjust

until it does (ped crossing)

• Check capacity
• If significantly below capacity, reduce green time
• If close increase
• Compute LOS and delay and check

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Determination for Left Turn Phasing

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Left turn phasing

• Additional phases increase lost time
• Consider protected or protected/permitted:
• Consider protected or protected/permitted:

– VLT >= 200 veh/hr – VLT*(vo/No) >= 50,000 Where – VLT = left-turn flow rate – Vo = opposing thru movement flow rates – No = number of lanes for opposing through movement

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Left turn phasing

• Usually not provided when Vlt < two

hi l l ( k ) vehicles per cycle (sneakers)

• When protected left is used for opposing

left, consider even if not needed

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Protected

• Safest
• Recommended when 2 of following are

met

– Left-turn flow rate > 320 veh/h – Opposing flow rate > 1,100 veh/hr – Opposing speed limit >= 45 mph – Opposing speed limit >= 45 mph – Two or more left turn lanes

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Protected

• Recommended when 1 of following is met

Three opposing traffic lanes with > 45 mph speed – Three opposing traffic lanes with >= 45 mph speed limit – Left turn flow rate > 320 and % of HV > 2.5% – >= 7 left turn accidents in 3 years have occurred – Average stopped delay to left turning traffic is accepatble for fully protecte phasing and engineer judges that additional left-turn accidents will occur

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Traffic Management and Control (ENGC 6340)

anual 2000 from Highway Capacity Ma

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Baseline Assumptions

• D/D/1 queuing (deterministic (D) arrival/
• D/D/1 queuing (deterministic (D) arrival/

deterministic (D) departure/ 1 server.

• Approach arrivals < departure capacity

– (no queue exists at the beginning/end of a cycle)

• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Quantifying Control Delay

• Two approaches

– Deterministic (uniform) arrivals (Use D/D/1) – Probabilistic (random) arrivals (Use empirical

equations)

• Total delay can be expressed as
• Total delay can be expressed as

– Total delay in an hour (vehicle-hours, person-hours) – Average delay per vehicle (seconds per vehicle)

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Traffic Management and Control (ENGC 6340)

D/D/1 Signal Analysis (Graphical)

Arrival Departure Rate Arrival Rate Rate

Vehicles

Queue dissipation

Time

Maximum delay Maximum queue Total vehicle delay per cycle

Red Red Red Green Green Green

• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Signal Analysis – Random Arrivals

Webster’s Formula (1958)

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Traffic Management and Control (ENGC 6340)

Definition – Level of Service (LOS)

• Chief measure of “quality of service”

– Describes operational conditions within a traffic stream – Does not include safety Different measures for different facilities – Different measures for different facilities

• Six levels of service (A through F)
• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Signalized Intersection LOS

• Based on control delay per vehicle

How long you wait on average at the stop – How long you wait, on average, at the stop light

from Highway Capacity Manual 2000

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Typical Approach

• Split control delay into three parts

P 1 D l l l d i if i l – Part 1: Delay calculated assuming uniform arrivals (d1). This is essentially a D/D/1 analysis. – Part 2: Delay due to random arrivals (d2) – Part 3: Delay due to initial queue at start of analysis time period (d3). Often assumed zero.

( )

d d PF d d + +

( )

3 2 1

d d PF d d + + =

d = Average signal delay per vehicle in s/veh PF = progression adjustment factor d1, d2, d3 = as defined above

• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Uniform Delay (d1)

⎞ ⎜ ⎛ g C 1 5

( )

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − ⎠ ⎜ ⎝ − = C g X C g C d , 1 min 1 1 5 .

1

d = delay due to uniform arrivals d1 = delay due to uniform arrivals (s/veh) C = cycle length (seconds) g = effective green time for lane group (seconds) X = v/c ratio for lane group

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Meaning of signal progression

Simple Progression On A One-way Street

• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Progression adjustment factor

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Progression adjustment factor

2012/3/11 Traffic Control Design TC6 95

• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Incremental Delay (d2)

( ) ( )

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − + − = cT kIX X X T d 8 1 1 900

2 2

⎦ ⎣

d2 = delay due to random arrivals (s/veh) T = duration of analysis period (hours). If the analysis is based on the peak 15-min. flow then T = 0.25 hrs. k = delay adjustment factor that is dependent on signal controller mode. For pretimed intersections k = 0.5. For more efficient intersections k < 0.5. I t filt i / t i dj t t f t Adj t f I = upstream filtering/metering adjustment factor. Adjusts for the effect of an upstream signal on the randomness of the arrival pattern. I = 1.0 for completely random. I < 1.0 for reduced variance. c = lane group capacity (veh/hr) X = v/c ratio for lane group

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• Dr. Essam almasri

Traffic Management and Control (ENGC 6340)

Initial Queue Delay (d3)

• Applied in cases where X > 1.0 for the

l i i d analysis period

– Vehicles arriving during the analysis period will experience an additional delay because there is already an existing queue

• When no initial queue…

– d3 = 0