6. signalized Intersectionssite.iugaza.edu.ps/wp-content/uploads/file/TMC2012/chapter...

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Dr. Essam almasriTraffic Management and Control (ENGC 6340)

6. signalized Intersections

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1. HCM 2000, chapter 162. safety.fhwa.dot.gov/intersection/signalized/sig_int_pps051508

References

/short/sigint_short.ppt3. 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

32conflict 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 solutionWe must find an appropriate compromise

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Warrants for the use of traffic signals

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

Traffic flowPedestrian safetyAccident experienceAnd the elimination of traffic conflict.

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Quick guide: 3Quick guide:For traffic flow:Traffic signals are justified if the following traffic flow exists for eight hours on an average day.

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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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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./hourped./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 aspectsThe 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

MeaningStop & keep

stopping

Prepare to go but do not

moveGo

Clear the intersection but do not

cross the stop line

Duration (s) 2 3 9


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

Terms

p y greceives a “green”Cycle Length (C): time (seconds) for the signal to complete one full cycle. Interval: an interval of time during which none of the lights at a signalized intersection changesCh i t l ll i di ti f iChange interval: yellow indication for a given movement

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TermsClearance interval: all red, after yellowGreen interval: green indication for aGreen interval: green indication for a particular movementRed interval: red indication for a particular movementAll-Red: red indication for all approachesPhase: the aspect of a cycle allocated to one the aspect of a cycle allocated to one or more streams of trafficor more streams of traffic

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Example: “T” intersection of two one-way streets

Cycle: a complete rotation through all the indications gprovided. 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 opposing 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 on 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 15


Types of Signal Timing• Isolated Signals:

• Fixed / Pretimed• Fixed / PretimedSignals which have a designated cycle which does not change regardless of flow or time of day

• Semi-actuatedSignals 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 actuatedSignals 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 timeGreen: 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 designvolume 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 minutesj pPHF = 0.85Calculated Volume = 1200 v/hr

DHV=1,200 vph = 1,411 vph0.85

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

• Represents capacity for the lane grouph 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 RateNumber of vehicles that could enter the intersection after initial startup if constant queue p qexisted 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 groupfw = lane width adjustment factorfHV = heavy vehicle adjustment factorfg = grade adjustment factorfp = parking adjustmentfbb = bus blockage factorffa = 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 factorfRT = right turn adjustment factorfLbp = pedestrian and bike adjustment factor for left turn movementfRbp = 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 orFor 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

others require less• Becomes the “design” lane• If sufficient time is given to the critical lane, all otherIf 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

executeexecute• 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/capacity36

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Critical Lane ExampleCritical Lane ExampleFind critical lanes for each phase

(v/s)north = 250/1700 = 0.15Phase 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 ExampleCritical Lane Examplev/s for critical lane group

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

(v/s)south = 0.1838

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ExampleFor 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 1200NB R,T 500 1700SB L,T 450 1330SB 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 RatioNB L,T 0.50NB R,T 0.29SB L,T 0.34SB R,T 0.45 39


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 DistanceIntersection clearance timePedestrian 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 frictionG = Grade, as a percentage

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Next, we calculate the time required for a vehicle to


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) 45



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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If you have an intersection where the pedestrian movements y pare not regulated by a separate pedestrian signal, you need to protect these movements by providing enough intergreentime 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 pof the cycle begins.

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The formula for this calculation is shown below.Pedestrian Crossing Time:PCT = W/VWhere:

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.48

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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 ylength

• Webster's:– most common– minimizes intersection delay– Gives optimum cycle length as a function of lost time

and critical flow ratio 50

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Cycle LengthCo = 1.5L + 5

1 - Σ(Yi)where:

Co = optimum cycle lengthL = sum of the lost time for all phasesYi = 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 secondsonce 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 upSome 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 qto 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 i54

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Time to discharge Queue• Green time to discharge queue of vehicles• T = l1 + nhTn 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 phasefor next phase

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Total lost time• Lost time due to vehicles starting up at

beginning of green and vehicles stopping at endbeginning of green and vehicles stopping at end of 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 ili = G i + y – G ili = Gai + y Gei

Where:li = lost time for phase iGai = actual green time for phase iy = yellow interval for phase IGei = effective green time for phase iei

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Lost time includes start-up delay plus any portion of yellow not used for vehicle movement

Image source: http://hcmdev.kittelson.com/Case1/popup_terms/effgreen_popup.htm 59


Effective green time• Amount of time during cycle that vehicles are moving for

a particular movementp– 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 imovement are not moving

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Total Lost Time

• Total lost time for a cycle is given by:

L = Σli + RWhere

L = lost time per cycleli = lost time for phase ii pR = total all red during cycle

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ExampleGiven: 3 phases, Calculate the optimum cycle length based on the following information

Phase Critical Flow Ratio Lost Time (sec)1 0.23 62 0.13 43 0.26 7

Solution:

Co = 1.5L + 5 = __1.5(6+4+7) +5___ = 1.5(17) + 51 - Σ (V/s) 1 - (0.23+0.13+0.26) 1 - 0.62

Co = 80.3 sec, use 80 sec63


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 phasesAll 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 other phases

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Green Split Calculations• For phase I:

gi = (V/s)i * GteΣ (V/s)

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

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Total Available Green

• Gte = C – L

Where:Gte = total effective green time per cycleC = actual cycle lengthL = total lost time

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Example

Given:Given:2 phase cycles = same for both phases= 900 pcu/hravailable green time = 60 sec

Phase 1: critical flow rate = 500 pcu/hrPhase 2: critical flow rate = 250 pcu/hr

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ExampleGiven:2 phase cycles = same for both cycles = 900 pcu/hr

il bl ti 60available green time = 60 sec

Phase 1: critical flow rate = 500 pcu/hr, flow ratio = 0.56Phase 2: critical flow rate = 250 pcu/hr, flow ratio = 0.28

Solution for phase I:

g (V/s) * G 0 56 * 60 4040 secsecg1 = __(V/s)1_* GTE___ = __0.56 * 60____ = 40 40 secsecΣ (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 giventhat 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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• 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/secp– WALK interval is contained in the green

interval of the corresponding approach

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Minimum Green IntervalPt = 3.2 + _L_ + 2.7(Nped) for WE > 10 ft

Sp WEp E

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

where:Pt = pedestrian crossing time (sec) for pedestrian signalL = width of intersection (feet)Sp = velocity of the pedestrian (usually 4 ft/sec) --depends on ped.Nped = number of pedestrians crossing during an intervalped p g g3.2 = pedestrian start-up timeWE = effective crosswalk width (feet)

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gmin = Pt - Igmin twhere:gmin = minimum green time (sec)Pt = pedestrian crossing time (sec)I = clearance interval (sec)I clearance interval (sec)

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ExampleGiven:Intersection width = 60 feet 12 peds/intervalSp = 4 feet/sec 9 ft crosswalkClearance time is 6 sec.

Gt = 3.2 + _L_ + 0.27(Nped) for WE <= 10 ftSp WE

G = 3 2 + 60 ft + 0 27(12) = 18 6 secGt 3.2 + _60 ft__ + 0.27(12) 18.6 sec4 ft/sec 9

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ExampleGiven:Intersection width = 60 feet 12 peds/intervalSp = 4 feet/sec 9 ft crosswalkClearance 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 criticalAllocate available green based on critical flow ratios

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

green intervals/minimum green intervalsg g• Adjust cycle timing if necessary

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Adjustments

• Once done need to see if results workM 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 metThree 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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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)


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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D/D/1 Signal Analysis (Graphical)

ArrivalDeparture

Rate ArrivalRate

Rate

Vehi

cles

Queue dissipation

Time

Maximum delay

Maximum queue

Total vehicle delay per cycle

Red Red RedGreen Green Green


Signal Analysis – Random ArrivalsWebster’s Formula (1958)

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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)


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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Typical Approach

• Split control delay into three partsP 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.

( ) ddPFdd ++( ) 321 ddPFdd ++=

d = Average signal delay per vehicle in s/veh

PF = progression adjustment factord1, d2, d3 = as defined above


Uniform Delay (d1)

⎞⎜⎛ gC 150

( ) ⎥⎦⎤

⎢⎣⎡−

⎠⎜⎝−

=

CgX

CgC

d,1min1

15.01

d = delay due to uniform arrivalsd1 = 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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Meaning of signal progression

Simple Progression On A One-way Street


Progression adjustment factor

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Progression adjustment factor

2012/3/11 Traffic Control Design TC6 95


Incremental Delay (d2)( ) ( ) ⎥

⎦

⎤⎢⎣

⎡+−+−=

cTkIXXXTd 811900 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 fI = 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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Initial Queue Delay (d3)

• Applied in cases where X > 1.0 for the l i i danalysis 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

6. signalized Intersectionssite.iugaza.edu.ps/wp-content/uploads/file/TMC2012/chapter...

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