Analysis of Signalized Intersectionsocw.nctu.edu.tw/course/sc011/2012-08-16-1.pdf · In signal timing design, green times are estimated to provide necessary capacity In intersection

Analysis of Signalized Intersections

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What is Intersection analysis

Inverse application of the signal timing design In signal timing design, green times

are estimated to provide necessary capacity

In intersection analysis, signal timing is known and used to estimate the existing capacity

Two methods

Critical Movement Approach Apply adjustment factors to the

demand volume

HCM Methodology Saturation flow rates are reduced to

reflect non-ideal prevailing conditions

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Steps for Critical Movement Approach

1. Identify the lane geometry and use 2. Identify hourly demand volumes 3. Specify the signal timing 4. Convert demand volumes to equivalent passenger-car

Volumes 5. Convert passenger-car equivalents to through-car

equivalents 6. Convert Through-car equivalents under prevailing

conditions to though-car equivalents under ideal conditions 7. Assign lane flow rates 8. Find critical-lane flows 9. Determine capacity and v/c ratios 10. Determine delay and level of service

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1. Proportion of heavy vehicles 2. Proportion of local buses 3. Lane widths 4. Approach grade 5. Parking conditions on approach 6. Pedestrian interference levels

Identify hourly demand volumes

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1. Proportion of heavy vehicles 2. Proportion of local buses 3. Lane widths 4. Approach grade 5. Parking conditions on approach 6. Pedestrian interference levels

Identify hourly demand volumes

Identify signal timings

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1 2g G y ar l l= + + − −Effective green time Actual green time Actual yellow time Actual all-red time Start-up lost time Clearance lost time

gGy

ar1l2l

Convert Demand Volume to Equivalent Passenger Car Volume

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(1 )pc HV HV LB LB HV LBV VP E VP E V P P= + + − −

Passenger-car Equivalents for Local Buses (Stop in Travel Lane)

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Passenger-car Equivalents for Local Buses (Stop in Parking Lane)

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Convert Passenger-Car Equivalent to Through-Car Equivalent

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Left Turn Vehicles Protected left turns = 1.05 Permitted depends on opposing flow and

number of opposing lanes Right Turn Vehicles Depends on the pedestrian volume in

conflicting crosswalk

Through Car Equivalent for Left-Turning Vehicles

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Through Car Equivalent for Right-Turning Vehicles

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Though-car equivalents under ideal conditions

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* * * *tcu

w g p LU

VvPHF f f f f

=

Adjustment factor for: Lane width Grade Parking Lane utilization

Lane Width Adjustment

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Grade Adjustment

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Parking Adjustment

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Lane Utilization Adjustment

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Assign Lane Flow Rates

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Where a separate LT lane exist, assign all LT tcus to this lane group. If more than one lane exists, divide the tcu/h equally among the lanes

Where a separate RT lane exist, assign all RT tcus to this lane group. If more than one lane exists, divide the tcu/h equally among the lanes

For all mixed lane group(LT/TH/RH, LT/TH, TH/RT)divide the total tcu/h equally among all lanes, except that all LT tcus must be in the LH lane and all RT tcus in RH lane

Find Critical Lane Flow Rates for Each Signal Phase

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From A1 to A3 Ring 1 148+420=568 Ring 2 203+330=533

Maximum = 568

From B1 to B3 Ring 1 120+380=500 Ring 2 220+250=570

Maximum = 570 1138

Capacity and v/c Ratio

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From A1 to A3 Ring 1 148+420=568 Ring 2 203+330=533

Maximum = 568

From B1 to B3 Ring 1 120+380=500 Ring 2 220+250=570

Maximum = 570 1138

1900( / )i ic g C=

11900( / )

n

SUM ii

c g C=

= ∑/i i iX v c=

1/

n

c i ii

X v c=

=∑

Delay and Level of Service

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1 2*i i id d PF d= +

Approach delay for lane group i Uniform delay for lane group I Overflow plus random delay for lane group i Progression adjustment factor

id1id2id

PF

Uniform Delay and Overflow delay

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2

10.5 [1 ( / )]

1 [min(1, )*( / )]i

ii i

C g CdX g C−

=−

22

16225[( 1) ( 1) ]ii i i

i i

Xd X Xc N

= − + − +

Uniform Delay:

Overflow Delay:

Progression Factor

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Level of Service

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Example

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Step 1 and 2: Geometry and volume

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Step 3:Signal Phase

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Step 4: Conversions to Equivalent Passenger Car Flow

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EB Through movement 1100 veh/h, 10% heavy vehicle and 20 buses/hour Heavy=1100*10%*2.0=220 Bus=20*3.1=62 Passenger_car=1100*(1-10%)-20=970 Total=Heavy+Bus+Passenger_car=1252

Step 4: Conversions to Through-Car Equivalent

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EB left turn Protected, equivalent=1.05

NB left turn One-way street, No conflicting through Go through pedestrian crosswalk Pedestrian volume 100 ped/h Treated like right turn, equivalent=1.21

Step 5: Conversions to Equivalent Under Ideal Condition

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No parking, fp=1.0 EB lane width is 11 feet, fw=0.97 EB Through has two lanes f=0.952

Step 6: Assign Flow to Lanes

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WB approach 183 tch/h for right turn and 1242 for

through Total 1424 uniformly split between two

lanes Leftmost lane 712 through only Rightmost lane carries 183 right turn and

1241-712=529 through

Step 6: Assign Flow to Lanes

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Step 7: Critical Volume

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Step 8: Capacity and v/c ratio

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Step 8: Capacity and v/c ratio

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Step 9: Delay and LOS

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Uniform Delay:

Step 9: Delay and LOS

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Overflow Delay:

Step 9: Delay and LOS

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Total Delay = d1*PF+d2:

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Steps for HCM Approach

1. Input data

2. Define movement groups and adjusted flow rate

3. compute lane group flow rate

4. input or compute phase duration

5. Compute capacity

6. Compute delays and LOS

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Step 2: Movement and lane groups

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Step 3: Estimating the Saturation Flow

Adjustment factors include: Lane width Heavy vehicles Grade Parking Local bus blockage Area type Pedestrian/bicycle interference

0 w HV g p bb a LU RT LT Rpb Lpbs s Nf f f f f f f f f f f=

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Adjustment for Lane Width

Lanes width less than 10 ft Lane width between 10 and 12.9 ft Lane width larger than 12.9 ft

0.96wf =

1.0wf =

1.04wf =

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Adjustment for Heavy Vehicles

Lanes width less than 10 ft Lane width between 10 and 12.9 ft Lane width larger than 12.9 ft

0.96wf =

1.0wf =

1.04wf =

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Adjustment for Grade

1 / 200gf G= −

G Grade in %

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Adjustment for Parking

180.9 ( )3600

mNP = − ( 1)p

N PfN− +

=

180.1 ( )3600 0.05

m

p

NNf

N

− −= ≥

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Adjustment for Local Bus Blockage

14.41.0 ( )3600

BNB = − ( 1)bb

N BfN− +

=

14.4( )3600 0.05

B

p

NNf

N

−= ≥

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Adjustment for Type of Area

0.9af =CBD location:

Other location: 1.0af =

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Adjustment for Lane Utilization

1

gLU

g

vf

v N=

Demand flow rate for the lane group gv

1gv Demand flow rate for highest lane volume

N Number of lanes in the lane group

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Adjustment for Protected Turns

0.85RTf = For exclusive RT lane

0.95LTf = For protected LT lane

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Adjustment for Pedestrian and Bicycle Interference with Turns

Estimate Pedestrian Flow Rate During Green Phase Estimate the Average Pedestrian Occupancy in the Conflict

Zone Estimate the Bicycle Flow Rate During the Green Phase Estimate the Average Bicycle Occupancy in the Conflict

Zone Estimate the Conflict Zone Occupancy Estimate the Unblocked Portion of the Phase Determine Adjustment Factors

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Step 4: Determine Lane Group Capacities and v/c Ratios

Capacity of a lane group

v/c ratio of a lane group

Critical v/c ratio for intersection

( / )i i ic s g C=

( / )( / )

i ii

i i

v v sXc g C

= =

maxmin

max

( / ) *( )iC c

i

CX v sC L

=−∑

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Step 5: Critical Lane Group Identification

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Step 6: Estimate Delay and LOS

Uniform Delay

Incremental Delay

Additional Delay Per Vehicle Due to Queue

1 2 3d d d d= + +

1d

2d

3d

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Step 6: Estimate Delay and LOS

2

10.5 [1 ( / )]

1 [min(1, )*( / )]C g Cd

X g C−

=−

22

8900 [( 1) ( 1) ( )]kIXd T X XcT

= + − + − +

2 2 2

33600 ( )

2 2 2b e eo e eo bQ Q Q Q Q Qd t

vT c c+ − −

= + −

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Step 6: Aggregate Delay

i ii

Ai

i

d vd

v=∑∑

A AA

IA

i

d vd

v=∑∑

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Step 7: Interpret the Results

v/c ratios X for every lane group Critical v/c ratio X for the intersection Delays and LOS for each lane group Delays and LOS for each approach Delays for overall intersection

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Step 7: Interpret the Results

Scenario I: Xc<1.0,all Xi<1.0, no capacity deficiency Scenario II;

Xc<1.0,some Xi>1.0, reallocation of green time needed

Scenaio III: Xc>1.0,some or all Xi>1.0, change of phase plan, cycle length, or physical design is needed

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Example

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Volume Adjustment

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Saturation Flow Rate Estimation

Saturation Flow Adjustment

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Saturation Flow Adjustment

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Saturation Flow Adjustment

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Saturation Flow Adjustment

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Saturation Flow Adjustment

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Capacity Analysis

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Delay and LOS

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What is the result if applying HCM to the former Critical Movement analysis example?

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