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Chapter 20 2

Four critical aspects of signalized intersectionoperation discussed in this chapter

1. Discharge headways, saturation flow

rates, and lost times

2. Allocation of time and the critical lane

concept

3. The concept of left-turn equivalency

4. Delay as a measure of service quality

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Chapter 20 3

20.1.1 Components of a Signal Cycle

Cycle lengthPhase

Interval

Change interval

All-read interval(clearance interval)

Controller

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Chapter 20 4

Signal timing with a pedestrian signal: Example

Interval Pine St. Oak St. %

Veh. Ped. Veh. Ped.

1 G-26 W-20 R-31 DW-31 36.4

2 FDW-6 10.9

3 Y-3.5 DW-29 6.4

4 R-25.5 AR 2.7

5 G-19 W-8 14.5

6 FDW-11 20.0

7 Y-3 DW-5 5.5

8 R-2 AR 3.6

Cycle length = 55 seconds

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Chapter 20 5

20.1.2 Signal operation modes and left-turn

treatments & 20.1.3 Left-turn treatments

Operation modes:

Pretimed (fixed) operation

Semi-actuated operation

Full-actuated operation

Master controller,

computer control, adaptive

traffic control systems

Left-turn treatments:

Permitted left turns

Protected left turns

Protected/permitted

(compound) or

permitted/protected left turns

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Chapter 20 6

Factors affecting the permitted LT

movement

LT flow rate

Opposing flow rate

Number of opposing

lanes

Whether LTs flow

from an exclusive LTlane or from a shared

lane

Details of the signal

timing

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Chapter 20 7

CFI (Continuous Flow Intersection

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Chapter 20 8

DDI (Diverging Diamond Interchange)

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Chapter 20 9

Four basic mechanisms for building an

analytic model or description of a signalizedintersection

Discharge headways at a signalized intersection

The critical lane and time budget concepts

The effects of LT vehicles

Delay and other MOEs (like queue size and the

number of stops)

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Chapter 20 10

20.2 Discharge headways, saturation flow,

lost times, and capacity

1 2 3 4 5 6 7

h

Vehicles in queue

(i) Start-up lost time

nhlT

il

hs

!

(!

!

1

1 )(

3600Saturation flow rate

C

gsc

earyl

llt

aryY

tYGg

iii

L

iii

Liii

!

!

!

!

!

2

21

Capacity

Cycle length(Sample problem in p.467)

Effective

green

Startup lost time

Clearance lost time

Total lost time

Extension

of green

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20.2.6 Saturation flow rates froma nationwide survey

Chapter 20 11

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Chapter 20 13

20.3.2 Finding an Appropriate Cycle Length

)/3600)(/(1

/36001

min

hcvP F

NtC

h

NtC

c

Ldes

c

L

!

!

Desirable cycle length, incorporating

PHF and the desired level of v/c

ii

i

i

svratioflowY

Y

LC

)/(_

1

55.1

1

0

!

!

!

J

The benefit of longer cyclelength tapers around 90 to 100

seconds. This is one reason why

shorter cycle lengths are better.

N = # of phases. Larger N, more

lost time, lower Vc.

(Review the sample problem on page 473.)

Doesnt this look like the Webster model?

Eq. 20-13

Eq. 20-14

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Chapter 20 14

Websters optimal cycle length model

!

! J

1

0

1

55.1

i

isv

CC0 = optimalcyclelengthforminimum delay,sec

= Totallosttimepercycle,sec

Sum (v/s)i = Sumofv/sratiosforcriticallanes

Delay is not so sensitive

for a certain range of

cycle length This is the

reason why we can round

up the cycle length to,

say, a multiple of 5seconds.

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Chapter 20 15

20.3.2 Finding an Appropriate Cycle Length

(Review the sample

problem on page 473)

Marginal gain in

Vc decreases as

the cycle length

increases.

Desirable cycle length, Cdes

Cycle

length

100%

increase

Vc 8% increase

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Chapter 20 16

20.4 The Concept of Left-Turn (and Right-

Turn) Equivalency

In the same amount of time, the left

lane discharges 5 through vehiclesand 2 left-turning vehicles, while the

right lane discharges 11 through

vehicles.0.3

2

511

:

1125

!

!

!

LT

LT

E

and

E

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Chapter 20 17

Left-turn vehicles are affected by

opposing vehicles and number of

opposing lanes.

The LT equivalent increases as the opposing flow increases.

For any given opposing flow, however, the equivalent

decreases as the number of opposing lanes is increased.

5

1000 1500 1900

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Chapter 20 18

Left-turn consideration: 2 methods

Given conditions: 2-lane approach

Permitted LT

10% LT, TVE=5

h = 2 sec for through

Solution 1: Each LTconsumes 5 times more

effective green time.

vphgplh

s

hh

ave

avg

128680.2

36003600

sec/80.2)00.2)(9.0()00.10)(1.0(

!!!

!!

Solution 2: Calibrate a factor that would multiply the saturation flow

rate for through vehicles to produce the actual saturation flow rate.

? A ? A

714.0)15(10.01

1

)1(1

1

)0.1)(1(

18002

3600

!!!

!!

!!

LTLT

LTLTLTavg

LT

EP

hPhEP

h

h

hf

vphgpls vphgpls 1286)714.0(1800 !!

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Chapter 20 19

20.5 Delay as an MOE

Common MOEs:

Delay

Queuing

No. of stops (orpercent stops)

Stopped time delay: The time avehicle is stopped while waiting to

pass through the intersection

Approach delay: Includes stopped

time, time lost for acceleration and

deceleration from/to a stop

Travel time delay: the difference

between the drivers desired total time

to traverse the intersection and the

actual time required to traverse it.

Time-in-queue delay: the total time

from a vehicle joining an intersection

queue to its discharge across the stop-

line or curb-line.

Control delay: time-in-queue delay +

acceleration/deceleration delay)

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Chapter 20 20

20.5.2 Basic theoretical models of delay

At saturation flow rate, s

Uniform arrival

rate assumed, v Here we assumequeued vehicles

are completely

released during

the green.

Note that W(i) is

approach delayin this model.

The area of the

triangle is the

aggregate delay.

Figure 20.10

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Chapter 20 21

Three delay scenarios

This is great.This is acceptable.

You have to do something

for this signal.

A(t) = arrival

function

D(t) = discharge

function

UD = uniform

delay

OD = overflow delay due to

randomness (random delay).

Overall v/c < 1.0

OD = overflow delay

due to prolonged

demand > supply

(Overall v/c > 1.0)

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Chapter 20 22

Arrival patterns compared

HCM uses the Arrival Type factor to adjust the delay computed as

an isolated intersection to reflect the platoon effect on delay.

Isolated intersections

Signalized arterials

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Chapter 20 23

Websters uniform delay model, p480

-

-

!!

-

!!

!!!

-

!

vs

vs

C

gCst

C

g

Cvs

v

vs

vR

t

stvtvRtRv

C

gCR

c

c

ccc

1

1

1

The area of the triangle is the aggregated

delay, Uniform Delay (UD).

-

-

!! vs

vs

C

g

CVheightRbaseUDa

2

2

12

1

):)(:(2

1

UDa

Total approach delay

To get average approach

delay/vehicle, divide this by vC

? A ? Asv

CgCUD

!1

1

2

2

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Chapter 20 24

Modeling for random delay, p.481

UD = uniform

delay

OD = overflow delay due to

randomness (in reality random

delay). Overall v/c < 1.0

? A ? A

? A

? ACgcvvccvv

cv

sv

CgCD

!

2312

22

65.0

/121

1

2

Adjustment term for

overestimation

(between 5% and 15%)

Analytical model

for random delay

D = 0.90[UD + RD]

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Random delay

derivation

Chapter 20 25

Chapter 20.

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Chapter 20 26

Modeling overflow delay

? A

? A

? A

? A 2

)(1//1

/1

21

1

2

22

CgCcvCg

CgC

sv

CgCUDo

!

!

!

because c = s (g/C), dividebothsides

byv andyouget(g/C)(v/c) = (v/s).

And v/c = 1.0.

cvT

cTvTTODa !!22

1 2

The aggregate overflow delay is:

Because the total vehicledischarged during Tis cT,

12

! cvT

OD

See the right column of p.482 for the

characteristics of this model.

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Average overflow delay between

T1 and T2

Chapter 20 27

12

21

! cvTT

OD

Average delay/vehicle =

(Area of trapezoid)/(No.

vehicles within T2-T1).

Derive it by yourself.

Hint: the denominator is

c(T2-T1).

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Chapter 20 28

20.5.3 Inconsistencies in random and

overflow delay

? A ? A ? A ? ACgcvvc

cvvcv

svCgCD

!

2312

22

65.0

/1211

2 1

2! cvTOD

The stochastic modelsoverflow delay is

asymptotic to v/c = 1.0

and the overflow

models delay is 0 at

v/c =0. The real

overflow delay is

somewhere between

these two models.

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Chapter 20 29

Comparison of various overflow delay model

20.5.4 Delay model in the HCM 2000

The 4th edition dropped the HCM 2000 model (I dont know why). It

looks like Akceliks model (eq. 20-26).

These models try to address delays for 0.85

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Chapter 20 30

20.5.5 Sample delay computations

We will walk through sample problems(pages 495-496).

Start reading Synchro 6.0 User Manual

and SimTraffic 6.0 User Manual. We

will use these software programsstarting Wednesday, October 21, 2009.