University of Sulaimani Civil Eng. Dept Adv. Traffic Eng.

:Master course

Chapter 6 (II) : Pretimed Traffic Signal Design

1 November 2023 Prepared by : Dr. Hirsh M. Majid 1

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Syllabus_5 : Pretimed Traffic Signal Design

• Conflict points
1. Crossing 16
2. Merging 8
3. Diverging 8

1 November 2023 Prepared by : Dr. Hirsh M. Majid 2

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Syllabus_5 : Traffic Signal Design

Some terms commonly used in the design of signal times.
1. Controller: A device in a traffic signal installation that changes
the colors indicated by the signal according to a fixed or variable
plan.
2. Cycle (Cycle length): The time in seconds required for one
complete color sequence of signal indication.
3. Phase (signal phase): That part of a cycle allocated to a stream of
traffic or a combination of two or more streams of traffic having
the right-of-way simultaneously during one or more intervals.
4. Interval: Any part of the cycle length during which signal
indications do not change.
5. Change interval (yellow) and clearance interval (all-red): The
total length of time in seconds of the yellow and all-red signal
indications. This time is provided for vehicles to clear the
intersection after the green interval before conflicting movements
are released.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 3

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 4

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 5

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

• The ITE recommends the following methodology for determining

the length of the yellow or change interval:

Where:
y=length of the yellow interval, s
t= driver reaction time, s
S85= 85th percentile speed of approaching vehicles, or speed limit, as
appropriate, mile/h
a= deceleration rate of vehicles, ft/s2
G= grade of approach with it’s sign (- for down grade, + for up grade), %
64.4= twice the acceleration rate due to gravity, which is 32.2 ft/s2

1 November 2023 Prepared by : Dr. Hirsh M. Majid 6

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

• The ITE also recommends the following policy for determining the
length of all-red clearance intervals:
For cases in which there is no pedestrian traffic:

For cases in which significant pedestrian traffic exists:

15

For cases in which some pedestrian traffic exists:

1 November 2023 Prepared by : Dr. Hirsh M. Majid 7

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Where: ar= length of the all-red phase, seconds

w= distance from the departure STOP line to the far side of the farthest
conflicting traffic lane, feet
P=distance from the departure STOP line to the far side of the farthest
conflicting crosswalk, feet
L=length of a standard vehicle, usually taken to be 18 to 20 feet
S15= 15th percentile speed of approaching traffic, or speed limit, as
appropriate, mile/h
If only the average approach speed is known, the percentile speeds may be
estimated as:
S15=S-5 S85=S+5 ……. (4)
Where: S85=85th percentile speed, mile/h. S15= 15th percentile speed, mile/h
S=average speed, mile/h
Where approach speeds are not measured and the speed limit is used, both
the yellow and all-red intervals will be determined using the same value of
speed. This, however, is not a desirable practice.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 8

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Use of these ITE policies to determine yellow and all-red intervals assures
that drivers will not be presented with a ‘dilemma zone’, which occurs
when the combined length of the change and clearance intervals is not
sufficient to allow a motorist who cannot safely stop when the yellow
initiated to cross through the intersection and out of conflicting vehicular
and/or pedestrian paths before those flows are released.

• Where yellow and all-

red phases are mistimed
and a dilemma zone is
created, agencies face
possible liability for
accidents that occur as
a result.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 9

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Determining lost times

The 2010 edition of the HCM indicates that lost time vary with the length
of the yellow and all-red phases in the signal timing. The HCM-2010
recommends the use of the following default values for this determination:

• Start-up lost time, l1=2.0 sec/phase

• Motorist use of yellow and all-red, e = 2.0 sec/phase (it could be called
extension of effective green = 2.0 sec, HCM-2010)

Using these default values, lost time per phase and lost time per cycle may
be estimated as follows:
j=y+ar

l2=j-e

tL=l1+l2
1 November 2023 Prepared by : Dr. Hirsh M. Majid 10
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Where:
l1= start-up lost time, sec/phase, l2=clearance lost time, sec/phase
tL=total lost time, sec/phase, y=length of yellow change interval, sec
ar=length of all-red clearance interval, sec
j=total length of change and clearance intervals, sec

Note that when the HCM recommended default values for l1 and e (both
2.0 sec) are used, the lost time per phase, tL is always equal to the sum of
the yellow and all-red intervals, j. Because the lost time for each phase may
differ, based on different yellow and all-red intervals, the total lost time per
cycle is merely the sum of lost times in each phase, or:
𝑛

𝐿𝑖
𝑖
Where: L=total lost time per cycle, sec
tLi= lost time for phase i, sec, n= number of discrete phases in cycle
1 November 2023 Prepared by : Dr. Hirsh M. Majid 11
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: Compute the appropriate change and clearance intervals for a

signalized intersection approach with the following characteristics:
Average approach speed= 35 mile/h
Grade=- 2.5%
Distance from STOP line to far side of the most distant lane = 48 ft
Distance from STOP line to far side of the most distant cross-walk = 60 ft
Standard vehicle length = 20 ft
Reaction time=1.0 sec
Deceleration rate= 10 ft/s2
Some pedestrians present
To apply equations (2) and (3), estimates of the 15th and 85th percentile
speeds are needs. Using equation (4):
S85=35+5=40 mile/h
S15=35-5=30 mile/h

1 November 2023 Prepared by : Dr. Hirsh M. Majid 12

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example cont’d…. Using equation (2), the length of the change or

yellow interval should be:

Equation (3c) is used to compute the length of the clearance or all-

red phase because there are some, but not significant, pedestrian
flows present. The length of the clearance interval is the maximum
of:

In this case, 1.5 seconds would be applied.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 13

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example cont’d….
lost time
The yellow interval was computed as 4.2 seconds, and all-red
interval was found to be 1.5 seconds. Using the recommended
default values for l1 and e, respectively, lost times would be
computed as:
j=4.2+1.5=5.7 sec

l2=5.7-2.0=3.7 sec

tL=2.0+3.7=5.7 sec

1 November 2023 Prepared by : Dr. Hirsh M. Majid 14

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Cycle length of fixed (pretimed) signals

Webster Method: Webster has shown that for a wide range of
practical conditions minimum intersection delay is obtained when
the cycle length is obtained by the equation:

1 November 2023 Prepared by : Dr. Hirsh M. Majid 15

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Cycle length of fixed (pretimed) signals

1 November 2023 Prepared by : Dr. Hirsh M. Majid 16

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Cycle length of fixed (pretimed) signals

Total lost time:
yi

yi

1 November 2023 Prepared by : Dr. Hirsh M. Majid 17

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Cycle length of fixed (pretimed) signals

1 November 2023 Prepared by : Dr. Hirsh M. Majid 18

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Cycle length of fixed (pretimed) signals

y1
y2
yi

Minimum green time:

Pedestrian speed traversing the street

1 November 2023 Prepared by : Dr. Hirsh M. Majid 19

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Cycle length of fixed (pretimed) signals

Minimum green time:
Pedestrian speed traversing the street

1 November 2023 Prepared by : Dr. Hirsh M. Majid 20

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course
Example: For the intersection shown in figure below, determine a suitable signal
timing for the intersection using the four-phase system shown below. Use a yellow
interval of three seconds and the saturation flow given. (Use webster method)

1 November 2023 Prepared by : Dr. Hirsh M. Majid 21

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 22

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course
Solution :
1. Determine equivalent hourly flows by dividing the peak-hour volumes by the
PHF (e.g., for left-turn lane group of phase D, equivalent hourly
flow=352/0.95= 371 )

1 November 2023 Prepared by : Dr. Hirsh M. Majid 23

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course
Compute the total lost time. Assume there is not an all-red phase then R = 0

Determine the optimum cycle length:

1 November 2023 Prepared by : Dr. Hirsh M. Majid 24

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 25

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Yellow time = 3.0 sec; the actual

green time Gai for each phase is
obtained as:

Draw the Timing Diagram:

In the lecture …….

1 November 2023 Prepared by : Dr. Hirsh M. Majid 26

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 27

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: The traffic flow for a three-legged intersection is as shown

below. Given that the lost time per phase is 3.5 sec, amber (yellow) time = 3
sec/phase. Suggest a phase plan, find the cycle length and green time for
each phase.
282
A 250
425 B
500

Saturation flow
Phase Direction
veh/h

300
250
Phase S 1800 C
A S+R (20%) 1800 Note: The influence of heavy vehicles
Phase S 1800 that affect the saturation flow has
B already been considered.
S+L (15 %) 1800
PHF = 1
Phase R 1800
C L 1800
1 November 2023 Prepared by : Dr. Hirsh M. Majid 28
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Taking into account the turning movements

Left turn adjustment factor fLT = 0.85 (for exclusive lane)
= 1.0 – 0.15 PLT
Right turn adjustment factor fRT = 0.9 (for exclusive lane)
=1/(1+ PRT (eRT -1))
Modified
Saturation
Phase Direction saturation
flow veh/h
flow veh/h
S 1800 1800
Phase A
S+R 1800 1285
S 1800 1800
Phase B
S+L 1800 1760
R 1800 1620
Phase C
L 1800 1530

1 November 2023 Prepared by : Dr. Hirsh M. Majid 29

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Phase A Phase B Phase C

Qi 425 500 282 250 250 300
Si 1800 1285 1800 1764 1620 1530
Qi/si 0.24 0.39 0.16 0.14 0.15 0.20
0.39 0.16 0.20
Co= 1.5 x 3.5 x 3 + 5 / (1- (0.39+0.16+0.2)) = 83 sec use Co = 85 sec
Gte = 85 – 3 x 3.5 = 74.5 sec
Ge1 = 0.39/0.75 x 74.5 = 38.74 sec use 38.5 sec
Ge2 = 0.16/0.75 x 74.5 = 15.89 sec use 16 sec
Ge3 = 0.20/0.75 x 74.5 = 19.87 sec use 20 sec
Gai = Gei + li – 3.0
Ga1 = 38.5 + 3.5 – 3 = 39.0 sec
Ga2 = 16 + 3.5 – 3 = 16.5 sec
Ga3 = 20 + 3.5 – 3 = 20.5 sec

1 November 2023 Prepared by : Dr. Hirsh M. Majid 30

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Co= 1.5 x 3.5 x 3 + 5 / (1- (0.39+0.16+0.2)) = 83 sec use Co = 85 sec

Ga1 = 38.5 + 3.5 – 3 = 39.0 sec
Ga2 = 16 + 3.5 – 3 = 16.5 sec
Ga3 = 20 + 3.5 – 3 = 20.5 sec

39 3 43
Phase A

42 16.5 3 23.5
Phase B

61.5 20.5 3
Phase C

1 November 2023 Prepared by : Dr. Hirsh M. Majid 31

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: The traffic flow for a three-legged intersection is as shown

below. Given that the lost time per phase is 3.5 sec, amber (yellow) time = 3
sec/phase. Suggest a phase plan, find the cycle length and green time for
each phase. Phase B

Phase A

Volume veh/h Saturation

Phase Direction flow
P B T veh/h
S 370 20 5 1800
Phase A Phase C
S+R (20%) 401 27 15 1800
S 240 18 2 1800 P factor = 1
Phase B Bus factor = 2
S+L (15 %) 202 18 4 1800
Truck factor = 3
R 180 20 10 1800 PHF = 1
Phase C
L 215 20 15 1800
1 November 2023 Prepared by : Dr. Hirsh M. Majid 32
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: The traffic flow for a three-legged intersection is as shown

below. Given that the lost time per phase is 3.5 sec, amber (yellow) time = 3
sec/phase. Suggest a phase plan, find the cycle length and green time for
each phase.
Phase B

Phase A

370 + 20x2 + 5 x 3 = 425 veh/h

401 + 27x2 + 15x3=500 veh/h
240 + 18x2 + 2x3 = 282 veh/h
202 + 18x2 + 4x3 = 250 veh/h Phase C

180 + 20x2 + 10x3 = 250 veh/h

215+ 20x2 + 15x3 = 300 veh/h
All the rest is same as previous example ……

1 November 2023 Prepared by : Dr. Hirsh M. Majid 33

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Homework
Example: The traffic flow for a four-legged intersection is as shown
below. Given that the lost time per phase is 2.4 sec. Saturation
headway is 2.1 sec (for simplicity assume the same value for all
directions), amber (yellow) time = 3 sec/phase. Suggest a phase plan,
find the cycle length and green time for each phase.

Note: The influence of heavy vehicles

and turning movements and all other
factors that affect the saturation flow
have already been considered.
PHF = 1.0

1 November 2023 Prepared by : Dr. Hirsh M. Majid 34

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Phase A Phase B Phase C Phase D

1 2 3 1 2 3 1 2 3 1 2 3
Qi 140 400 215 196 367 170 187 433 220 233 417 120
Si 1714 1714 1714 1714 1714 1714 1714 1714 1714 1714 1714 1714
Qi/si 0.08 0.23 0.125 0.114 0.214 0.1 0.11 0.25 0.128 0.136 0.24 0.07

0.23 0.214 0.25 0.24

Phase B

Phase C
Phase A

Co = (1.5x2.4x4+5)/(1-0.934)=293.9 sec
Try another arrangement for phases

Phase D
1 November 2023 Prepared by : Dr. Hirsh M. Majid 35
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Phase 1 Phase 2 Phase 3 Phase 4

Qi 433 417 233 215
Si 1714 1714 1714 1714
Qi/si 0.25 0.24 0.14 0.13

Co = (1.5x2.4x4+5)/(1-0.76)=80.83

1 November 2023 Prepared by : Dr. Hirsh M. Majid 36

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

The standard values for saturation flow, S according to Webster are given
as in the table below.

Width 3.0 3.5 4.0 4.5 5.0 5.5

in m
PCU/hr 1850 1890 1950 2250 2250 2900

In the absence of the data approximately value of saturation flow is

estimated assuming 160 PCU per 0.3 meter width of the approach. (Ref:
Signal design for T-intersection by using webster’s method in nandyal
town, kurnool district of andhra pradesh)

1 November 2023 Prepared by : Dr. Hirsh M. Majid 37

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

How to find pcu

Motorcycle/ Car Bus/Truck

Bicycle
No of vehicle 30 50 15
PCU 30 x 0.5=15 50 x 1 + 50 15 x 3 = 45
Total 15+50+45=110

1 November 2023 Prepared by : Dr. Hirsh M. Majid 38

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Determining the sum of critical-lane volumes

To estimate an appropriate cycle length and to split the cycle into
appropriate green times for each phase, it is necessary to find the critical-
lane volume for each discrete phase or portion of the cycle.
The critical-lane volume is the per-lane volume that controls the required
length of a particular phase.

Making this determination is complicated by two factors:

• Simple volumes cannot be simply compared. Trucks require more time
than passenger cars, left and right turns require more time than through
vehicles, vehicles on a downgrade approach require less time than vehicles
on a level or upgrade approach. Thus intensity of demand is not measured
accurately by simple volume.

• Where phase plans involve overlapping elements, the ring diagram must
be carefully examined to determine which flows constitute critical-lane
volumes.
1 November 2023 Prepared by : Dr. Hirsh M. Majid 39
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Ideally, demand volumes would be converted to equivalents based on

all of the traffic and roadway factors that might affect intensity.

For initial signal timing, however, this is too complex a process.

Demand volumes can, however, be converted to reflect the influence
of the most significant factors affecting intensity: left and right turns.

This is accomplished by converting all demand volumes to

equivalent through vehicle units (tvu’s). Through vehicle equivalents
for left and right turns are shown in Tables 1 and 2, respectively.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 40

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Table 1: Through-vehicle equivalents for Left-Turning Vehicles, ELT

Opposing Flow Vo (veh/h) Number of opposing lanes, No
1 2 3
0 1.1 1.1 1.1
200 2.5 2.0 1.8
400 5.0 3.0 2.5
600 10.0* 5.0 4.0
800 13.0* 8.0 6.0
1000 15.0* 13.0* 10.0*
≥1200 15.0* 15.0* 15.0*
ELT for all protected left turns = 1.05
*The LT capacity is only available through ‘sneakers’

Table 2: Through-vehicle equivalents for right-turning vehicles, ERT

Pedestrian volume in conflicting crosswalk, (peds/h) Equivalent
None (0) 1.18
Low (50) 1.21
Moderate (200) 1.32
High (400) 1.52
Extreme (800) 2.14
1 November 2023 Prepared by : Dr. Hirsh M. Majid 41
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Ideally, demand volumes would be converted to equivalents based on

all of the traffic and roadway factors that might affect intensity.

For initial signal timing, however, this is too complex a process.

Demand volumes can, however, be converted to reflect the influence
of the most significant factors affecting intensity: left and right turns.

This is accomplished by converting all demand volumes to

equivalent through vehicle units (tvu’s). Through vehicle equivalents
for left and right turns are shown in Tables 1 and 2, respectively.

Vo …. Through plus right turn volume on the approach opposing the

subject left turn movement veh/h

1 November 2023 Prepared by : Dr. Hirsh M. Majid 42

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

In using these tables, the following should be noted:

• Opposing volume, Vo, includes only the through volume on the
opposing approach, in veh/h
• Interpolation in Table 1 for opposing volume is appropriate, but
values should be round to the nearest tenth
• For right turns, the ‘conflicting crosswalk’ is the crosswalk through
which right-turning. Vehicles must pass
• Pedestrian volumes indicated in Table 2 represent typical situations
in moderate-sized communities. Pedestrian volumes in large cities,
like New York, Chicago, or Boston, may be much higher, and the
relative terms used (low, moderate, high, extreme) are not well
correlated to such situations.
• Interpolation in Table 2 is not recommended.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 43

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Once appropriate values for ELT and ERT have been selected, all right- and
left-turn volumes must be converted units of ‘equivalent through-
vehicle’. Subsequently, the demand intensity per lane is found for each
approach or lane group.
VLTE=VLT*ELT
VRTE=VRT*ERT

Where: VLTE = left-turn volume in equivalent through-vehicle, tvu/h

VRTE= right-turn volume in equivalent through-vehicle, tvu/h

These equivalents are added to through vehicles that may be present in a

given approach or lane group to find the total equivalent volume and
equivalent volume per lane in each approach or lane group:
VEQ=VLTE+VTH+VRTE
VEQL=VEQ/N

Where: VEQ= total volume in a lane group or approach, tvu/h

VEQL=total volume per lane in a lane group or approach, tvu/h/ln,
N= number of lanes
1 November 2023 Prepared by : Dr. Hirsh M. Majid 44
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Finding the critical-lane volumes for the signal phase plan requires determining the
critical path through the plan (i.e., the path that controls the signal timing). This is
done by finding the path through the signal phase plan that results in the highest
possible sum of critical-lane volumes.
The passenger car equivalent for all heavy vehicles is 2.0. Passenger-car
equivalents for local buses are more complex and shown in Table-3
Table 3: Passenger-car equivalents for local buses at signalized intersections
Local bus equivalents vary with a number of
underlying conditions, including the
percentage of local buses in the traffic
stream, the total volume in the affected
traffic stream, and the number of lanes in
the affected lane group. Exclusive LT lanes
are generally not included as ‘affected
lanes’. The type of bus stop also affects
these equivalents. If the bus stops in a travel
lane, the impact of the blockage is more
severe than when the bus stops in a parking
lane or in an offline bus bay.
1 November 2023 Prepared by : Dr. Hirsh M. Majid 45
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 46

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Finding the critical-lane volumes for the signal phase plan requires
determining the critical path through the plan (i.e., the path that controls
the signal timing). This is done by finding the path through the signal phase
plan that results in the highest possible sum of critical-lane volumes.
Example: Figure below shows a ring diagram for a signalization with
overlapping phases, lane volumes –through, left and right- are shown for
each movement in the phase diagram. Find VEQL and the critical path
(critical lane volume). Given:
-The cycle is divided into two phases A and B. Phase A is divided into two
rings
-West bound and east bound left turns have protected lane
-Pedestrian volume in conflicting crosswalk, (peds/h)=50
-Traffic volume for each direction is shown.
-Through and right directions have only one lane.

1 November 2023 Prepared by : Dr. Hirsh M. Majid 47

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Volume Volume Lane group

Approach Movement Equivalent
veh/h tuv/h volume tvu/h/ln ØA1
143 veh/h 238 veh/h
L 143
EB T 481
ØA2 57 veh/h
R 57
L 238 531 veh/h
481 veh/h
WB T 531 ØA3

R 57 57 veh/h

L 21 200 veh/h

NB T 200 21
39 23 21
ØB
R 39
200 veh/h
L 21
SB T 200
Ring 1
R 23 Ring 2

1 November 2023 Prepared by : Dr. Hirsh M. Majid 48

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution:
Volume Volume Lane group
Approach Movement Equivalent
veh/h tuv/h volume tvu/h/ln ØA1
143 veh/h 238 veh/h
L 143 1.05 150 150
EB T 481 1 481
550 ØA2 57 veh/h
R 57 1.21 69
L 238 1.05 250 250 531 veh/h
481 veh/h
WB T 531 1 531 ØA3
600
R 57 1.21 69 57 veh/h

L 21 2.5 52.5 200 veh/h

NB T 200 1 200 300 21

39 23 21
ØB
R 39 1.21 47.19
200 veh/h
L 21 2.5 52.5
SB T 200 1 200 280
Ring 1
R 23 1.21 27.83 Ring 2

1 November 2023 Prepared by : Dr. Hirsh M. Majid 49

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution:
Lane group
Approach Movement
volume tvu/h/ln ØA1 Solution:
150 tuv/h 250 tuv/h
Ring 1=150+600 = 750 tuv/h
L 150
Ring 2 = 250+550=800 tuv/h
EB T
550 ØA2 VcA=800 tuv/h
R
VcB=300 tuv/h
L 250 600 tuv/h
550 tuv/h
WB T ØA3
600 Vc= 800+300
R
Vc= 1100 tuv/h
L 300 tuv/h

NB T 300
ØB
R
280 tuv/h
L
SB T 280
Ring 1
R Ring 2

1 November 2023 Prepared by : Dr. Hirsh M. Majid 50

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Determining the desired cycle length

An equation is used to find the desired cycle length, based on tvu volumes,
and a default value for saturation flow rate. The default saturation flow
rate, 1615 tvu’s (1500 to 1700) per hour of green, assumes typical
conditions of lane width, heavy-vehicle presence, grades, parking,
pedestrian volumes, local buses, area type, and lane utilization.
The desired cycle length is computed as:

𝑑𝑒𝑠
𝑐

Where Cdes=desired cycle length, sec

L=total lost time per cycle, sec/cycle
PHF=peak-hour factor
v/c = target v/c ratio for the critical movements in the intersection (0.85 to 0.95)

Use of the peak-hour factor ensures that the signal timing is appropriate for
the peak 15 minutes of the design hour.
1 November 2023 Prepared by : Dr. Hirsh M. Majid 51
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Splitting the Green

Total effective green time in the cycle (gTOT):
gTOT=C-L

Effective green time for each phase (gi):

gi=gTOT*(Vci/Vc)
gTOT= total effective green time in the cycle, sec
Vci= critical lane volume for phase or subphase i, veh/h
Vc= sum of the critical-lane volumes, veh/h

Acutal green time for each phase (Gi):

Gi=gi-Yi+tLi
gi= effective green time for phase i, sec
Yi= total yellow and all-red intervals for phase i, sec
tLi= total lost time for phase i, sec
1 November 2023 Prepared by : Dr. Hirsh M. Majid 52
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: Consider the example illustrated previously in Figure

above. The sum of the critical-lane volumes for this case was shown
to be 1100 veh/h. What is the desirable cycle length for this three-
phase signal if the total lost time per cycle is 4 sec/phase*4
phases/cycle = 12 sec/cycle, the peak-hour factor is 0.92 and the v/c
ratio is 0.90? Find the effective green for each phase.
Solution:
𝑑𝑒𝑠

Thus, a 70-second cycle would be adopted in this case.

- For the critical path, the following critical lane volumes were
obtained:
• 250 veh/h/ln for the sum of phases A1 and A2
• 550 veh/h/ln for phase A3
• 300 veh/h/ln for phase B

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example cont’d
Lost time = 12 sec, cycle length =70
gTOT=C-L  gTOT=70 – 12 = 58 sec

gi=gTOT*(Vci/Vc)  gA1+A2= 58 * (250/1100) = 13.2 sec

gA3 = 58 * (550/1100)=29.0 sec
gB= 58 * (300/1100)=15.8 sec
gA1 and gA2
gA1= (13.2+29)*(150/(150+600))=8.4 sec
gA2 = 13.2-8.4 = 4.8 sec

1 November 2023 Prepared by : Dr. Hirsh M. Majid 54

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

1 November 2023 Prepared by : Dr. Hirsh M. Majid 55

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: Figure below illustrates the intersection of two four-lane

arterials with significant demand volumes and exclusive left-turn lanes
provided on each approach.

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Step 1: Check left turn protected lane.

Where :
= cross-production rule
=opposing through movement flow rate, veh/h
=number of lanes for opposing through movement

Recommended selection criteria for protected left-turn

1 November 2023 Prepared by : Dr. Hirsh M. Majid 57
University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Step 2: Convert volumes to through vehicle equivalents.

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Step 3: Determine critical lane volumes.

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Step 4: Determine yellow and all-red intervals

Speed limit = 45 mile/h =
The speed limits on both arterials are the same, so the yellow intervals for all three
phases will also be the same:
85

, ,

The all-red intervals will reflect the need to clear the full width of the street plus
the width of the far crosswalk.
The width of the N-S street = 55 ft
The width of the E-W street = 60 ft
The width of a crosswalk is 10 ft
For phase A : the width to be cleared (P) is 60+10 = 70 ft
For phase B: P=60+10=70 ft
For phase C: P=55+10 =65 ft

1 November 2023 Prepared by : Dr. Hirsh M. Majid 60

University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution:

15

Where L=20 ft assumed as length of a typical vehicle.

, =1.4 sec
. ×

=1.3 sec
. ×
Step 5: Determination of lost times

Then: is the same as the sum of the yellow plus all-red intervals, Y:
, ,

Then the total lost time per cycle, L= 5.7+5.7+5.6 = 17 sec

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Step 6: Determine the desirable cycle length

A cycle length of 110 seconds would be selected.

Step 7: Allocate effective green to each phase

The cycle length = 21.6+ 42.5 + 28.9 + 17 = 110 O.K.

Note that when the default values for (both 2 sec) are used, actual green
time, G, equal effective green time, g.
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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Phasing diagram

Phase A

Phase B
Phase C

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Step 8 : Check pedestrian requirements:

…… For

…… For
Where:
= minimum pedestrian crossing time, s
L = length of the crosswalk, ft
=Average walking speed of pedestrians, ft/s
=number of pedestrians crossing per phase in a single crosswalk, peds
=width of crosswalk, ft
Note that pedestrians will be permitted to cross the E-W artery only during Phase
B. Pedestrians will cross the N-S artery during Phase C. The number of pedestrians
per cycle for all crosswalks is the default pedestrian volume for moderate activity,
200 peds/h, divided by the number of cycles in an hour = 3600/110 = 32.7cycles/h.
Thus =200/32.7= 6.1 peds/cycle.

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Solution: Required pedestrian green times are:

Therefore, no changes to the vehicular signal timing are required to accommodate

pedestrians safely. Note that pedestrians are more than accommodated by the
vehicular greens, so it is not necessary to allow pedestrians in the crosswalk during
y and ar intervals.
- During Phase A, all pedestrian signals would indicate ‘DON’T WALK’.
- During Phase B, the pedestrian clearance interval (the flashing DON’T WALK)
would be or 60/4 = 15 sec. The WALK interval is whatever time is left in
G+Y, (or G+y, or G) counting from the end of Y (or y or G): using G+Y = 48.2-
15=33.2 sec.
- During Phase C, is 55/4=13.8 sec, and the WALK interval would be 34.5-13.8
= 20.7 sec (again using the end of Y).

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Example: Figure below illustrates a typical T-intersection, with exclusive lanes

for various movement as shown. Note that there is only one opposed left-turn in
the WB direction.

Solution:

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

The Institute of Transportation Engineers (ITE) recommends that

both yellow and all-red intervals be used at all signals. The function
of these critical intervals is as follows:
Change interval (yellow): This interval allows a vehicle that has
no safe stopping distance away from the STOP line, when the
GREEN is withdrawn, to continue at the approach speed and enter
the intersection legally on yellow. ‘Entering the intersection’ is
interpreted to be the front wheels crossing over the intersection
curb line.
Clearance interval (all-red): Assuming that a vehicle has just
entered the intersection legally on yellow, the all-red must provide
sufficient time for the vehicle to cross the intersection and clear its
back bumper past the far curb line (or crosswalk line) before
conflicting vehicles are given the GREEN.

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University of Sulaimani Civil Eng. Dept Adv. Traffic Eng. :Master course

Syllabus_6 : Traffic Signal Design

• Yellow time
•All-red time
•Cycle length
•Phase
•Lost time

1 November 2023 Prepared by : Dr. Hirsh M. Majid 68