Conen 442 module1b: Traffic Studies

Traffic Studies
A- Review for Statistics
B- Volume Studies
C- Speed Studies

Basic Statistics: Review
 What are Statistics?
 The art of abstracting Real World via
sampling and deriving general
“estimates” that describes the Real
World at a certain degree of
confidence.
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CONEN 442 Transportation Engineering S2021
104
Real World
sample
Sample Date
&
Data Reduction
Descriptive
Measures for
Real World
(@ deg. Of
confidence)
Math.
Model
Decision
Making
&
Design

Basic Statistics: Review
 When do we need Statistics?
When we can not measure all the data values for the
population.
 Before starting: What do we need to address?
Sample Size (how many measurements are
sufficient?)
What Confidence should I have in the results?
What statistical model distribution (math model) that
better describes the observed data?
Did a traffic engineering solution affected the status
of the Real World significantly?(before & after
analysis)
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Basic Statistics:
Sample Reduction & Visualization
Frequency Histogram
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Cumulative Frequency
Percentile %
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
55 65 75 85 95 105 115 125 135
Cumulative
Frequency% Observations
0
5
10
15
20
25
30
35
55 65 75 85 95 105 115 125 135
Frequency
Observations

Basic Statistics:
Common Statistical Estimators
Mean:
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ns
Observatio
of
number
N
i
n
observatio
x
mean
sample
x
where
N
x
x
i
N
i
i






)
(
:
1
Median:
- Is the middle value of
all the sample data (
i.e. 50% of the data are
above this value)
Mode:
Is the value that occurs
most frequently
 Measures of Central Tendency:

Basic Statistics:
Variance:
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108
ns
Observatio
of
number
N
i
n
observatio
x
mean
sample
x
Variance
sample
S
where
N
x
x
S
i
N
i
i









)
(
:
)
1
(
)
(
2
1
2
2
Standard Deviation:
 Measures of Dispersion:
Variance
sample
S
Deviation
dard
S
S
where
N
x
x
S
S
N
i
i








2
1
2
2
tan
:
)
1
(
)
(

Basic Statistics:
Coefficient of Variation:
The ratio between the
standard deviation and the
mean.
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109
mean
sample
x
deviation
Standard
STD
Variation
of
t
Coefficien
C
where
x
STD
C




var
var
:
Skewness:
Describes the asymmetry in
the data sample.
 Measures of Dispersion:
STD
mode)
mean
Skewness


(

Basic Statistics:
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110
 MS Excel Functions:
 Mean  = average(range array)
 Mode  = mode(range array)
 Median  = median(range array)
 Variance  = var(range array)
 Standard Deviation  = stdev( range array)
 Skewness  = skew( range array)

Basic Statistics: Useful MS Excel “Tricks” 1
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111
 For Plotting Frequency Diagram:
For a sample of speed observations do the following:
 Delete the lowest value and the highest value from the sample because those are called
“outliers”
 Define the range of the data using the functions: =min(data range) & = max(data range)
 Divide that range into equal intervals
 Estimate the frequency of values grater than the lower limit of each interval , use the following
functions: = freq(data range, “> value”)
 Subtract the values from the previous interval, then you get the frequency for that interval.
 The sum of all values should be the number of observations (N)
 Define the mid of the interval as (x) and the freq. of interval as (y)
 PLOT using column chart type

Basic Statistics: Useful MS Excel “Tricks” 2
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112
 Plotting Cumulative Frequency% Diagram:
For the same sample do the following:
 Define a percentile sequence (y) starting from 0% to 100% in 5% increments.
 For each percentile value (y) in the sequence determine the corresponding
observation value (x):
= Percentile(data range, percentile value (y))
 Plot using XY- line chart type

Basic Statistics:
Standard Error, True Mean & Sample Size
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 Standard Error:
The standard error (E) in the sample mean ( X ) is function in the
sample size and the standard deviation of the population ( the
sample SD can be used instead):
size
sample
the
is
-
N
instead
used
be
can
sample
the
for
SD
The
population
the
for
deviation
standard
the
is
-
where
N
E




Basic Statistics:
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114
 True Mean: m
The standard error (E) for the sample mean ( X ) is assumed to follow a
normal distribution around the true mean ( m ).
Hence:
mean
sample
the
is
-
X
sample
the
of
error
standard
the
is
-
E
where
99.5%)
Confidence
of
Degre
(at
E
X
95%)
Confidence
of
Degree
(at
E
X
67%)
Confidence
of
Degree
(at
E
X
00
.
3
96
.
1
00
.
1






m
m
m

Basic Statistics:
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115
 Sample Size:
For a given allowable error ( err ) and a specific degree of
confidence , the sample size ( N ) can be determined as following:
mean
true
the
in
error
allwable
maximum
-
err
sample
the
of
deviation
standard
the
is
-
SD
where
99.5%)
Confidence
of
Degre
(at
err
SD
N
95%)
Confidence
of
Degre
(at
err
SD
N
67%)
Confidence
of
Degre
(at
err
SD
N
2
2
2
























)
00
.
3
(
)
96
.
1
(

Speed Studies
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Speed Studies: Spot Speed Studies
Spot Speed Studies:
 Is defined as the average speed of vehicles passing a point on a
highway. This is also known as the time mean speed.
 Usually conducted in free flow condition and not during congestion,
where the flow rate is:
750-1000 veh/hr/ln  for freeway
<500 veh/hr/ln  for other types
Speed Definition of Interest:
- Average or time mean speed
- Standard Deviation
- 85th % speed
- Median speed
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Uses of Spot Speed Data:
 To determine speed limit for applications
 To assess speed limit enforcement
 Specific Applications:
 For Level of Service (LOS) Assessment
 For Signal timing: Estimation of Yellow/All Red times.
 To determine appropriate sight distance
 For safety and accidents analysis
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Speed Studies: Measurement
Techniques
Manual Method: The Simple Stopwatch Method :
By using stopwatch and defining two reference points
with known distance (d) between the two points.
Then, Speed = d / t (m/s)
Advantages: Simple
Disadvantages:
High error due to stopwatch
depressing time variations.
Class Example
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119
40 m

Doppler Radar (Speed Gun):
It uses Doppler’s effect for speed measurements.
How Does it work?
 The radar transmits a pack of waves with initial frequency fini and initial
wavelength lini ,
 Due to the motion of the target vehicle, the wavelength of the reflected waves
lref will be longer or shorter than the initial wavelength lini
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120
direction
s
target'
the
on
depnding
V
f
target
ini
ini
ref 

 *
1
l
l
lini
lref
Transmitted wave
Reflected wave
Target
Radar

Doppler Radar (Speed Gun):
Advantages:
High Accuracy, but the readings must be corrected for aiming
angle.
Disadvantages:
Difficult to conceal, drivers associate Radar
with police which may cause them to
slow their speeds down and yielding
inaccurate results.
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Doppler Radar (Speed Gun): Readings Correction
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122
q

cos
Speed
TrueSpeed 

Spot Speed Studies:
Data Reduction & Analysis
The speed data is analyzed and reported as following:
A- Graphical: Frequency Histogram & Accumulative %
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0
5
10
15
20
25
30
35
50-60 60-70 70-80 80-90 90-100 100-110 110-120 120-130 130-140 140-150 150-160
Frequencey
Speed (km/hr)
MODE = 105 km/hr
The shown speed data
has
a Bimodal Distribution

Spot Speed Studies:
A- Graphical: Accumulative %
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124
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
20 40 60 80 100 120 140 160 180
Accumulative
%
Speed (km/hr)
Median
85
%
85th% Speed
15
%
15th% Speed

Spot Speed Studies:
B- Quantitative:
1- Mode
2- Median
3- Mean
4- Standard Deviation (SD)
5-85th% & 15th% Speeds
6- Pace(15 km/hr band)
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Spot Speed Studies:
C- Precision and Confidence Intervals:
Note: Most spot speed data tend to be normally distributed (however, this might
not applicable in the shown example histogram), then:
Standard Error:
True Mean:
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126
size
sample
the
is
-
N
sample
the
for
deviation
standard
the
is
-
SD
where
N
SD
E 
mean
sample
the
is
-
X
sample
the
of
error
standard
the
is
-
E
where
95%)
Confidence
of
Degree
(at
E
X 96
.
1


m

Spot Speed Studies:
D- Sample Size for Prescribed Precision with Confidence Intervals:
If the Prescribed precision was set to be +/- e, the needed
sample should not be less than the following number of
observations N @ a degree of confidence 95%:
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127
mean
true
the
in
error
the
i.e.
precision
needed
the
-
e
sample
the
of
deviation
standard
the
is
-
SD
where
e
SD
N
2








 )
96
.
1
(

Speed Studies: Before and After Analysis
Before and After Analysis:
 Usually carried out to evaluate the effectiveness of applying a specific
measure on the prevailing speed in an area or a segment.
 The before and after is basically a comparison testing between two samples
, with the objective of finding that the difference between the two samples is
significant or not.
 Hypothesis Testing
Any hypothesis test, has 4 possible outcomes:
1- Test Result: True, and Reality: True
2- Test Result: False, and Reality: False
3- Test Result: False, and Reality: True Error Type II
4- Test Result: True, and Reality: False Error Type I
Error Type I - must be avoided at all expenses
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True/True
False/Fals
e
False/Tru
e
True/Fals
e

The Statistical Testing (Z-test):
First, calculate the Pooled Standard Deviation for before & after
samples:
Second: Calculate Zd the Standard Normal distribution approximation for
the Observed difference between the before & after samples:
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129
resp.
after
&
before
size
Sample
N
N
resp.
after
&
before
Deviation
Standard
S
S
Deviation
Standard
Pooled
S
where
N
S
N
S
S
2
1
2
1





&
&
2
2
2
1
2
1


 )
difference
mean
population
ed
hypothesiz
d
Deviation
Standard
pooled
S
resp.
after
&
before
speed
Mean
X
X
after
&
before
between
Diffirence
Normalized
Z
S
d
X
X
Z
o
2
1
d
o
d









&
2
1

The Statistical Testing (Z-test) cont.:
Third, we use the normal distribution curve to find the probability
that a value equal to or less than Zd , assuming that both
samples are normally distributed , then:
A) If Prob.( Z<= Zd ) > 0.95 , that means the observed reduction in
speed is statistically significant.
B) If Prob.( Z<= Zd ) < 0.95 , that means the observed reduction in
speed is statistically insignificant.
For case A, that implies also that there is a 5% chance that
the observed difference in mean speed will be exceeded.
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Example:
The following is the before and after summary for speed
enforcement project that was deployed with a target of
reducing average speed to 60 mph.
Before After
Mean Speed: 65.3 63 (mph)
SD: 5 6 (mph)
N: 50 60 observation
Solution
P(Z<2.19) = 0.9857 = 98.57 % >95%
Then: The observed reduction in speed was statistically significant
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131
mph
N
S
N
S
S 05
.
1
60
6
50
5 2
2
2
2
2
1
2
1






 ) 19
.
2
05
.
1
0
63
3
.
65




d
Z

Example (cont.):
Now, the question did we reach the target?
That means the true mean is between: (61.48 - 64.52) mph
The Answer is NO, the reduction is not sufficient, and we did not
achieve the 60 mph target
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132
mph
63.0
E
X 52
.
1
0
.
63
60
6
*
96
.
1
96
.
1 





m

Volume Studies
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Traffic Volume Studies:
Volume studies:
 Traffic counts are the most basic of traffic studies
and are the primary measure of demand; virtually
all aspects of traffic engineering require volume as
an input, including highway planning and design,
decisions on traffic control and operations, detailed
signal timing, and others.
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Automated and Manual counting techniques are used to produce
estimates of the following:
1. Volume: is the number of vehicles (or persons) passing a point during
a specified time period, which is usually one hour, but need not be it
can be a day, month, year…etc.
2. Rate of flow: is the rate at which vehicles (or persons) pass a point
during a specified time period less than one hour, expressed as
an equivalent hourly rate.
3. Demand is the number of vehicles (or persons) that desire to travel
past a point during a specified period (also usually one hour).
Demand is frequently higher than actual volumes where congestion
exists. Some trips divert to alternative routes, while other trips are
simply not made.
4. Capacity is the maximum rate at which vehicles can traverse a
point or short segment during a specified time period. It is a
characteristic of the roadway.
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Example for Volume, Demand & Capacity:
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Example: When demand exceeds capacity. What happens?
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Traffic Volume Studies: Manual Counting 1
Manual counting is typically used at intersections, however, it can
be used for highways for 1-2 hours, for LOS assessment.
Tally Sheets:
Recording data onto tally sheets is the simplest means of
conducting manual counts. The data can be recorded with a
tick mark on a pre-prepared field form. A watch or stopwatch is
necessary to measure the desired count interval. A blank traffic
volume count intersection tally sheet is provided in Appendix B.
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Mechanical Counter:
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Mechanical Counting Board (for Intersections):
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Electronic Manual Counting Board (for Intersections):
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Traffic Volume Studies: Automated Counting 1
Portable Counters:
 Portable counters serve the same purpose as manual counts
but with automatic counting equipment.
 The period of data collection using this method is usually
longer than when using manual counts.
 The portable counter method is mainly used for 24-hour
counts. Pneumatic road tubes are used to conduct this
method of automatic counts
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Portable Counters: Pneumatic Tube Counters
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Permanent Counters:
 Permanent counters are used when long-term counts are to be
conducted. The counts could be
 performed every day for a year or more. The data collected
may be used to monitor and evaluate
 traffic volumes and trends over a long period of time.
Permanent counters are not a cost-effective
 option in most situations. Few jurisdictions have access to this
equipment
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Permanent Counters: Inductive Loop Detectors
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Permanent Counters: Inductive Loop Detectors
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Video Imaging:
 Observers can record count data by videotaping traffic.
 Traffic volumes can be counted by viewing videotapes
recorded with a camera at a collection site.
 A digital clock in the video image can prove useful in noting
time intervals.
 Videotaping is not a cost-effective option in most situations.
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Video Imaging:
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Conen 442 module1b: Traffic Studies

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