Chapter 10: Speed, Travel Time, and
Delay Studies
Chapter objectives: By the end of these chapters the student will be
able to (we spend 2 lectures for this chapter):

Explain when speed, travel time, and delay studies are needed

Determine how many samples are needed
Collect and reduce speed data
Compute descriptive statistics
Apply a Chi-square test to speed data
Conduct a before and after study

Collect and reduce travel time data






Explain the types of delays experienced at signalized intersections
Collect and reduce intersection delay data
Chapter 10
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10.1 Introduction
They are used to evaluate the performance of a traffic
facility, like arterials and signalized intersections. “Speed”
here is a so-called a spot speed measured by a radar gun,
etc., at a point in the facility. If you determine travel time
and compute speed for a relatively long section, then it is a
space speed.
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10.2.2. Uses of spot speed data
Spot speed studies are conducted to estimate the
distribution of speeds of vehicles in a stream of traffic
at a particular location on a highway.
Used for:
 Establish the effectiveness of new or existing speed limits and/or
enforcement practices
 Establish trends to assess the effectiveness of national policy on
speed limits and enforcement
Specific design applications (like sight distance)
 Specific control applications (yellow/all red timing – the size of
dilemma zone depends on speed)
 Investigation of high-accident locations at which speed is suspected
to be a causative factor
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10.2.1 and 10.2.4 Speed definitions of interest
Average speed
Speed data
Not grouped
Grouped
u = uj/N
Standard
deviation
Speed data
Not grouped
Grouped
s=
f(ui – u)2
N-1
Variance
s2
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Median speed
The speed at the middle value in a series of spot
speeds. Or, 50th-percentile speed
Modal speed
The speed value that occurs most frequently in a
sample of speeds
ith-percentile
speed
The spot speed below which i percent of the
vehicles travel, e.g. 85th-percentile speed
Pace
The range of speed that has the greatest number
of observations; usually 10-mph range
85%
50%
Chapter 10
See table
10.1.
5
10.2 Spot Speed Studies
Once data are collected, the first thing you do is to compute
several descriptive statistics to get some ideas about the
distribution of the speed data. (Note that many statistical analyses
used in traffic engineering assume data are normally distributed.
 So, the goal is to check whether they are really normally
distributed.)
Typical descriptive statistics are:
 Average speed
 Variance and standard deviation
(These concepts
appeared in
chapter 7.)
 Median speed
 Modal speed (or Modal speed range  Needs a histogram)
 The ith-percentile spot speed
 Pace  Usually a 10-mph interval that has the greatest
number of observations.
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Speed Sample Size
For percentile speed comparisons
This table is for
two-sided tests.
K = z-score
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Location, time of day, and duration…
The objective and scope of the study dictate these.
Basic data collection
Like deciding speed limits  Find
locations where system characteristics
change and TWTh
Speed trend analyses
Avoid external influences such as
traffic lights, busy access roads; offpeak, TWTh  mid blocks of streets,
straight,level sections of highways
All other specific purposes  Conduct
Specific traffic
engineering problems it at the location of interest and time
of day
At least 1 hour or at least 30 data (if you want to assume normal
distribution, but usually you should collect at minimum 100 speeds.)
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10.2.3 Analysis of Spot Speed
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Chapter 10
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Pace
Chapter 10
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Chi-square (2-) test
(So called “goodness-of-fit” test), p.143
Example: Distribution of height data in Table 7-9.
N
H0:The underlying distribution is uniform.
 
2

( ni  f i )
fi
i 1
H1: The underlying distribution is NOT uniform.
2
25
20
15
10
5
Observed Freq
The authors intentionally used the uniform distribution to make the computation simple. We will
test a normal distribution in class using Excel.
Theoretical Freq
6.8-7.0
6.6-6.8
6.4-6.6
6.2-6.4
6.0-6.2
5.8-6.0
5.6-5.8
5.4-5.6
5.2-5.4
5.0-5.2
0
Steps of Chi-square (2-) test

Define categories or ranges (or bins) and
assign data to the categories and find ni = the
number of observations in each category i. (At
least 5 bins and each should have at least 5 observations.)


Compute the expected number of samples for
each category (theoretical frequency), using
the assumed distribution. Define fi = the
number of samples for each category i.
Compute the quantity:
N
 
2

i 1
( ni  f i )
fi
2
Steps of Chi-square (2-) test (cont)


2 is chi-square distributed (see Table 7-11,
p.145). If this value is low if our hypothesis is
correct. Usually we use  = 0.05 (5%
significance level or 95% confidence level).
When you look up the table, the degree of
freedom is f = N – 1 – g where g is the number
of parameters we use in the assumed
distribution. For normal distribution g = 2
because we use µ and  to describe the shape of
normal distribution.
If the computed 2 value is smaller than the
critical c2 value, we accept H0.
Why g = 2 for normal distribution?
See Eq. 7-7 in p.125.
What’s the Chi-square (2-) test testing?
Assumed
distribution
Expected
distribution (or
histogram)
You need to know how to pull
out values from the assumed
distribution to create the
expected histogram.
Chi-square (2-)
test tests this
relationship.
Actual
histogram
p.207 Before and After Spot Speed Studies

Two questions that must be answered:
 Is the observed reduction in average speeds real? – checked
by comparison of the means test (Was there any statistical
difference?) – Use the simple z- or t-test depending on the
number of samples and select a one-way or two-way test
depending on the hypothesis you want to test.)
 Is the observed reduction in average speeds the intended 5
mph (or whatever the value expected) – checked by the
confidence interval to see if the targeted speed is within the
confidence interval of the after speed value (Was the goal
achieved? Use only the results of the “after” distribution.
This is done by two-way test. Why?)
Review 7.8.2.
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Part 2: Was the target speed achieved?
Example in p.209
Part 1: One-way (zc = 1.645) or
two-way test (zc = 1.96)?
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10.3 Travel-time (travel delay) studies
* Determines the amount of time required to travel from one
point to another on a given route. Often, information may
also be collected on the locations, durations, and causes of
delays
•Indicate the level of service
•Identify problem locations
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Applications of travel time and delay data
(p.211)
Many uses of
travel time data
Efficiency check
Collection of
rating data
Problem location
identification
Model calibration
Evaluation of
performance before
and after improvement
(like ramp metering vs.
no metering)
Chapter 10
Collect data for
economic analysis
(user costs)
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10.3.1 Field study techniques
Methods requiring a test vehicle:
 t / 2 , N 1   
N 

d


2
Floating car
technique
The test car “floats” with the traffic. Attempts to
pass as many vehicles as those that pass the test
vehicle. (More or less average travel time. Meant for
2-lane 2-way highways. Difficult on multilane
highways)
Maximum car
technique
Drive as fast as is safely practical in the traffic
stream without ever exceeding the design speed of
the facility. (About 85th percentile speed, meaning
15th percentile travel time)
Average car
technique
Drive the test car at a speed that, in the opinion of
the driver, is the average speed of the traffic stream
(Get average travel time and less stressful)
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Methods not requiring a test vehicle:
License-plate
observation
Each observer located at strategic points record last
3 or 4 digits of license plates. Need to synchronize
the observer’s watch.
Interviews
Ask the drivers!
License-plate method  NG for a grid
network – too many routes
Use of ETC
for freeways
Sensys magnetic
sensor
Bluetooth
technology
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Chapter 10
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10.3.2 TT along an arterial: An
example of the statistics of TT


(Usually) the distribution of running times is
considered normal, but the distribution of travel
time is not (because stopped delays at the
intersections may follow a completely different
distribution).
Example: Mean running time = 196 sec, the SD of
the running time = 15 sec. See the discussion of
speeds obtained by these values in page 214. (This
problem is talking about running time only.)
Note that this discussion has nothing to do with Table 10.4.
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What about travel times?, p.214, Fig 10.3
Mean RT = 196 sec
Mean TT = 218.5 sec
SD of TT = 38.3 sec
No. of
signal
stops
Probability
of
occurrence
Duration
of stops
0
0.569
0 sec
1
0.300
40 secs
2
0.131
80 secs
This example has 20 travel-time data. This graph does not look normal
because travel time = running time + stopped delay. Running times
distribute like a normal distribution. Delay distribution is not as shown in
this table.
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Fig 10.3
Adding the average delay time to the
average running time (196 sec).
d av  0 . 569  0   0 . 300  40   0 . 131  80   22 . 5 sec
AverageTT
 196 . 0  22 . 5  218 . 5
10.3.3 Skipped.
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10.3.4 Travel-time displays
Use of travel time data:
• A travel time contour as an
example
Relation between ideal flow
and actual flow
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10.4 Intersection Delay Studies
Travel time and delay studies take delays at
signalized intersections but such samples
(observations) are not adequate to evaluate the
delay at a particular signalized intersection. 
Conduct an intersection delay study.
Measure of effectiveness  Delay
(Current HCM2010 uses the “average control delay”, but
previous one (before HCM 2000) used the “average stopped
delay.”
The average control delay: the total delay at an
intersection caused by a control device,
including both time-in-queue delay plus delays
due to acceleration and deceleration (We will
discuss these delays later in the semester).
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Delay Types





Stopped-time delay - completely stopped
Approach delay – Adds delays by acceleration and
deceleration to stopped-time delay
Time-in-queue delay = (time to cross the stop line)
– (time when joined a queue), meaning in between
the vehicle is in stop-and-go state. (Remember how
queued vehicles are released.)
Control delay = (time-in-queue delay) + (accel/decel
delay)
Travel-time delay = (actual travel time) – (desired
travel time)
(Just an intro. We will study these later.)
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4 assumptions made for control
delay field measurements (p.219)
Meant for undersaturated flow conditions (max queue is
about 20 to 25 vehicles.
2.
Does not directly measure acceleration-deceleration
delay. Use an adjustment factor to estimate this
component
3.
Uses an adjustment to correct for errors that are likely to
occur in the sampling process
4.
Must make an estimate of free-flow speed before
beginning a detailed survey (drive through the approach
before collecting data). Need to determine accel/decel
delay adjustment: see Tab 10.6.
Start at the beginning of the red phase of the subject lane
group. No overflow queue should exist from the previous
green phase (ideally).
1.
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HCM 2010: Intersection delay study method (by lane group)
Task 1: Observer 1 keeps track of the end of standing queues for each cycle
by observing the last vehicle in each lane that stops due to the signal. This
includes vehicles that arrive on green but stop or approach within one car
length of queued vehicles that have not yet started to move.
See Fig. 10-9 for a sample
survey form and Tab 10-7
for a sample data.
Observer 1
Observer 2
Task 2: Record the number of vehicles in
queue on the field sheet (at the end of the
interval). Vehicles in queue are those that
are included in the queue of stopping
vehicles (as defined in Task 1) and have
not yet exited the intersection.
Count arriving vehicles & the
number of vehicles that stops
once or more. Stopping
vehicles are counted only
once, regardless the number
of times they stop.
The count interval is typically between 10 sec and 20 sec. It should be an
integral divisor of the cycle length. Task 3: At the end the survey period,
vehicle-in-queue counts continue until all vehicles that entered the queue during
the survey period have exited the intersections. (Observer 1)
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Figure 10.9
Delay data
collection form
(fig 10.9 &
Handout)
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Average time-in-queue estimation
(10-15)
Chapter 10
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Adjustments for accel/decel delay
(10-16)
(10-18)
Table 10.6:
(10-17)
Table 10.6:
Correct!
Chapter 10
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(10-17) and (10-18)
veh/ln/cycle
Chapter 10
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731-733
Manual Method
733-735
735-737
100%
737-739
739-741
Percent Deviation
80%
741-743
743-745
60%
730-732
40%
732-734
734-736
20%
736-738
0%
738-740
740-742
-20%
742-744
Ave
-40%
0
5
10
15
20
Time Increment
Ave+std
Ave-STD
10 second interval seems to be the best compromise
according to my study with Jay Walker.
Chapter 10
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