Problem 1: Basic Freeway
Sections
Printable Version
Basic freeway
sections are among the most elementary of all highway facilities. They are
singledirectional links that tie one freeway juncture to the next. The
freeway junctures can be weaving sections, ramp junctions, or merge or
diverge points. Basic freeway sections are quickly identifiable because
there is no distinctive pattern to the lane changing, and no evidence exists of
distinctive subordinate traffic streams, as there would be at a weave, a
ramp, or a merge or diverge.
In this case study, two basic freeway sections exist on Route 7 between I87
and I787, both eastbound and westbound as shown in
Exhibit 43. The basic
freeway sections are approximately three miles in length and each direction
has characteristics that are unique.
The eastbound AADT is about 29,700 and the peak hour
volumes range up to about 3,250 in the AM peak and 2,400
in the PM peak.
The westbound section has an AADT of about 30,000 vehicles and peak hour volumes
of approximately 2,400 veh/hr in the AM peak and 3,500
in the PM Peak.
In this problem,
we'll use both of these directions to provide illustrations of a basic
freeway analyses. The eastbound direction
is fairly basic and will allow us to get familiar
with the input variables and the outputs, and to see how changes in some of
those variables influence the results. The
westbound direction has some distinct characteristics
that will allow us to look at issues related to the number of lanes
available, the designation of truck climbing lanes, and grades.
Here are some points to consider as you read through problem 1:
What time periods do you think should be selected for
doing an analysis of a basic freeway section?
What are the two or three most important characteristics of this subarea
that will likely define the operational performance of these basic freeway
sections? Do the defining characteristics differ by direction? How is the
configuration of each basic freeway section likely to affect downstream
system elements like merge points, diverge points, and weaving areas?
Discussion:
Take
a few minutes to consider these questions. When you are ready to
continue, click continue below to proceed.
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Problem 1 
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Subproblem 1a: Traffic Flow Patterns
Step 1. Setup
It is important to carefully determine what volume,
peak hour factor, and
speed values should be used in a basic freeway analysis. Ideally, a
combination of values that “typify” the conditions that exist during the
peak hour would be used. However, it’s often hard to determine what data
represent “typical” conditions. Often, not enough data is available to
determine what a typical condition is. That’s not a problem here because
plenty of information is available. In Subproblem 1a we will look at the
traffic data that was collected over a yearlong period.
Discussion:
The
data collection in this case study represents atypical conditions, where
traffic data along the study roadway has been monitored for years. If this
were not the case, how many volume studies would need
to be completed to ensure typical roadway conditions were sampled with some
degree of confidence? What other ways might be
available to account for the variability between data samples and typical
roadway conditions? Also, observe the variation in recorded traffic volumes
during similar time periods and consider the impact of this variation on
roadway performance. [
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SubProblem 1a 
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Subproblem 1a:
Traffic Flow Patterns
Flow Patterns
Just east of the bridge for Miller Road is a monitoring point used by the
Capital District’s Traffic Management Center, run by NYSDOT Region 1 and the
New York State Police. There is a doubleloop, 20foot speed trap in each
lane, eastbound and westbound. The inputs from these traps are monitored
24hours a day, 7days a week. Because the data is archived, we were able to
obtain a copy of the 15minute data collected at this location for 27
months, from 00:00 on April 25, 2000 to midnight on October 31, 2002.
For purposes of the case study, we studied these data for the 2001 calendar
year (Data points for 8,611 of the
8,760 hours in 2001 are shown in Exhibit 45, as the traps were out of service during the
few remaining hours where no data is available.) and discovered some
important things about the flow conditions. The first thing we learned
relates to the flows themselves. As can be seen in Exhibit 45, the flow rate
for a given hour varies widely. There
is a diurnal trend that can be identified. The diurnal pattern has
its minimum at 23:00 AM. The AM peak lasts from
about 59:00 AM, and it looks like the flow in the eastbound direction is heavier in the AM
peak than it is in the PM peak by almost 20%. The largest recorded volume in the AM peak
in 2001 was approximately
3,480 veh/hr, recorded on day 311 between 78:00 AM.

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SubProblem 1a 
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Exhibit 45.
Eastbound Traffic Volumes

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Subproblem 1a: Traffic Flow Patterns
The westbound direction shows a similar daily trend as can be shown in
Exhibit 46. There is the same diurnal pattern with a smaller AM peak and a
larger PM peak. The PM peak appears to begin at about 34:00 PM and persist
until 56:00 PM. (The largest recorded westbound hourly volume in 2001 was
3,830 veh/hr on the 324^{th} day of the year between 45:00 PM.)
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SubProblem 1a 
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Exhibit 46.
Westbound Hourly Traffic Volumes

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Subproblem 1a: Traffic Flow Patterns
Peak Hour Factor
There are always other questions about the performance of such facilities
such as the relationship between hourly volumes and the
peak hour factor,
speedflow relationships and flowdensity relationships.
Exhibit 47 shows the relationship between the hourly volumes and the peak hour
factors. The data for the entire year are again plotted. The westbound
direction is shown, and the eastbound plot is nearly identical. The average
value for the peak hour factor tends to increase as the volume increases.
There’s more variation in its value at low flows than at high flows. It ranges as low as 0.25 (that means
there was flow in only the peak 15minute time period) and it spans up to
1.0 for almost all volumes.
The data points associated with a PHF of
0.25 are likely to be outlier points, since this is an unlikely condition to
occur on a freeway with the nature of location of Alternative Route 7; more
likely, these data points reflect time periods when the automatic traffic
counters were not working properly, or the westbound lanes were closed
because of an incident, or some similar situation. So too with the few data
points that seem to suggest a PHF slightly greater than 1.0 since, by
definition, such a condition is not possible. Nevertheless, with such a
preponderance of data, the overall character of the relationship that exists
between PHF and hourly volume is clear. 
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SubProblem 1a 
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Exhibit 47.
Relationship between Hourly Volume and Peak Hour Factor

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Subproblem 1a: Traffic Flow Patterns
SpeedFlow
Exhibit 48 shows one of the lanespecific speedflow relationships. It
happens to be for Lane 1 Eastbound in the AM peak
time period, but it is similar to all the other peak hour plots (i.e., for
the other eastbound lane in the AM peak and for the westbound lanes in the
PM peak). The mean speed stays
at or near its maximum value (55 mph) from free flow conditions to capacity.
Moreover, at the high flow rates there are conditions where the speeds are
substantially lower as congestion impedes performance.
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SubProblem 1a 
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Subproblem 1a: Traffic Flow Patterns
FlowOccupancy
Exhibit 49 shows the corresponding flowoccupancy relationship for the same
lane and peak hour. The classical triangular shape depicted in textbooks is
evident, with a positive, linear relationship from (0,0) up to a maximum of
(15, 2264) between occupancy and flow for the uncongested conditions and
then a downward sloping trend toward (100,0) for congested conditions during
queue clearance.
All of these exhibits tell us we have a basic freeway section with typical
variations in the flows and the flow conditions. Moreover, from
Exhibits 45
and 46, it is apparent that the volume to select for the peak period analysis
is not that obvious. The volumes during the peak hour tend to vary a great
deal. In the AM peak hour (78:00 AM), for example, the volume ranges from
about 200 veh/hr up to nearly 3,500 veh/hr. The average is about 2,000 veh/hr.
None of these values seem to be correct for the analysis. The westbound
volume during the PM peak hour (45:00 PM) range from about 750 veh/hr to 3,800 veh/hr, averaging about 2,000 veh/hr. Again,
none of these values seem to be the best choice for a PM peak hour analysis.
We can gain further insight into the issues associated with that choice by
examining the flow rates associated with the four 15minute time periods
that occur during the AM and PM peak hours on weekdays during the year.
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SubProblem 1a 
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Exhibit 49.
FlowOccupancy Relationship, Eastbound First Lane

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Subproblem 1a: Traffic Flow
Patterns
Trends in the Traffic
Volumes
Exhibit 410 shows the distribution of weekday, 78:00 AM peak hour volumes for the
eastbound direction. On the one hand, it is apparent that the volumes can be
quite low. On the other, the values range up to 3,483 veh/hr. The mean value
is 2,916 veh/hr and the 50^{th}percentile is 3,096 veh/hr. The 90^{th}
percentile
is 3,340 veh/hr and the 95^{th}percentile is 3,385. The question is, which
value is the right one to select, one of these or some other?
Most
traffic engineers would think about the mean value when they talk about a
typical peak hour. But if you look at Exhibit 410, that seems like a pretty
low value to use in assessing the facility’s performance. For illustrative
purposes, in the next subproblem we’re going to use the 90^{th}percentile
volumes instead of the average volumes. This means that the
analysis results will represent conditions that will occur 90% of the year
during the AM peak hour. (We’ll come back and look at the facility’s performance during the
average peak hour conditions right after that.)
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SubProblem 1b 
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Exhibit 410. Distribution of 15minute Flow Rates during the AM Peak
Hour, Eastbound

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Subproblem 1b: Analysis of
the Eastbound Freeway Section
Step 1. Setup
In this subproblem we will analyze a freeway section. The
steps that we will use are outlined in Exhibit 411 below.
Discussion:
Take
a few minutes to consider the figure above. Click continue when you
are ready to proceed.
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Subproblem 1b 
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Subproblem 1b: Analysis of
the Eastbound Freeway Section
The eastbound
section has two lanes and is
divided into three segments:

a
onemile segment with a 12% upgrade to the vicinity of Miller Road 

a
onemile segment with a 12% downgrade, and


a final onemile segment
with a 57% downgrade ending at the I787 interchange.

The first task is to
specify the conditions. One important question is: where should we do the
analysis? Should we use the 57% downgrade, the 12% upgrade, or the 12%
downgrade? The HCM says: use the section that will produce the most
conservative estimate of the LOS. That is, worst case governs.
So we’ll use the 12%
upgrade section. In addition, because it is a mile long or more, we’ll assume
it’s a constant grade, not a rolling or mountainous section. (As an
aside, those categories don’t really have to do with where the
facility is. They relate a lot more to the vertical profile of the segment.
For example, a freeway running along a mountaintop is level even though
it’s in a mountainous region.)
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Subproblem 1b 
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Subproblem 1b: Analysis of
the Eastbound Freeway Section
The basic freeway analysis methodology is shown in
Exhibit 411. The inputs
required include
geometric data, a
freeflow speed (FFS) (or a free flow speed derived from a
basic freeflow speed) and volume information. The lefthand branch
addresses actions you have to take to obtain the freeflow speed while the
right hand branch focuses on the computation of a peak 15minute flow rate.
We’ll consider the lefthand branch first.
Freeflow speed (FFS)
can be measured in the field or estimated using the procedure outlined in
Chapter 23. We’ll consider
both.
The benefit of having speedflow
data as shown in
Exhibit 48 in this case study is that we can select a FFS and no adjustments
are necessary. If you look at that
figure, you can see that a
value in the range of 55 mph is a good
choice. This range reflects the average maximum speed when the flow rate
relatively low. We’ll assume that 55 mph is the right value.
However, it’s useful to see what FFS estimate we would get if we trace
through the branch labeled "if BFFS is input." We then take a basic
freeflow speed (BFFS) and make adjustments to it to account for lane width,
the number of lanes, the interchange density, and lateral clearances.
Nominally, the basic free flow speed (BFFS)
is how fast vehicles are traveling when the volumes are very light. The HCM
assumes the BFFS is BFFS is 70 mph in urban settings and 75 mph in rural
settings.
Exhibit 48 shows that both of these values are too high for this
facility. The maximum speed when the flow is almost zero is about 60 mph.
The HCM allows us to use a local value rather than the defaults. We’re going
to do that and assume the BFFS is 60 mph.
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Subproblem 1b 
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Subproblem 1b: Analysis of
the Eastbound Freeway Section
Using
the method to calculate FFS based on BFFS as shown in Chapter 23, our FFS is projected to be
55.5 mph, which is very close to what the data shows us in
Exhibit 48.
Now we need to revisit
Exhibit 411 and see that the next thing to do is to
calculate the peak 15minute flow rate.
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Subproblem 1b 
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Subproblem 1b: Analysis of
the Eastbound Freeway Section
Since we don’t have any formal data for the percentage of trucks/buses or
recreational vehicles in the traffic stream (during the peak hour), we’ll
use anecdotal observations and say that the percentage of trucks/buses is
about 5% (which means P_{T} is 0.05). We will assume there
is no significant volume of recreational vehicles in the traffic stream.
Referring to Equation 232 in
the HCM, we have V = 3,340 veh/hr, PHF = 0.90, N =
2, P_{T} = 0.05, P_{R} = 0, E_{T}
= 1.5, E_{R} = 1.2, and f_{p} = 1.0. This gives
us an average 15minute passengercar equivalent flow rate, v_{p} of 1,902 passenger cars per hour per
lane.
There’s one more thing to do before we assess the level of service (LOS) for
the facility, and that’s to compute the average passenger car speed
as shown on HCM page 235, using a set of equations based on Exhibit 412.
The equations break the speedflow relationship shown in Exhibit 412 into a
set of regions delineated as follows:
If (55 ≤ FFS
≤ 75 mph) and ( v_{p} ≤ 3,400 – 30* FFS ), then 
(4) 
S = FFS 
If (55 ≤ FFS
≤ 70 mph) and (3,400 – 30* FFS < v_{p} ≤ 1,700 + 10*FFS), then 
(5) 

And if (70 <
FFS ≤ 75 mph) and (3,400 – 30*FFS) < v_{p} ≤
2,400, then 
(6) 

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Exhibit 412.
Developing the Average Passenger Car Speed
(source: HCM Exhibit 233)

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Subproblem 1b: Analysis of
the Eastbound Freeway Section
The result for our
situation is S = 54.8 mph. If you take this value and divide it into
the peak 15minute flow rate, v_{p}, then you get the freeway
segment’s peak 15minute average density (passenger cars per mile per lane),
which is the basis for assessing the LOS (see
Dataset 1):
D
= v_{p} / S = 1,902 pcphpl / 54.8 mph = 34.7 pcpmpl
Where pcphpl means
passenger cars per hour per lane, mph is miles per hour, and pcpmpl is
passenger cars per mile per lane. The breakpoints in D for level of
service are as follows, all in passenger cars per mile per lane: A: 011; B:
1118, C: 1826, D: 2635, and E: 3545. Above 45 is LOS F.
For the circumstances
we’ve examined, where D = 34.7, the LOS is a high D, almost E. Since
we picked the 90^{th} percentile value to evaluate, this means that
10% of the time the eastbound LOS in the peak hour is D or worse, and 90% of
the time it is better than that.
Three
other significant conditions have the following levels of service:

For the average AM
peak hour, where the volume is 2,916 veh/hr, D is 30.2 pcpmpl and
the LOS is D (See
Dataset 2). 

For the high hour
recorded during the short count upon which the AADT is based, the volume
was 3,257 veh/hr, D is 33.8 pcpmpl and the LOS is D (see
Dataset 3). 

For the heaviest
hour observed in 2001, where the volume was 3,483 veh/hr, D is 36.5
pcpmpl and the LOS is E (see
Dataset 4). 
If we want to more
clearly characterize the performance of this location during the peak hour,
we ought to evaluate its performance during all of the 256 peak hours (78:00 AM
on a weekday) for which we have data. This isn’t a reasonable thought from a
practical standpoint, but it gives us a way to make an important point.
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Subproblem 1b 
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Subproblem 1b: Analysis of
the Eastbound Freeway Section
The question we’re
trying to answer is this: What is the performance of this facility like
during a reasonably heavy AM peak hour (some might refer to this as the
design hour)? To answer the question, we constructed a
spreadsheet that implements the HCM methodology shown in Equations (1)(4)
in a single row of a spreadsheet. The
spreadsheet contains a column for each of the following data items: day of
the year, day of the week, hour, eastbound volume, eastbound PHF,
percent trucks, percent recreational vehicles, heavy vehicle factor, driver
population factor, peak 15minute flow rate (v_{p}),
passenger car speed, and density. Subordinate tables contain the lane width,
the righthand shoulder clearance, and the number of lanes.
Three of these
data items are derived from the monitoring station data: V, the
volume for the hour; PHF, the peak hour factor (since these can be
computed from the underlying 15minute data), and S the passenger car
speed for the peak 15minute time period. P_{T} is set to 5%,
P_{R} is set to 0%, and f_{p} is set to 1.0
Exhibit 413. Peak Hour LOS Distribution 
LOS 
Max D 
# Hours 
Percent 
A 
11 
7 
2.7% 
B 
18 
7 
2.7% 
C 
26 
17 
6.6% 
D 
35 
208 
81.3% 
E 
45 
13 
5.1% 
F 
 
4 
1.6% 
Our findings are shown
in Exhibit 413 and Exhibit 414. For 208 of the 256 AM peak hours, or about 81.3%,
the LOS is D. That’s significant news. The predominant LOS is clearly D. For
5.1% of the peak hours it is E, for 1.6% it is F and for 6.6% it is C. (The
remaining 5.4% of the time it is A or B, probably on weekdays that are
holidays.) This seems consistent with field observations.
The implications of
Exhibit 413 are clear in terms of characterizing the performance of the
facility. You can be comfortable describing its average condition as D. You
could say that most of the time the LOS is D, in some heavilytraveled hours (6.7%
of the time or about once every two weeks) the LOS is E or F, and the
rest of the time it is A, B, or C. Chances are, your audience will
understand that. Certainly, your fellow traffic engineers will.

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1c 
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Exhibit 414.
Distribution of AM Eastbound Peak 15Minute
Density

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Subproblem 1c: Analysis of
the Westbound Freeway Section
Step 1.
Setup
We will now consider the conditions found along the westbound section, similar to subproblem 1a. Before we begin, think about why
conditions on the westbound section would be different than those on the
eastbound section? Consider roadway users, physical conditions, and heavy
vehicle needs.
Discussion:
Take
a few minutes to consider the question above. [ Back
] [ Continue ] with SubProblem 1c 
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Subproblem 1c: Westbound
Peak Hour
The first task is to
specify the conditions. The question again emerges: where should we do the
analysis? Should we use the 67% upgrade, the 12% upgrade, or the 12%
downgrade? The HCM says: use the section that will produce the most
conservative estimate of the LOS. That is, worst case governs. So we’ll use
the 67% upgrade section. In addition, since it is a mile long or more,
we’ll assume it’s a constant grade, not a “rolling” or “mountainous”
section.
For the other inputs,
we’ll have the following values: 3 lanes, 3,240 veh/hr (the average PM peak
hour volume), 55 mph as the free flow speed, 0.90 as the peak hour factor,
5% trucks/buses, and “local” drivers, i.e., ones that are familiar with the
facility.
The results are as
follows. A flow rate of 1,440 pcplph, a density of 26 pcplpm, a LOS of D,
and an average passengercar speed of 55 mph (see
Dataset 5).
With this kind of
output, we should see if two lanes would be enough. If we change the number
of lanes to two, the flow rate becomes 2,160 pcplph, the density is 42 pcplpm, the LOS is E, and the average passenger car speed is 52 mph. The third lane has a huge impact on the results
(see
Dataset 6).
Let’s look at the
issue about whether the truckclimbing lane is needed.
While this specific issue is not addressed in the HCM methodology for basic
freeway sections, we can analyze this by looking at the LOS for the section
without the presence of the truckclimbing lane and comparing that to the
LOS calculated if all trucks are removed from the passenger car travel
lanes.
First, let's look at the truckclimbing lane. We effectively have 5% trucks, or 162
trucks per hour, in the peak hour volume. If the E_{T} is 5, as HCM
Exhibit 239 suggests, the equivalent flow in passenger cars per hour
is 810 passenger cars per hour. That illustrates the impact of the trucks.
That’s almost a half lane’s worth of capacity.
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Subproblem 1c: Analysis of
the Eastbound Freeway Section
You can compute the
LOS by hand, but most software packages won’t let you do a single lane
analysis directly. So you need to do a workaround. To begin, you can assume a volume
of 1,620 passenger cars per hour and a twolane facility. That yields a LOS
of B and a density of 16.4 pcpmpl. So the truck climbing lane, if it’s used
just by the trucks, operates adequately (see
Dataset 7).
Next we need to check
the remaining two lanes to see how they would operate if no trucks were
present. The cars are 95% of the traffic stream, which means
a volume of 3,080 veh/hour. On two lanes, with 0% trucks, that yields a per
lane flow rate of 1,711 pcphpl, a density of 31.1 pcpmpl, and a LOS
of D. The average passenger car speed is 55 mph (see
Dataset 8).
Now let's consider the results
of this hypothetical scenario. If we assume all three lanes are used by all the traffic, we
get a density of 26.2 pcpmpl. If we separate the trucks into the truck
climbing lane, we get 16.4 pcpmpl for the truck climbing lane and 31.1
pcpmpl for the remaining two autoonly lanes. These results suggest that trying to
enforce exclusive use by trucks of the truckclimbing lane wouldn’t be a
good idea.
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Subproblem 1c: Analysis of
the Eastbound Freeway Section
Next, we should
examine the impacts that result from varying other variables. If we increase
the truck percentage to 10%, two things happen (see
Dataset 9):

First, the E_{T}
for the trucks drops from 5 to 3.5. That’s because the trucks have less
impact if they are a higher percentage of the traffic stream, up to a point.
At first glance this may seem counterintuitive, but upon reflection you can
see that it reasonably reflects conditions we all see quite regularly in the
field: as the percentage of trucks in the traffic stream becomes greater,
the trucks themselves begin to fill in the gaps that other trucks create,
and so their individual impact (in terms of the equivalent number of
passenger cars each truck represents) actually goes down. At the same time,
the cumulative effect of the trucks will continue to rise because of the
higher percentage of trucks in the traffic stream. This is also quite
reasonable and reflective of conditions seen regularly in the field.


Second,
density increases, from 26.2 pcpmpl to 27.3 pcpmpl.
The countervailing trend in the value of E_{T} is keeping
this growth in the truck percentage from having a more significant impact.

The fact that these
two trends offset one another is a very important thing to notice.
To complete the
sensitivity analyses, let’s look at the impacts from varying the driver
familiarity adjustment factor. Let’s try using 0.85 instead of 1.0, assuming
that the analysis is being done in the summer when a higher percentage of
the drivers are vacationers. The flow rate becomes 1,695 pcphpl, the density
becomes 30.8 pcpmpl, the LOS is D, and the average passenger car speed is 55
mph. This is a 17.6% increase over the value we found for the initial
conditions we studied. So there is
an impact on operations, even though the LOS is
still D (see
Dataset 10).
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Subproblem 1c: Analysis of
the Eastbound Freeway Section
We can close out this
analysis by looking at the performance of this facility across the entire
year. As was the case for the eastbound analysis, we have data for 256 hours
during 2001. The histogram, in Exhibit 415, shows that the predominant LOS is
C, with some evidence of D, E, A, and B. It’s clear that you can describe
the LOS of this westbound section as being predominantly C under the
conditions we assumed: 5% trucks/buses, 0% recreational vehicles, and 0%
daily users. If one or more of these assumptions change, the situation could be
different.
To explore how
different it might be, we changed just one variable, the assumption about
daily users. We did this because during the spring, summer, and fall
months many of the users on Friday afternoons are vacationers. If we
change this assumption, the value of f_{P} can range as low
as 0.85. The results of this analysis are presented below in Exhibit 416.
Exhibit 416. Driver Familiarity Adjustment 
LOS 
MaxD 
Reg Drive 
Vacation 
NHr 
Pct 
NHr 
Pct 
A 
11 
8 
3.1% 
7 
2.7% 
B 
18 
7 
2.7% 
2 
0.8% 
C 
26 
195 
76.2% 
20 
7.8% 
D 
35 
37 
14.5% 
210 
82.0% 
E 
45 
4 
1.6% 
11 
4.3% 
F 
>45 
5 
2.0% 
6 
2.3% 
The percentage of
hours at LOS F doesn’t change that much, from 2.0% to 2.3%, but the
predominant LOS changes substantially, from C to D. Now 82% of the time, the
LOS is D while only 7.8% of the time it is C.
Neither one of the
situations, either “Regular Drivers” or “Vacation” drivers exactly describes
peak hour situation. The truth is somewhere between. However, what we can
say is that the LOS is typically either C or D. Moreover, it’s Clike during
normal peak hours when the regular drivers predominate, and it’s Dlike
when the vacation drivers are present.
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