Problem 1: Maxwell Drive
Problem
1 Printable Version
The
intersection of Maxwell Drive with Route 146 (Intersection
C) is
signalized and fully actuated. About 2,000 feet to the east is the
intersection of Clifton Country Road and Route 146 (Intersection D),
4,000 feet to the west is the intersection of Moe Road and Route 146
(Intersection B), and 300 feet to the north is the Intersection of
Park Avenue and Maxwell Drive. All three of these upstream
intersections are signalized and fully actuated.
|
Exhibit 2-4. Maxwell Drive and
Route 146 Configuration |
As
Exhibit 2-4 shows, the eastbound approach of the Maxwell Drive/Route 146
intersection is three lanes wide (left, and
a double through) while the westbound approach is two lanes wide
(through and through/right). The eastbound left-turn bay is
approximately 100 feet, while the southbound left-turn bay is
approximately 125 feet. The
approach for Maxwell Drive itself (the southbound approach) is three
lanes wide (double left and right).
Base Case Phasing and Volumes
Analysis
Plans Description of Analyses
Sub-problem 1a: PM Peak Hour - Existing Conditions
Sub-problem 1b:
PM Peak Hour - With Conditions
Discussion
Discussion:
Think
about what we're about to do. Look at the aerial photograph in the
introduction. Why do we think it's reasonable to suggest that this
intersection is isolated? If we were doing a full-fledged traffic
impact assessment, what other sub-problems might we want to examine
other than the four listed above?
[ Back ] [
Continue
] to Base Case Condition |
Page Break
Problem 1: Maxwell Drive
Base
Case Phasing
|
Exhibit
2-5. Maxwell Drive Signal Phasing |
The base case signal phasing is shown in
Exhibit 2-5.
The first phase is eastbound-westbound with a permitted eastbound
left. The second is eastbound only with a protected eastbound left. The third phase is southbound.
This intersections uses actuated control, and field data suggest that phase 1 lasts 20-40 seconds. Phase 2 is
skipped about half the time; and when it is called, it lasts 8-12 seconds.
Phase 3 lasts 10-18 seconds. The cycle length ranges from 30-70 seconds
and averages 48 seconds.
Base Case
Volumes
|
Exhibit 2-6. Maxwell Drive Intersection Volumes for the
Existing AM & PM Peak Hour |
Exhibit 2-6 shows the intersection volumes for the base case AM and PM peak hours. In the AM peak, the largest volumes are the eastbound through and
the westbound through.
In the PM peak, the volumes are very similar but they are larger,
especially the turning movements (e.g., 215 westbound right turns in the
PM peak versus 84 in the AM peak.)
Discussion:
We've focused here on the phasing and the volumes. What other data do we
need to do the analysis? Take a few minutes to examine the HCM signalized
methodology to make sure you know what that complete list of data items
is. Think about the implicit assumptions we're making about other data
items.
|
to Analysis Plans |
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|
Exhibit 2-6. Maxwell Drive
Intersection Volumes for the Existing AM & (PM) Peak Hour
|
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Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
The intersecting volumes by 15-minute
intervals for the existing PM Peak are shown in Exhibit 2-7.
You can also see that the peak hour is from 17:00-18:00. The total
number of intersecting vehicles is 2,877 and the overall
peak hour factor (PHF)
is 0.94. The movement-specific peak hour factors range from 0.78 to 0.95,
with those for the major movements being fairly high and consistent, while
those for the the minor movements are lower and more variable. Moreover,
the minor movements seem to offset each other in terms of contributing to
the 15-minute volumes.
Exhibit 2-7.
Maxwell Drive PM peak hour volumes - Existing Conditions
|
PM Peak Hour 2002 |
Eastbound |
Westbound |
Southbound |
Intersection
Total |
LT |
TH |
Total |
TH |
RT |
Total |
LT |
RT |
Total |
16:00 |
43 |
232 |
275 |
231 |
37 |
268 |
64 |
38 |
102 |
645 |
16:15 |
32 |
207 |
239 |
236 |
54 |
290 |
68 |
32 |
100 |
629 |
16:30 |
46 |
231 |
277 |
239 |
54 |
293 |
71 |
52 |
123 |
693 |
16:45 |
43 |
228 |
271 |
231 |
42 |
273 |
65 |
38 |
103 |
647 |
17:00 |
57 |
230 |
287 |
244 |
70 |
314 |
90 |
50 |
140 |
741 |
17:15 |
49 |
230 |
279 |
281 |
45 |
326 |
108 |
55 |
163 |
768 |
17:30 |
52 |
219 |
271 |
255 |
54 |
309 |
75 |
34 |
109 |
689 |
17:45 |
36 |
189 |
225 |
276 |
50 |
326 |
79 |
49 |
128 |
679 |
Peak Hour
Volume |
194 |
868 |
1,062 |
1,056 |
219 |
1,275 |
352 |
188 |
540 |
2,877 |
Peak Hour
Factor |
0.85 |
0.94 |
0.93 |
0.94 |
0.78 |
0.98 |
0.81 |
0.85 |
0.83 |
0.94 |
For the
purposes of this problem, we will apply the overall PHF of 0.94. It is, of
course, also possible to apply each of the peak hour factors for the
individual movements as discussed above, but doing so would presume that
all of the individual movements peak during the same 15-minute time period
of the hour. This does not happen very often, and so application of the
overall PHF normally results in a more realistic assessment of
intersection operations during the peak 15-minute period.
Analyses:
Base Case
Analysis
Arrival Type Changes
Sensitivity to Data
Skipped Phases
Discussion:
Why is it important to look at the variations in flows across the peak
period? Is it reasonable to assume that the minor movements offset one
another? Why or why not?
with Sub-problem 1a |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Base Case Analysis
The base case run for the existing conditions uses the peak
hour volumes shown in
Exhibit
2-7, the overall PHF of 0.94, 7% trucks, an
arrival type of 2 for the eastbound approach, and an arrival type of 3 for
the westbound and southbound approaches. In addition, since the
eastbound left-turn phase is skipped half the time, the signal timings for
phase 2 are halved to reflect the fact that that phase arises only 50% of
the time. The
input data for the base case is available in
Dataset
1.
Exhibit 2-8 presents the base case
results for signal timings that about equalize the delays for the critical
movements in each phase. The movement-specific delays range from 5.3 to
20.8 seconds per vehicle and the average queue lengths range from 1.8 to
9.9 vehicles.
Exhibit 2-8. Maxwell Drive PM peak - Existing Conditions, Base Case
Results |
EB Arrival Type |
Heavy Vehicles |
Phase Skip |
Signal Timing |
Performance Measure |
EB |
WB |
SB |
OA |
L |
T |
R |
Total |
L |
T |
R |
Total |
L |
T |
R |
Total |
2 |
Yes |
Yes |
Base |
Delay |
18.2 |
5.3 |
- |
7.7 |
- |
16.7 |
16.7 |
17.3 |
- |
20.8 |
18.5 |
13.7 |
Queue |
1.8 |
4.2 |
- |
- |
- |
9.9 |
- |
2.4 |
- |
2.7 |
- |
- |
with Sub-problem 1a |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Arrival Type
Changes
Now let’s consider a
parametric analysis: what happens if the
arrival type changes from 2 to 1,
3, or 5 for the eastbound approach? For example, if we introduce
coordination that improves eastbound progression, the arrival type could
become 3, 4, or 5. If we make the progression worse by focusing the westbound flows, assuming there’s a tradeoff, it could
become 1. From Exhibit 2-9 we can
see that if the progression gets better, the eastbound delays could drop
as low as 2.2 seconds for the left and 0.6 seconds for the through. (Dataset
2 shows inputs for the arrival type 3
and Dataset 3
shows inputs for arrival
type 5.) These
values are a small fraction of the base case. The average queue lengths
could drop to 0.5 and 0.8 vehicles respectively. This urges an examination
of coordination options. (Refer to
Dataset
4 to see the details for arrival type 1).
From Exhibit 2-9 we can also see that if the coordination gets worse (arrival
type 1), the eastbound left-turn delay could increase to 27.2 seconds.
That’s 45% more than the base case of 18.8 seconds. For the through
movement, a
similar increase could take place, from 5.3 to 8.0 seconds, a 50%
increase. The average queue lengths could grow from 4.2 to 5.2 vehicles
for the through movement (24% increase) and 1.8 to 2.3 vehicles for the left-turn
movement (28%
increase). In fact, the latter situation could be a problem. The left-turn
storage capacity is only 5 vehicles and the 95th-percentile
queue length (not shown in the table) is 4.7 vehicles; so with arrival
type 1, we’re nearly at that limit.
Exhibit 2-9.
Maxwell Drive Effects of Variations in the Eastbound Arrival Type |
Data-set |
EB Arrival Type |
Heavy Vehicles |
Phase Skip |
Signal Timing |
Performance
Measure |
EB |
WB |
SB |
OA |
L |
T |
R |
Tot |
L |
T |
R |
Tot |
L |
T |
R |
Tot |
1 |
2 |
Yes |
Yes |
Base |
Delay |
18.2 |
5.3 |
- |
7.7 |
- |
16.7 |
16.7 |
17.3 |
- |
20.8 |
18.5 |
13.7 |
Queue |
1.8 |
4.2 |
- |
- |
- |
9.9 |
- |
2.4 |
- |
2.7 |
- |
- |
2 |
3 |
Yes |
Yes |
Base |
Delay |
11.9 |
3.5 |
- |
5.0 |
- |
16.7 |
16.7 |
17.3 |
- |
20.8 |
18.5 |
12.7 |
Queue |
1.3 |
2.9 |
- |
- |
- |
9.9 |
- |
2.4 |
- |
2.7 |
- |
- |
3 |
5 |
Yes |
Yes |
Base |
Delay |
2.2 |
0.6 |
- |
0.9 |
- |
16.7 |
16.7 |
17.3 |
- |
20.8 |
18.5 |
11.2 |
Queue |
0.5 |
0.8 |
- |
- |
- |
9.9 |
- |
2.4 |
- |
2.7 |
- |
- |
4 |
1 |
Yes |
Yes |
Base |
Delay |
27.2 |
8.0 |
- |
11.5 |
- |
16.7 |
16.7 |
17.3 |
- |
20.8 |
18.5 |
15.1 |
Queue |
2.3 |
5.2 |
- |
- |
- |
9.9 |
- |
2.3 |
- |
2.7 |
- |
- |
Discussion:
If we were to do a parametric study of arrival types for the
westbound approach we’d find similar trends. The analysis would be
useful, because better coordination ought to be possible with the signal
at Clifton Country Road. What we’d need is a common cycle length and
appropriate splits and offsets. It would also be useful to see if flow could
be improved if we closed the exit from the fast food restaurant just east
of the stopbar or did something to the intervening unsignalized
intersection (with Old Route 146) that produces mid-block traffic that
disrupts progression. We’ll look at these issues when we do
Problem 6, the arterial analysis.
to Sub-problem 1a |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Sensitivity to
Data
Quite often, traffic engineers collect intersecting volumes
for a given site on a single day. The reason is simple: primary data
collection is expensive. So the question is, how certain can we be that
the assessment of facility performance on our “typical” day is really
typical of the intersection? We
need data for 20-30 days for the time period being studied to be
reasonably confident of the interval on the average delay. But that doesn’t
detract from the fact that it’s a significant issue.
For this particular
intersection, we have traffic data from three different days
for the PM peak hour
volumes. How different are the delays and
levels of service that their volumes predict? Exhibit 2-10 presents the delay
estimates based on the three sets of data. You can view the input data for
Dataset 1,
Dataset
5 and Dataset 6
(the base case and two variations of input data, respectively).
In
this instance, the delays are similar for all three datasets. The largest
differences arise on the southbound approach where the average delays for
the southbound left range from 15.8 to 17.3 seconds and the delays for the
southbound right range from 18.7 to 26.7 seconds. The message isn’t that
you should expect to be this lucky every time you do an analysis, but
to be sensitive to this issue and prepared to find
that others have reached different conclusions for the same site based on
different, equally defensible data. Each of the data sets in the table
below include heavy vehicles, base signal timing, skipped phases, and has
an eastbound
arrival type 2.
Exhibit 2-10.
Maxwell Drive Comparative Results from Three Datasets
|
Dataset |
Performance Measure |
EB |
WB |
SB |
OA |
LT |
TH |
Tot |
TH |
Tot |
LT |
RT |
Tot |
1 |
Delay |
18.2 |
5.3 |
7.7 |
16.7 |
16.7 |
17.3 |
20.8 |
18.5 |
13.7 |
Queue |
1.8 |
4.2 |
- |
9.9 |
- |
2.4 |
2.7 |
- |
- |
5 |
Delay |
18.8 |
6.0 |
8.0 |
16.8 |
16.8 |
17.2 |
26.7 |
20.9 |
13.9 |
Queue |
2.0 |
5.8 |
- |
10.0 |
- |
2.3 |
3.4 |
- |
- |
6 |
Delay |
18.5 |
6.1 |
7.9 |
16.7 |
16.7 |
15.8 |
18.7 |
17.1 |
12.8 |
Queue |
1.9 |
6.1 |
- |
10.0 |
- |
1.4 |
2.3 |
- |
- |
Discussion:
What
has been your experience with the variability in traffic flows? Do you see
variations in flows in the field? In delays? Is there merit in looking at a
high as well as an average set of volumes for a given condition? How do
you communicate to others the differences in the results you obtain?
to Sub-problem 1a |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Skipped
Phases
Most actuated controllers are capable of skipping phases. If no
traffic is present to call the phase, the controller moves on
to the next movement or returns to a rest condition. This presents a
challenge for most analytical analysis methodologies that examine an
average cycle for the signal. We are going to look at skipped phases from the following
perspectives:
Discussion:
Think of some other traffic analysis models with which you are familiar.
How do they deal with skipped phases? Is simulation a good way to study
this issue? What might be the problems in using simulation? If you did use
simulation, how many cycles would you need to study to obtain credible
information about the signal's performance? Would you need to do multiple
runs? Using multiple seeds?
[ Back ] [ Continue
] with Skipped Phases |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Skipped
Phases: General Ideas
Actuated signals not
only vary the phase durations but they also skip phases when specific
movements aren’t called, as at this intersection. The
eastbound protected left (phase 2 in
Exhibit
2-5) is sometimes skipped.
Before we see what effect that has on how you should do the analysis,
let’s discuss movements and phases. We need to make sure that you
understand how the word “phase” is used in the context of the HCM.
Eight-phase, dual ring, NEMA controllers are often set up as shown in
Exhibit 2-11. The diagram shows
the movement sequences in the A and B rings. The green indications
progress through the A and B rings simultaneously, in parallel, and the two barriers (between
movements 2&6 and 3&7 and between movements 4&8 and 1&5)
are crossed simultaneously in both rings.
|
Exhibit 2-11. Typical Dual-Ring NEMA Phasing |
The
typical way in which the signal indications progress is as follows: greens
are first displayed for movements 1&5, the eastbound and westbound protected
lefts. These lefts lead the through movements assuming both are called. When actuations cease for either movement 1 or
5, for example movement 1 in this case, the green in the A Ring changes from movement 1 to
movement 2, while movement 5 is still green. When movement 5 terminates, the green in the B ring
changes from movement
5 to 6. An alternate sequence of distinct intervals can occur if the signal
changes from 1&5 to 1&6 and then 2&6. Thus, the following
phase sequences can occur left of the middle barrier: 1&5 to 1&6
to 2&6 (three intervals); 1&5 to 2&5 to 2&6 (again three
intervals); 1&5 to 2&6 simultaneously (two intervals); 2&6 alone
(1 and 5 both skipped). To the right of the barrier, four
similar sequences are possible.
Discussion:
Consider some signalized intersections that you know well. Write down the
dual ring phasing for them. Then construct the sequence of phases that are
the input to the HCM analysis. Make sure you understand how they relate to
one another.
to Skipped Phases |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Skipped
Phases: Consideration at Maxwell Drive
At Maxwell Drive, the signal phasing is different from
what’s shown in
Exhibit 2-11. First,
the eastbound left lags rather than leads the WB through (and right).
Second, only movement 4 exists to the right of the middle barrier. The
signal phasing is shown in Exhibit 2-12. When movement 5 is green, permissive EB lefts are allowed. If all of the lefts can turn while movement 5 is
green, the 2&5 combination is skipped and the signal progresses from
1&5 directly to 4. If it’s not skipped, the sequence is 1&5,
2&5, and then 4.
|
Exhibit 2-12.
Maxwell Drive Phasing Diagram |
How
should this phenomenon be modeled, especially since the HCM doesn’t ask
for dual-ring phasing, minimum greens, maximum greens, gaps, etc. that are
part of an actuated signal? It asks for information about a
prescribed phase sequence where each phase is a specific combination of
green indications. Thus, when a phase is sometimes skipped, what do you
do?The answer is that,
if you're working from observational data alone, then you
adjust the modeled signal timings so that they reflect an
average cycle given that specific phase(s) will sometimes be
skipped. In this case, phase 2 (see
Exhibit 2-5) averages 10 seconds of green
when it comes up, followed by a 3-second yellow and a 1-second
all-red. Since the phase is skipped every other cycle, the signal timings you use in the HCM for this phase
should be: 5 seconds of green, 1.5 seconds of yellow, and 0.5 seconds of
all-red.
to Skipped Phases |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Skipped
Phase: What if skipped phases are ignored?
The next question is: do skipped phases make a difference? Indeed, they do.
Exhibit 2-13 shows what happens if you don’t account for the fact that the phase is
skipped. In the base case condition
(Dataset
1), we’ve accounted for the
skipped phases by using the 5+1.5+0.5 second timings we described earlier.
In the Dataset 7, we’ve used the 10+3+1 second timings
instead. In the case of Dataset 7, the delays for the
westbound through-and-right are almost 3 times larger (42.7 seconds versus
16.7). This is because the cycle length is 5 seconds longer. That may be
an unexpected result, but one that makes sense.
The v/c ratio started out at 0.87 with the 5.0+1.5+0.5 timings and it
becomes 1.01 when the 10+3+1 timings are used. That change in v/c ratio
will produce a dramatic result. The change is arguably dramatized
because the signal timings for the other phases haven’t been adjusted to
reflect the change in the phase 2 timings. If we do that, and strive to
get a balance in v/c ratios instead of delays, we can obtain the results
presented in Dataset
8. The v/c ratios for the critical movements are nearly
balanced at 0.75, 0.66, and 0.75, and the westbound delays are now lower
than in the base case at 15.2 sec/veh. However, you should note that the
delays for all the other movements are higher. The delay for the eastbound
left is now 35.5 sec/veh instead of 18.8; for the eastbound through, it’s 6.9 instead of 5.3; and for the southbound approach, it is now
32.9 and 42.2 sec/veh instead of 17.3 and 20.8 sec/veh respectively for the left and
right. The table below includes eastbound arrival type 2 and includes
heavy vehicle considerations.
Exhibit
2-13.
Maxwell Drive Effects of Skipped Phases |
Dataset |
Phase Skip |
Signal Timing |
Performance Measure |
EB |
WB |
SB |
OA |
LT |
TH |
Tot |
TH |
RT |
Tot |
LT |
RT |
Tot |
1 |
Yes |
Base |
Delay |
18.2 |
5.3 |
7.7 |
16.7 |
16.7 |
17.3 |
20.8 |
18.5 |
13.7 |
v/c |
0.39 |
0.39 |
- |
0.87 |
- |
0.56 |
0.64 |
- |
- |
Queue |
1.8 |
4.2 |
- |
9.9 |
- |
2.4 |
2.7 |
- |
- |
7 |
No |
Adjust |
Delay |
19.5 |
6.0 |
8.4 |
42.7 |
42.7 |
22.6 |
30.6 |
25.4 |
26.8 |
v/c |
0.33 |
0.38 |
- |
1.01 |
- |
0.65 |
0.74 |
- |
- |
Queue |
2.0 |
4.8 |
- |
16.0 |
- |
2.9 |
3.3 |
- |
- |
8 |
No |
Adjust |
Delay |
35.5 |
6.9 |
12.1 |
15.2 |
15.2 |
32.9 |
42.2 |
36.1 |
18.0 |
v/c |
0.47 |
0.35 |
- |
0.75 |
- |
0.66 |
0.75 |
- |
- |
Queue |
3.0 |
6.5 |
- |
12.8 |
- |
4.3 |
4.9 |
- |
- |
These three solutions
also illustrate the huge variations in delay that can be achieved
depending on the signal timings you use. It’s important to tell your
client and the other stakeholders what signal timing philosophy you’re
using so they know, or have some idea, what results to expect. Ideally,
you’re using a philosophy that reflects what the signal will do in the
field, but since that is heavily influenced by timing parameters employed
(minimum greens, maximum greens, gap times and a host of other values),
it’s hard to exactly duplicate the field performance.
As an alternative to this
observational approach, you might also consider applying one of the signal
timing estimation procedures described in Chapter 16, Appendix B of the
HCM. The decision on which approach is most appropriate depends on the
available data, the required accuracy, and available time and resources.
with Sub-problem 1a |
Page Break
Sub-problem 1a: Maxwell Drive PM
Peak Hour - Existing Conditions
Discussion:
In problem 1, we've learned the effects of changing the arrival type, we’ve
seen what differences in performance might exist if different sets of data
are used for the same site, and we’ve seen what you should do to address
skipped phases. More generally, we’ve seen that you need to be explicit in
describing to the client how you’ve addressed these issues in establishing
the base case results. Somebody else might get results that are quite
different from yours, depending upon how they address these issues. You’ve
got to be careful about the assumptions you make in correctly representing
the conditions that exist in the field.
to Sub-problem 1b |
Page Break
Sub-problem 1b: Maxwell Drive PM
Peak Hour
- With Conditions
Let’s
now explore some modeling issues in the context of the PM With conditions
for the Maxwell Drive intersection. The intersecting volumes for both the PM
Without and PM With condition are shown in Exhibit 2-14. We will focus on the PM With condition.
It will be useful to see (by the
differences) the traffic growth we’ve assumed between the base case volumes (Exhibit
2-7) and the PM Without conditions as well as the site-generated traffic
we’ve added between the PM Without and the PM With conditions.
Exhibit 2-14.
Maxwell Drive 2004 PM Peak Hour Volumes
|
2004 Conditions |
Eastbound |
Westbound |
Northbound |
Southbound |
TEV |
LT |
TH |
RT |
LT |
TH |
RT |
LT |
TH |
RT |
LT |
TH |
RT |
PM Without |
202 |
902 |
0 |
0 |
1,098 |
228 |
0 |
0 |
0 |
366 |
0 |
195 |
2,991 |
PM With |
202 |
902 |
150 |
150 |
1,098 |
228 |
150 |
90 |
150 |
366 |
60 |
195 |
3,741 |
TEV:
Total Entering Vehicles
Analyses:
Configuration
Issues
HCM Planning
Method
Cycle Length
Education
Critical
Movement Techniques
Operational
versus
Planning Analyses
Uncertainty Issues
[ Back ] [ Continue
]
to Configuration Issues |
Page Break
Sub-problem 1b: Maxwell
Drive PM Peak Hour - With Conditions
Configuration Issues
Finding the best lane configuration for a
new or revised intersection is one of the most exciting things a traffic
engineer does. When a plan you develop works well, it’s invigorating to
see it in action.
For Maxwell Drive, with
the new site traffic, we have an opportunity to see what designs will work
best. There isn’t going to be just one right answer; most likely, there
will be several. That’s usually the case with design problems.
We’re going to start
by examining the volumes for the "with" condition (presented in
Exhibit
2-14), independent of what actually exists on the ground right now. For example, the
intersection was originally constructed wide enough to accommodate a
southbound through lane if a fourth leg were ever to be added to the
intersection. In the interim, the extra width has been used to accommodate
dual southbound left-turn lanes. But, are dual left-turn lanes really
going to be needed? The volumes suggest that we’re likely
to need at least one southbound left-turn lane, and maybe two. Two would
produce a per-lane match between the northbound and southbound lefts,
ignoring lane utilization. If we don’t use two, we might be able to
convert the second one into a through lane or a
through-and-something lane. Although the northbound lefts are not as
heavy (150) as the southbound lefts, they are significant. A left-turn
lane (opposing the southbound left-turn lane) would be wise. The through volumes are small both north and southbound.
That means one through lane should be plenty. We could even combine the throughs and rights.
Now, let’s
study lane configuration options. At the same time, we need to think about
the signal timing plan. There are two tools to do this. One is the HCM planning method for
signalized intersections. The other is critical lane
analysis. It’s a simple, back-of-the-envelope technique for
seeing what geometric/signal timing combinations might work. (The critical
lane technique is discussed in most traffic engineering textbooks and
handbooks, and it’s the method for signal timing presented in the HCM.)
In each of these two
analyses, we’re going to look at different lane configurations, phasing,
signal timing, and cycle length. Acceptable cycle lengths range from
40-120 seconds, although longer and shorter values are possible.
Discussion:
It's important to note in this sub-problem that several analysis
techniques are being applied/explored. You should think about whether
there are others you might have used and the results you would have
gotten.
[ Back ] [ Continue ]
to HCM Planning Method |
Page Break
Sub-problem 1b:
Maxwell Drive PM Peak Hour - With Conditions
HCM Planning
Method
In the case of the HCM planning
method, we need to supply the intersecting volumes, the left-turn
treatment (protected, permissive, compound, etc.), the number of lanes
(left, through, and right; the model decides if they’re shared), the
peak hour factor, the minimum and maximum cycle lengths, the coordination
situation (yes or no), and whether parking is present. The model
determines whether the configuration will work, reports the capacity
condition (above capacity, at, nearly at, below, etc.), and presents a
phasing plan.
For the Maxwell Drive, with the new site-generated traffic, Exhibit 2-15
presents the planning analysis results of nine model scenarios. Some show solutions that
might be implemented in the field. Others
show how the model thinks. In all scenarios, the peak hour factor is
0.94, the lost time per movement is 4 seconds (this is firm),
there isn’t any coordination, there aren’t any parking maneuvers, the
minimum cycle length is 10 seconds, and the maximum cycle length is 200 seconds. You can
see the input data for Scenario P-1 in
Dataset
9.
Exhibit 2-15. Maxwell Drive Results from Nine Planning Model Scenarios |
Scenario |
Number of Legs |
Left Turns |
Capacity Condition |
Cycle Length |
East |
West |
North |
South |
LT |
TH |
RT |
LT |
TH |
RT |
LT |
TH |
RT |
LT |
TH |
RT |
P-1 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
Prot |
At |
171.4 |
P-2 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
3 |
1 |
1 |
3 |
1 |
Prot |
At |
171.4 |
P-3 |
1 |
2 |
1 |
1 |
2 |
1 |
2 |
1 |
Prot |
At |
104.5 |
P-4 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
Perm |
At |
18.5 |
P-5 |
1 |
2 |
0 |
1 |
2 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
Perm |
Under |
80.0 |
P-6 |
1 |
2 |
0 |
1 |
2 |
0 |
2 |
1 |
1 |
2 |
1 |
1 |
Prot |
At |
76.5 |
P-7 |
2 |
3 |
0 |
2 |
3 |
0 |
2 |
1 |
1 |
2 |
1 |
1 |
Prot |
At |
38.5 |
P-8 |
2 |
3 |
0 |
2 |
3 |
0 |
2 |
1 |
1 |
2 |
1 |
1 |
Prot |
Near |
45.0 |
P-9 |
2 |
3 |
0 |
2 |
3 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
Prot |
At |
53.5 |
[ Back ] [ Continue ] to
Cycle Length Discussion |
Page Break
Sub-problem 1b: Maxwell Drive PM Peak Hour - With
Conditions
Scenario P-1
is a good place to start our discussion. It represents a legitimate option.
The left turns are protected and the lanes are configured in a logical way.
(If there are no right- or left-turn lanes, the model assumes the movements
are shared with the through movement.) Let's conduct some "what-if" analyses
that go beyond the results and data sets presented in the previous Exhibit.
The model estimates a cycle length of 171.4 seconds (for a condition where
cycle length is the minimum possible). That’s too long. If the number of
northbound and southbound through lanes is increased to 3, as in Scenario
P-2, nothing happens. That’s because the through movement is not the
critical movement, and so it does not determine the cycle length. If you
reconfigure the north and southbound approaches so there are two left-turn
lanes and one through-and-right lane, the cycle length drops to 104.5
seconds. This is better, but it assumes it's possible to have simultaneous
opposing dual lefts, which isn’t allowed in New York State. If permissive
lefts are assumed, the model drops the cycle length to 18.5 seconds. That’s
too short for most practical situations. The model is reporting the shortest
cycle length that puts the intersection at capacity using the equations used
to set the signal timings. A more practical value, like 80 seconds, makes
the model show that the intersection is under capacity for that cycle
length. At a cycle length of 20 seconds, the model shows the intersection is
near capacity and, with cycle lengths of 25 seconds or above, it shows the
intersection operating under capacity.
Now we’ll do some sensitivity analyses, mostly
to illustrate trends. If we assume dual lefts northbound and southbound,
along with exclusive lanes for the throughs and rights, the cycle length
drops to 76.5 seconds (from the previous 104.5). If we add dual lefts and
three through lanes eastbound and westbound, the cycle length drops to 38.5
seconds.
If we take that same lane configuration and consider a more reasonable cycle
length, say 45 seconds, the model shows the intersection is near capacity.
If we go back to single left-turn lanes northbound and southbound, the model
calculates a cycle length of 53.5 seconds.
Discussion:
Notice
that we only kept one dataset for all of the planning analysis runs. You can
generate the other results very easily. Simply change the lane configuration
in the dataset. You might explore other options, too. See if you think the
trends in the cycle lengths identified are reasonable given the
configuration options you explore.
[ Back ] [ Continue
] with Cycle Length Education |
Page Break
Sub-problem 1b: Maxwell Drive PM
Peak Hour - With Conditions
Cycle Length
Education
For a pre-timed signal, the standard equation for computing the minimum
cycle length is:
(1) |
|
where vi
is the volume for the critical movement in phase i, si
is the saturation flow rate for the critical movement in phase i,
N is the number of phases per cycle, and L is the lost time per
phase.
For actuated signals
with dual-ring controllers like the one we portrayed in
Exhibit 2-11, it
helps to expand Equation (1) into three equations. The first one computes
the v/s ratio for sequential pairs of movements to the left
and right of the middle barrier in the A and B rings:
(2) |
|
Here
pq takes on the values 1&2, 3&4, 5&6, and
7&8 corresponding to the four quadrants of the dual ring pattern.
The second equation
computes the maximum v/s ratio for the left and right halves
of the dual ring pattern:
(3) |
(v/s)L
= max((v/s)12,(v/s)56)
and (v/s)R
= max((v/s)34,
(v/s)78) |
The third equation
takes the two results from Equation (3) and computes a minimum cycle length:
(4) |
|
|
Page Break
Sub-problem 1b: Maxwell Drive PM
Peak Hour
- With Conditions
Critical Movement
Technique
A
sequence of specific movements (in specific lanes), one for each phase,
determines the minimum cycle length. In a dual ring controller, configured
as shown in
Exhibit 2-11, some sequence of the four movements -
either 1,2,3,4; 1,2,7,8; 5,6,3,4; or 5,6,7,8 - will define the minimum
cycle length.
Exhibit 2-16 shows the
results that were obtained using the critical lane analysis for eight
different scenarios. We have assumed that the
saturation flow rates for the various
lane groups are as indicated by the note below the table and that the
lost time per phase is as shown in the second column.
Exhibit 2-16. Maxwell Drive Critical Movement Analysis
Results
|
Scenario |
Lost Time (sec) |
Number of Lanes |
Cycle Length |
Notes |
Eastbound |
Westbound |
Northbound |
Southbound |
LT |
TH |
RT |
LT |
TH |
RT |
LT |
TH |
RT |
LT |
TH |
RT |
C-1 |
3 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
139.4 |
N & S RT lanes dominate N & S TH and RT timings |
C-2 |
4 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
175.5 |
Scenario 1 except 4 sec lost time per movement |
C-3 |
3 |
1 |
2 |
1 |
2 |
1 |
2 |
1 |
2 |
93.5 |
N & S TH & RT incorrectly grouped together |
C-4 |
3 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
114.9 |
N & S Right turns allowed concurrent with E & W LT's |
C-5 |
3 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
87.2 |
Scenario 2 with new WB RT lane |
C-6 |
3 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
204.9 |
N & S TH/RT in single lanes |
|
C-7 |
3 |
1 |
2 |
1 |
2 |
2 |
1 |
2 |
1 |
106.7 |
Scenario 6, except simultaneous double LT's N& S |
C-8 |
3 |
1 |
2 |
1 |
2 |
3 |
3 |
84.4 |
Separate N & S Phases |
[ Back ] [ Continue ]
with Critical Movement Technique |
Page Break
Sub-problem 1b: Maxwell Drive PM Peak Hour - With Conditions
Discussion:
Do
you see any weaknesses in the critical movement analysis approach? Any
approximations? What would you do to compensate for these shortcomings? How
do shared lanes complicate the situation? What about intersections where
there are no left-turn lanes?
[ Back ] [ Continue ]
to Operational vs. Planning Analyses |
Page Break
Sub-problem 1b:
Maxwell Drive PM Peak Hour - With Conditions
Exhibit 2-17
Maxwell Drive Operational Analyses
|
Scenario |
Cycle Length |
Performance Measure |
EB |
WB |
NB |
SB |
OA |
LT |
TH/RT |
Tot |
LT |
TH/RT |
Tot |
LT |
TH |
RT |
Tot |
LT |
TH |
RT |
Tot |
C-4 Dataset 10 |
65.0 |
Delay |
38.8 |
19.5 |
22.6 |
15.4 |
34.4 |
32.5 |
17.3 |
39.5 |
24.3 |
25.1 |
38.0 |
31.0 |
28.1 |
34.2 |
28.7 |
Queue |
4.6 |
10.3 |
- |
2.2 |
17.6 |
- |
2.3 |
2.0 |
2.8 |
- |
8.0 |
1.2 |
3.9 |
- |
- |
C-7 Dataset 11 |
90.0 |
Delay |
63.4 |
25.9 |
32.0 |
23.0 |
44.9 |
42.6 |
19.5 |
50.5 |
38.6 |
21.2 |
62.6 |
38.2 |
37.9 |
Queue |
6.5 |
13.7 |
- |
3.1 |
23.0 |
- |
1.4 |
7.2 |
- |
3.6 |
8.3 |
- |
- |
C-8 Dataset 12 |
93.0 |
Delay |
65.0 |
29.0 |
34.8 |
24.3 |
54.2 |
51.1 |
34.6 |
72.3 |
57.8 |
39.3 |
76.4 |
54.5 |
46.9 |
Queue |
6.8 |
15.0 |
- |
3.3 |
25.8 |
- |
1.9 |
8.7 |
- |
5.4 |
9.4 |
- |
- |
What have we
learned from this? We’ve seen that we can make the signal work, in an
operational analysis, for the conditions that the planning analyses
suggested should work. We have also seen that the cycle lengths are
sometimes different. One final observation is that it seems possible with
the operational analysis to fine-tune the problem solution in some cases
so that better than at-capacity performance can be achieved through
careful selection of the phasing plan and the
lane configuration.
[ Back ] [ Continue ]
to Uncertainty Issues |
Page Break
Sub-problem 1b: Maxwell Drive PM Peak Hour - With Conditions
Uncertainty Issues
Estimating site-generated traffic is a
challenge. It’s difficult to say with assurance how much traffic will be
generated. Thus, a sensitivity analysis has value. It pays to
look at variations in volume, both up and down from the projected numbers, to
see what trends exist in cycle length, level of service, queue length,
etc.
For this particular intersection, let’s look at three situations: the base
case (Dataset 10),
a condition with 30% more site-generated traffic (Dataset
13), and a condition with 30% less site generated traffic (Dataset
14).
The results are presented in Exhibit 2-18. It’s
interesting that increasing the site-generated volumes by 30% raises the
cycle length substantially from 65 to 77 seconds. The delays also increase
from an average of 28.7 seconds to 34.4 seconds. However, when the
site-generated traffic is lower by 30% there isn’t a significant change.
The cycle length stays at 65 seconds, the average delay drops only
marginally from 28.7 to 28.5 seconds.
Exhibit 2-18.
Maxwell Drive Effects of Generated Traffic |
Scenario |
Cycle Length |
Performance Measure |
EB |
WB |
NB |
SB |
OA |
LT |
TH |
RT |
Tot |
LT |
TH |
RT |
Tot |
LT |
TH |
RT |
Tot |
LT |
TH |
RT |
Tot |
Dataset 10 C-4 |
65.0 |
Delay |
38.8 |
19.5 |
22.6 |
15.4 |
34.4 |
32.5 |
17.3 |
39.5 |
24.3 |
25.1 |
38.0 |
31.0 |
28.1 |
34.2 |
28.7 |
Queue |
4.6 |
10.3 |
- |
2.2 |
17.6 |
- |
2.3 |
2.0 |
2.8 |
- |
8.0 |
1.2 |
3.9 |
- |
- |
Dataset 13 |
77.0 |
Delay |
39.3 |
24.7 |
27.0 |
28.4 |
43.3 |
41.4 |
19.8 |
39.4 |
27.5 |
27.3 |
44.7 |
33.9 |
27.6 |
38.2 |
34.4 |
Queue |
5.1 |
13.2 |
- |
3.9 |
21.3 |
- |
3.5 |
2.9 |
4.3 |
- |
9.5 |
1.8 |
4.3 |
- |
- |
Dataset 14 |
65.0 |
Delay |
38.8 |
18.6 |
22.0 |
11.0 |
34.4 |
32.7 |
16.6 |
31.0 |
23.0 |
22.4 |
38.0 |
29.7 |
28.1 |
34.2 |
28.5 |
Queue |
4.6 |
9.7 |
- |
1.4 |
17.6 |
- |
1.6 |
1.3 |
1.9 |
- |
8.0 |
0.8 |
3.9 |
- |
- |
|
Exhibit 2-19.
Maxwell Drive Delay Patterns among Scenarios |
It’s hard to see the
trends in delays, etc. directly from the table. A graphic is useful.
Exhibit 2-19 shows a radar plot of the delay trends. Each axis of the wheel is used
to present the delay for a given movement. The lines and symbols show the
delay for a given scenario. All five operational solutions discussed in
Exhibit 2-17 and
Exhibit 2-18 are included. If you look at the plots for C-4
(the base case) and Datasets 11 and
12, that trend is clear. The pattern for
Dataset 11 is outside the pattern for C-4, which makes sense since the site
traffic volumes for Dataset 11 are 30% greater than for C-4. The pattern for
Dataset 12 is inside the pattern for C-4 for a similar reason. The
site-related traffic is 30% less than in C-4. The patterns for scenarios C-7
and C-8 are different. Most notably, in both of those scenarios there are
more lanes available for the northbound and southbound lefts. In C-7, we’ve
provided two left-turn lanes on both approaches. In C-8, there are three
lanes being shared among the lefts, throughs, and rights, both northbound
and southbound. As a result, the SL delays in particular, and the NL delays
to a lesser extent, are noticeably smaller than they otherwise might
be if the extra lane capacity had not been provided (i.e., the pattern in
C-4 would have still applied).
[ Back ] [ Continue
]
to Discussion |
Page Break
|
Exhibit 2-19.
Maxwell Drive Delay Patterns among Scenarios
|
Page Break
Problem 1: Maxwell Road
Discussion
We’ve used this intersection to
study a number of issues. It has been a logical place to start the case
study, since it’s the intersection where the traffic volumes have changed
the most. We’ve found that the intersection’s geometry will have to
change substantially. We’ve needed a new northbound approach and we’ve
found it useful to reconfigure the southbound approach. Our best solution
uses three lanes southbound (left, through, and right) and three lanes
northbound (left, through, and right). This lets us serve the
northbound and southbound right turns concurrent with the eastbound and
westbound lefts, which shortens the cycle length and reduces delays and
queues.
We haven’t presented
all of the analyses that would be required to do a complete traffic impact
assessment. Rather, we’ve used certain conditions to illustrate
important ideas related to the use of the HCM. We’ve used the PM
Existing condition to look at arrival patterns, skipped phases, and
differences in LOS stemming from the use of data from different sources.
We’ve used the PM With condition to look at changes in LOS due to the
addition of the site-related traffic, the relationship between geometric
improvements and LOS, differences between planning and operational
analyses, and the role of uncertainty in affecting the results obtained.
We don’t know for
sure that the new configuration we’ve identified is the best.
We’ve focused only on the PM With condition. It’s possible that the AM
With or some other condition would work better with some other
configuration. That’s something you’d have to do to complete the impact assessment.
Discussion:
Are
there other issues that we could have addressed? What would they be? What
technique would you have used to find the best configuration? Do you think a
more detailed analysis would have produced a different result?
[ Back ]
[ Continue ] to Problem 2 |
|