ID# C201001

Problem 1: Maxwell Drive

Printable VersionProblem 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

ID# C201002

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

 
Page Break

Exhibit 2-6. Maxwell Drive Intersection Volumes for the Existing AM & (PM) Peak Hour

 

Page Break

ID# C201A01

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

ID# C201A02

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.

We use arrival type 2 for the eastbound approach because the signal at Moe Road tends to synchronize de facto with the one at Maxwell Drive, even though they are both fully actuated. The average cycle lengths at the two intersections tend to be about the same, and they start discharging traffic at about the same time. The distance between the signals is such that the first vehicle in the respective platoons (Moe-to-Maxwell and Maxwell-to-Moe) tends to arrive just as the signals are reaching maximum green. The signals then turn red, a queue forms, and the pattern repeats. This is more typical for the eastbound approach than for the westbound, because the cycle length at Clifton Country Road is much longer. The two signals are never synchronized in such an antagonistic way.

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

ID# C201A03

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

ID# C201A04

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

ID# C201A05

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:

bullet

General Idea

bullet

Consideration at Maxwell Road 

bullet

What happens if you ignore skipped phases?

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

ID# C201A06

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

ID# C201A07

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

ID# C201A08

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

 

ID# C201A09

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

ID# C201B01

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

ID# C201B02

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

ID# C201B03

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

ID# C201B04

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

ID# C201B05

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)

This is the process being followed in the spreadsheet we used for the analysis.

Equations (2) through (4) show that Equation (1) can be obtained easily. First, realize that N equals 4. Second, see that the sequence of critical movements is either: 1,2,3,4; 1,2,7,8; 5,6,3,4; or 5,6,7,8. Third, notice that the sum of the vi/si ratios identified in the denominator of Equation (1) is the same as the left and right half based sum shown in Equation (4).  

Discussion:
In practice, we don't often use equations in the formal style they are presented here. The equations are helpful, though, because they are a shorthand-way of expressing ideas. You might check-out the spreadsheet and see if you can identify how equations (2), (3) and (4) have been implemented.

[ Back ] [ Continue ] to Critical Movement Techniques

 

Page Break

ID# C201B06

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

Note: Saturation flow rates: 1,800 for throughs, 1,700 for rights, 1,500 for lefts, 1,700 for double lefts, 1,800 for 3-lane group

From the table, we see the following: in Scenario C-1, the cycle length we obtain is shorter than that in the planning analysis. (This scenario is the same as the first scenario we studied in the planning model analysis.) This is because we used 3 seconds of lost time per phase instead of 4. If we use 4 seconds, as is the case with Scenario C-2, we get a cycle length very similar to the one we obtained in the planning analysis (175.5 seconds versus 171.4). This means the two methods are very similar for that condition.

[ Back ] [ Continue ] with Critical Movement Technique

 
Page Break

ID# C201B07

Sub-problem 1b: Maxwell Drive PM Peak Hour - With Conditions

In Scenario C-3 we’ve tested to see what happens if the throughs and rights are erroneously grouped together for the north and southbound approaches, thus assuming that some of the right turning vehicles will be in the through lane. You’ve created a double-right where the second right-turn lane is co-mingled with throughs. That’s a very uncommon (but not impossible) condition. In Scenario C-4, we’ve taken advantage of the fact that we have separate lanes for the northbound and southbound rights and had them move concurrent with the eastbound and westbound lefts. By doing this, we can accommodate all of the northbound and southbound lefts while the eastbound and westbound rights are moving. That means the signal timing for the northbound and southbound through-and-right movements (4 and 8) only needs to provide green time for the northbound and southbound through movements, not the rights. (The difference is 90 instead of 150 vehicles per hour northbound and 60 instead of 195 vehicles per hour southbound.)

Scenario C-5 puts the westbound right turns in a separate lane. This shrinks the westbound total volume and closely matches it to the eastbound through-and-right volume. The eastbound and westbound flows are more similar and the cycle length can be shortened. Scenario C-6 puts the northbound and southbound through-and-right movements in a single lane. The cycle time jumps to 204.9 seconds. In Scenario C-7, we offset that increase in demand for green time by providing double left turns northbound and southbound. The cycle length drops back to 106.7 seconds. Scenario C-8 shows the northbound and southbound approaches are handled in separate phases. We also assumed that the three lanes would be used “optimally” to accommodate the combined lefts, throughs, and rights. Assuming that’s possible, the cycle length drops to the lowest value encountered, 84.4 seconds.

What have we learned from this? First, we’ve seen that different lane use plans produce very different cycle lengths. Implicitly, they also produce very different phasing plans. We’ve also seen that there are ways to combine certain movements, like the northbound and southbound rights and the eastbound and westbound lefts, to get more productivity out of the intersection and reduce the cycle time. 

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

ID# C201B08

Sub-problem 1b: Maxwell Drive PM Peak Hour - With Conditions

Operational versus Planning Analyses
In all the analyses we’ve done so far for the PM With condition, we’ve done planning level analyses using the HCM and we’ve explored the use of critical lane analysis. We can also evaluate signal timings and lane configurations, at a more detailed level, using an operational level analysis.

We don’t need to explore all of the configuration options presented in Exhibit 2-15 and Exhibit 2-16. Only a few of them are worth investigating further. From Exhibit 2-16, let’s look at scenarios C-4, C-7, and C-8. 

In the case of Scenario C-4, we have single left-turn lanes eastbound and westbound as well as two through lanes, shared with the rights. Northbound and southbound, we have single left-turn lanes and separate lanes for the throughs and rights. The detail that distinguishes it from Scenario C-1 is that the northbound and southbound rights can move concurrent with the eastbound and westbound lefts. That allows the cycle length to be much shorter. Dataset 10 (C-4), Dataset 11 (C-7) and Dataset 12 (C-8) contain the input data these three scenarios.

As Exhibit 2-17 shows for Scenario C-4, a cycle length of 65 seconds can be obtained using the operational analysis.  This cycle length is much shorter then the 114.9 second cycle length that was obtained from the critical movement analysis. The overall delay is 28.7 seconds, the maximum delay is 39.5 (northbound through), and the maximum average queue is 17.6 vehicles (westbound through-and-right). For Scenario C-7, a 90-second cycle length from the operational analysis is compared to a 106.7 second cycle length from the planning analysis. The delays and queue lengths are considerably larger than C-4, so the C-7 solution is not better. For C-8, we can’t match the 84.4 seconds from the critical lane analysis. The shortest cycle length we can make work is 93.0 Some movements have LOS F if the cycle length is shorter.

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

ID# C201B09

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

ID# C2010D1

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