Cycle length that maximizes capacity

[tradephoric]

I'm sure a lot of people here have seen the Mythbusters segment where Jamie and Adam test the efficiency of a roundabout vs. the 4-way stop.  For those of you who haven't, here it is:

I'm picturing a similar test, but this time it would involve a signalized intersection and testing the effects of cycle lengths.  Basically do long or short cycle lengths move more traffic through a signalized intersection under saturated conditions.  Driving volunteers would be asked to drive straight through a simple 2-phase traffic signal (no right or left turns would be made).  All legs would have a speed limit of 45 mph and the N/S legs would get the same amount of green time as the E/W legs (equal splits).  Several tests would be done, with the signal running between 60 second and 180 second cycles.  The total number of vehicles passing through the intersection would be counted for each test to determine what cycle length moves the most vehicles through the intersection.

The final test would be setting up a roundabout, and again asking the volunteers to drive straight through the roundabout (no right or left turns would be made).  The roundabout results would then be compared to the results of the signal. 

Question 1:  What cycle length would move the most vehicles through the intersection?

Question 2:  Would the signal outperform the roundabout?

[hotdogPi]

It would depend on how many vehicles there are at the intersection.

(Also, the size of the roundabout.)

[tradephoric]

It would depend on how many vehicles there are at the intersection.

Basically do long or short cycle lengths move more traffic through a signalized intersection under saturated conditions.  Picture an intersection with mile backups in all 4 directions. 

[Alps]

Turning volumes are really the variable that drives the effectiveness of a roundabout vs. other alternatives. Roundabouts serve large volumes of left turns better, at the expense of through traffic though.

[Jardine]

Making everybody stop while the lights reconfigure slows down throughput.  Longer times minimizes wasted cycling times, but people don't want to wait 10 minutes either, even if more cars/hour can get through the intersection with really long cycle times.

[tradephoric]

I think there are two counteracting arguments... 

Case for high cycle lengths:
Every time a signal changes phases, there is an associated "˜lost time'.  High cycle lengths reduce the number of times a signal will cycle per hour, thus resulting in less lost time per hour.  The useable green time, known as the effective green, will increase as the cycle length increases.  Below is a chart showing the effective green time for a variety of signal phases and cycle lengths (assuming 4 second of lost time per phase).



Case for short cycle lengths:
Research has suggested that the peak saturation flow rate of a signalized intersection occurs roughly 30 seconds into the phase green time.  After that, the saturation flow rate slowly tapers off as the phase time increases.  Essentially, the saturation flow rate of an intersection isn't a constant value and changes based on the length of the phase green time (with longer phase green leading to lower saturation flow values).  The chart below attempts to illustrate the concept.

[jeffandnicole]

On that second chart, i don't understand the vph and how that can be calculated when there is no mention of the length of the red light.

(edited because iphone didn't understand I wanted to say light instead of night)

[tradephoric]

On that second chart, i don't understand the vph and how that can be calculated when there is no mention of the length of the red night.

The saturation flow rate is defined as the flow in vehicles per hour that can be accommodated by the lane group assuming unlimited green time and infinite queue.  It's not the true value of vehicles that will flow through the intersection in one hour. as it doesn't factor in the red time.

Edit:  That last line didn't make much sense.  Not too many vehicles should be traveling through the intersection during the red.

[tradephoric]

A recent study, Revisiting the Cycle Length–Lost Time Question With Critical Lane Analysis — 2012, was performed testing the throughput of a saturated intersection running a variety of cycle lengths.  The intersection was a 3-phase intersection, with 20.1 seconds of lost time per cycle, and constant phase splits for each cycle length tested.  The following graph summarizes the results of the study:



The study found that a 100 second cycle length maximized the throughput of the intersection.  In addition, an 80 second cycle length had a higher throughput than a 135 second cycle length.  The study suggests that an increase in cycle length doesn't necessarily lead to an increase in throughput.  A lot of previous research backs up the results of this study (excerpt taken from page 6):

• Teply (1) examined saturation flow rates and found that saturation flow reached its maximum around 40 seconds into green, beyond which it decreased.


• Li and Prevedourous (2) reported saturation flow with respect to queue position and found that, for through movements, the flow rates reached their maximum at approximately the twelfth vehicle in queue, gradually decreasing thereafter.


• Khosla and Williams (3) examined headway with respect to vehicle position at several intersections, and found a gradual increase in saturation headways and a reduction in flow after approximately 40-50 seconds of green.


• Denney et al. (4) examined headway with respect to queue position, and found that it gradually increased for vehicles further back in queue, with varying behavior by lane. The behavior became less deterministic after approximately the 30th vehicle in queue. Because of strong differences in behavior by lane, the increase in headway was attributed to the impact of departing right-turning vehicles.

References:
1.  Teply, S. "Saturation Flow at Signalized Intersections Through a Magnifying Glass."  Proc. Eighth International Symposium on Transportation and Traffic Theory, Toronto: Toronto University Press, pp. 145-162, 1983.
2.  Li, H. and P.D. Prevedourous. "Detailed Observations of Saturation Headways and Start-Up Lost Times."  Transportation Research Record No. 1802, pp. 44-53, 2002.
3.  Khosla, K. and J.C. Williams. "Saturation Flow at Signalized Intersections During Longer Green Time."  Transportation Research Record No. 1978, pp. 61-67, 2006.
4.  Denney, R.W., E. Curtis, and L. Head. "Long Green Times and Cycles at Congested Traffic Signals."  Transportation Research Record No. 2128, pp. 1-10, 2009.

[Alps]

That graph corresponds very well with intuition/observation and traffic engineering knowledge. 90s-120s is what we shoot for in cycle lengths. Under 90s works well in low-volume cases, while over 120s is only for LOS F on multilane roads meeting each other at rush hour.

[tradephoric]

A short cycle length that maximizes throughput isn't always practical for a simple reason: pedestrian crossings.  When a side-street phase runs a relatively short percentage of the total cycle length, it's easy for a pedestrian actuation to lead to the phase over-running.  The chart below illustrates the effect long pedestrian crossings can have on cycle length:



For example, suppose a side-street has a pedestrian crossing length of 150 feet.  Assume the side-street phase runs 25% of the total cycle length.  To prevent a pedestrian actuation from causing the side-street phase from over-running, a 208 second cycle length would be required.  This chart, more than anything, demonstrates the need for short pedestrian crossings to prevent inefficient signal operations. 

Calculations following guidance in MUTCD:

14
The total of the walk interval and pedestrian clearance time should be sufficient to allow a pedestrian crossing in the crosswalk who left the pedestrian detector (or, if no pedestrian detector is present, a location 6 feet from the face of the curb or from the edge of the pavement) at the beginning of the WALKING PERSON (symbolizing WALK) signal indication to travel at a walking speed of 3 feet per second to the far side of the traveled way being crossed or to the median if a two-stage pedestrian crossing sequence is used. Any additional time that is required to satisfy the conditions of this paragraph should be added to the walk interval.

(150 + 6) / 3 = 52 seconds <- Required pedestrian interval
52 / 208 = 25% <- 208 second cycle required to maintain a 25% side-street split

[Duke87]

A 150 foot wide crossing could comfortably fit 10-12 lanes of traffic. If you have that without a median where a pedestrian can stop, it's unsafe regardless of cycle length.

I also might question your sanity if you're attempting to cross that street on foot and 3 feet per second is the fastest you're capable of walking. The idea of granny hobbling across 12 lanes of traffic seems like something silly out of a cartoon.

[tradephoric]

A 150 foot wide crossing could comfortably fit 10-12 lanes of traffic. If you have that without a median where a pedestrian can stop, it's unsafe regardless of cycle length.

Orlando, Florida has the highest pedestrian danger index according to a ranking by Transportation for America, a nonprofit group that measures transportation safety.  Here is a map of intersections around the Orlando area that have continuous crosswalks of over 140 feet (many above 150 feet).



Maybe you're onto something that long pedestrian crossings are inherently unsafe.   However, my point had nothing to do with pedestrian safety.  Instead, long pedestrian crossings can reduce the throughput of an intersection since a pedestrian actuation can cause a signal phase to overrun.

[jeffandnicole]

I also might question your sanity if you're attempting to cross that street on foot and 3 feet per second is the fastest you're capable of walking. The idea of granny hobbling across 12 lanes of traffic seems like something silly out of a cartoon.

I guess the handicapped and those hobbling on crutches are prohibited from crossing the street as well?

[NE2]

I guess the handicapped and those hobbling on crutches are prohibited from crossing the street as well?

Of course. They're supposed to stay at home on their fainting couches.

[Brian556]

In the Orlando area, the SR 535 / SR 536 (World Center Dr) intersection has cycle length/ congestion issues. I was on SB SR 535, and it was realllllly backed up. The green time for my direction was very short. I was wondering why the heck it would be this way. It seemed like longer cycles would have made the congestion much less severe.

[NE2]

That whole area has tourist issues at this time of year.

[Alps]

A short cycle length that maximizes throughput isn't always practical for a simple reason: pedestrian crossings.  When a side-street phase runs a relatively short percentage of the total cycle length, it's easy for a pedestrian actuation to lead to the phase over-running.  The chart below illustrates the effect long pedestrian crossings can have on cycle length:

But no, not at all. You're assuming that the side street MUST ALWAYS BE 25% of the total cycle. In reality, what happens is that the side street is NORMALLY 25% of the total cycle - let's say 30 s and the main street is 90 s in a typical 120. When the ped button is called, let's use your 52s example. The main street is then only 68s in the next cycle to compensate and stay on cycle.

[tradephoric]

Two options exist at signals with long pedestrian crossings, neither are good:

Option A: Run a short cycle length, but then a pedestrian actuation can cause the main-street to get squeezed (as described by Steve).

Option B: Run a high cycle length, using the graph to determine the minimum cycle length that would prevent a pedestrian actuation from squeezing the main-street.  However, this can lead to a reduction in throughput since saturation flow rates decline at very high cycles.

The solution?  Reduce the length of pedestrian crossings.

[roadfro]

The solution?  Reduce the length of pedestrian crossings.

Except reducing the length of the crossing is not exactly an easy solution in most situations...

You can't always have a narrower street due to volumes. A bulb-out isn't always practical. Pedestrian refuges on the median are not something you can just throw in to existing intersections without affecting vehicle geometry (maybe in new design where you can acquire additional right of way for a wider median), and the two-stage crossing increases pedestrian delay (and may negatively effect voluntary compliance with the ped signals). About the only easy thing is to reduce curb radii at the corners or use right turn islands to minimize crossing distance.