Leading vs. lagging PPLT’s

[Brandon]

Leading.  Yellow trap is a phenomenon I really don't like, and a consistent use of leading left turns eradicates yellow trap from your system.   Though this Texas approach sounds like a cool idea now that I'm reading about it.

If the signal is always lagging, then there is no yellow trap.  The signal simply goes from green arrow to yellow arrow to red arrow, not different than a protected-only signal.  A yellow trap would only exist if the opposing traffic still has a green ball a la Dallas Phasing.  Many Metro Detroit signals are setup for lagging left turns rather than leading left turns, and they are setup in such a fashion as to lack a yellow trap.  I find I prefer them as one can enter the intersection, and if he/she cannot turn left, merely has to wait until the signal has a protected green arrow to complete the turn safely.  Leading PPLTs lead to having traffic block the intersection when the signal turns red.

[jakeroot]

I've seen so many intersections where people wait for a gap to make a left turn.  As there usually is no gap, they end up making the turn once the light turns red and this delays cross street. 

To be fair, the cross street is typically only delayed by a couple of seconds when this happens.  A lot of times (in my experience), oncoming traffic is more willing to stop at a yellow light if they see people waiting to turn left and, as such, hardly any red time is used for left turns.  And, even when that's not the case, most of the left-turning happens during the all-red phase.

It's a common misnomer that I hear from people who aren't big fans of waiting in the intersection: "I'll be blocking the intersection if it turns red". As you indicate, that's rarely (if ever) the case, as most left turns can be made before the red light. Traffic, at least around here, is not required to stop on yellow, but usually will if they see traffic waiting to turn. In the off-chance that two or more cars end up in the intersection when the light turns red, no biggie: the traffic just finishes the turn as quickly as possible. As long as the destination leg isn't full of cars, it doesn't count as "blocking", at least in the "blocking the box" sense, as you're still able to clear the intersection. Just because it happens after the light turns red, doesn't make it illegal. Or even rude, as long as you're watching the light and turn ASAP.

[mrsman]

I've seen so many intersections where people wait for a gap to make a left turn.  As there usually is no gap, they end up making the turn once the light turns red and this delays cross street. 

To be fair, the cross street is typically only delayed by a couple of seconds when this happens.  A lot of times (in my experience), oncoming traffic is more willing to stop at a yellow light if they see people waiting to turn left and, as such, hardly any red time is used for left turns.  And, even when that's not the case, most of the left-turning happens during the all-red phase.

It's a common misnomer that I hear from people who aren't big fans of waiting in the intersection: "I'll be blocking the intersection if it turns red". As you indicate, that's rarely (if ever) the case, as most left turns can be made before the red light. Traffic, at least around here, is not required to stop on yellow, but usually will if they see traffic waiting to turn. In the off-chance that two or more cars end up in the intersection when the light turns red, no biggie: the traffic just finishes the turn as quickly as possible. As long as the destination leg isn't full of cars, it doesn't count as "blocking", at least in the "blocking the box" sense, as you're still able to clear the intersection. Just because it happens after the light turns red, doesn't make it illegal. Or even rude, as long as you're watching the light and turn ASAP.

While it's not a big deal for cross traffic to wait for the left turners who are blocking the intersection before proceeding, it is far better if this can be avoided in the first place.  If thru traffic is at moderate to heavy traffic levels, there won't be any gap to turn.  The only time to turn will be at the end of the cycle or during the protected phase.  Under those circumstances, wouldn't it make the most sense to have the protected phase at the end of the cycle?  The protected phase will clear all of the left turners who are stuck in the intersection safely.

I can tell you that whenever I am making the left turn in a permissive setting, and I don't have a gap in traffic, I will wait in the intersection and only make the turn at the end of the cycle.  Sometimes, opposing traffic will run the red - so I will only make the turn when I am sure that the opposing traffic has stopped for me, even if it is so long that cross traffic now has the green.  Granted, it is only a few seconds of delay, but the optimum is to avoid this in the first place, by placing the protected phase at the most appropriate time.

Of course, lagging left turns must designed very carefully to avoid yellow trap.  The FYAs are one way of doing it.  The other common ways are prohibiting the opposing left, restricting the opposing left with a red arrow, or providing a simultaneous lagging left at the very end of the cycle (right after thru traffic gets yellow orb and even a few seconds of red orb).  Each of these do have downsides - the simultaneous lagging left could provide a wasted green arrow (as trade mentioned a few posts up). 

Lagging lefts do provide an important clearance function.  Consider this intersection, Barrington/San Vicente in L.A.:

https://www.google.com/maps/@34.0534792,-118.4654103,3a,75y,313.84h,82.61t/data=!3m6!1e1!3m4!1s-qEguRLSL1ciu6WwWO4vhA!2e0!7i16384!8i8192

S.V. is a very wide street.  There are several very wide streets in L.A. that once hosted streetcars in the old days.  It is so wide that one could almost think of this as being two separate one-way streets that are close to each other.  As traffic on B wants to make the left onto SV, they need to wait for a gap.  There is no regular protection here.  At the end of the phase, there are many cars that are sitting in the middle of the intersection (due to the SV median being so wide).  A lagging left operates on both sides to clear the traffic that is stuck in the middle, before SV traffic gets their green.  The NB and SB signals in the median go to yellow and red (simultaneously) first, even though the 3M signals at the far side of the intersection are still showing green.  [The 3M signals are only visible to those already in the intersection, not those approaching.] This will prevent any new cars from entering the intersection.  Then, the 3M green arrow signal comes on, to perform the clearance function - a lagging left that will clear all of B traffic, whether going straight or making the left onto SV, that got stuck in the middle.  A few seconds later the 3M signal goes yellow and then red.

Here's a view where the median signal is red, but the 3M signals are yellow at the very end of the lagging phase:

https://www.google.com/maps/@34.0536795,-118.4656371,3a,75y,141.42h,80.95t/data=!3m7!1e1!3m5!1sRw1ELLCGdPJGoJ2VJGbcIg!2e0!5s20180501T000000!7i16384!8i8192

[kphoger]

While it's not a big deal for cross traffic to wait for the left turners who are blocking the intersection before proceeding, it is far slightly better if this can be avoided in the first place.

FTFY.

[jakeroot]

I've seen so many intersections where people wait for a gap to make a left turn.  As there usually is no gap, they end up making the turn once the light turns red and this delays cross street. 

To be fair, the cross street is typically only delayed by a couple of seconds when this happens.  A lot of times (in my experience), oncoming traffic is more willing to stop at a yellow light if they see people waiting to turn left and, as such, hardly any red time is used for left turns.  And, even when that's not the case, most of the left-turning happens during the all-red phase.

It's a common misnomer that I hear from people who aren't big fans of waiting in the intersection: "I'll be blocking the intersection if it turns red". As you indicate, that's rarely (if ever) the case, as most left turns can be made before the red light. Traffic, at least around here, is not required to stop on yellow, but usually will if they see traffic waiting to turn. In the off-chance that two or more cars end up in the intersection when the light turns red, no biggie: the traffic just finishes the turn as quickly as possible. As long as the destination leg isn't full of cars, it doesn't count as "blocking", at least in the "blocking the box" sense, as you're still able to clear the intersection. Just because it happens after the light turns red, doesn't make it illegal. Or even rude, as long as you're watching the light and turn ASAP.

While it's not a big deal for cross traffic to wait for the left turners who are blocking the intersection before proceeding, it is far better if this can be avoided in the first place.  If thru traffic is at moderate to heavy traffic levels, there won't be any gap to turn.  The only time to turn will be at the end of the cycle or during the protected phase.  Under those circumstances, wouldn't it make the most sense to have the protected phase at the end of the cycle?  The protected phase will clear all of the left turners who are stuck in the intersection safely.

I can tell you that whenever I am making the left turn in a permissive setting, and I don't have a gap in traffic, I will wait in the intersection and only make the turn at the end of the cycle.  Sometimes, opposing traffic will run the red - so I will only make the turn when I am sure that the opposing traffic has stopped for me, even if it is so long that cross traffic now has the green.  Granted, it is only a few seconds of delay, but the optimum is to avoid this in the first place, by placing the protected phase at the most appropriate time.\

My preferences for leading vs lagging has changed from my earlier post in this thread. Bear with me, as this does have something to do with your post.

During most hours of the day, I would agree that lagging is more ideal. When a left-turning vehicle approaches an intersection midday, and there is only a few opposing vehicles, definitely default to lagging (with FYAs). Oncoming traffic can go with their green. Meanwhile, left turning traffic can pull forward and then turn behind the straight-ahead traffic. Really no need for any protected phase.

But, if my experience with Cities: Skylines means anything (doesn't mean much, but like I said, bear with me), it's that leading left turns do have higher capacities than lagging left turns. Unlike lagging left turns at peak times (fully-saturated phase with no gaps), leading left turns have two periods where traffic turns left: at the beginning with a green arrow, and at the end when the light turns red. I understand that you are opposed to that second period of turns, if it can be avoided, although I find the capacity improvements with those extra left turns to be worth a second consideration. Assuming it can be done safely.

To explain, I've created a video that shows what I mean. Note that the double left turn has no gaps, so waiting traffic can only turn after the red light is activated. I've artificially reduced the green time to prove my point, but I think you might be able to understand what I'm getting at. There are basically two points in which traffic turns left. With lagging lefts, assuming oncoming traffic is fully-saturated, there is only one point in which they can turn: with the green arrow.

Few things to note in the video: (1) it starts with the end of another leading phase, (2) the side-street is very quiet so it lags instead, and (3) the traffic signals are visible, but hard to see; you can see them change to red. There is a 1-second all-red phase.

https://youtu.be/_QyB0WDDPlM

[mrsman]

My preferences for leading vs lagging has changed from my earlier post in this thread. Bear with me, as this does have something to do with your post.

During most hours of the day, I would agree that lagging is more ideal. When a left-turning vehicle approaches an intersection midday, and there is only a few opposing vehicles, definitely default to lagging (with FYAs). Oncoming traffic can go with their green. Meanwhile, left turning traffic can pull forward and then turn behind the straight-ahead traffic. Really no need for any protected phase.

With all manner of PPLT, we are discussing a balance for all users of the intersection.  Balancing safety and balancing delay.  The assumption always is that thru traffic is the main movement through an intersection, but that there is also an important left turning movement that needs to be served.  But the left turn is not the main movement, the thru movement is.  To the extent that we serve the left turn movement, it means we take time away from the main movement.  As you correctly note, in a mid-day scenario, we may have 2 or 3 cars waiting to turn left.  Very likely they can make their turn during gaps in the thru movement.  If the signal had a lagging turn, and the left turners do in fact make their turn during the thru phase, then the green arrow doesn't even need to come on in the first place, thereby the thru traffic (the main traffic) is not adversely impacted.  If the signal were leading left, the signal would provide the 2 or 3 cars with a green arrow at the beginning, even though in many circumstances, it is totally unnecessary, thereby delaying thru traffic.

And in the cases where the traffic is a bit more moderate, the lagging left is still available to service anyone who wasn't able to make it during the gap.  Likely, the amount of time for this service is less than the amount of time for the leading left, since the signal will service everyone at the beginning and nobody will even have the opportunity to go during green time.

We can think of the service of the green arrow as being similar to the service of a minor cross street in a regular intersection.  The signal will rest on green to service main street traffic.  The signal should not change unless there is minor street traffic.  Moreover, the signal should not change right away to serve the minor street traffic, since you will be delaying the majority just to serve one car.  There will be a preset time, (let's say 90 seconds) that if the minor street traffic had to wait for 90 seconds and it is still waiting, then we will give the minor street a brief green to handle the movement.  Sometimes, it is not necessary to provide any green at all - b/c the traffic on the minor street made a successful RTOR during the 90 second wait.  Sometimes, during the waiting period an additional number of cars have approached on the side street.  By providing the waiting period, we can now serve all the vehicles at the side street at the same time and be more efficient for the signal as a whole.  This is because every signal cycle has yellow and all-red phases, so to serve two cars at one phase is far more efficient than serving one car with one phase and a second car at a separate time with a separate phase. 

But, if my experience with Cities: Skylines means anything (doesn't mean much, but like I said, bear with me), it's that leading left turns do have higher capacities than lagging left turns. Unlike lagging left turns at peak times (fully-saturated phase with no gaps), leading left turns have two periods where traffic turns left: at the beginning with a green arrow, and at the end when the light turns red. I understand that you are opposed to that second period of turns, if it can be avoided, although I find the capacity improvements with those extra left turns to be worth a second consideration. Assuming it can be done safely.

To explain, I've created a video that shows what I mean. Note that the double left turn has no gaps, so waiting traffic can only turn after the red light is activated. I've artificially reduced the green time to prove my point, but I think you might be able to understand what I'm getting at. There are basically two points in which traffic turns left. With lagging lefts, assuming oncoming traffic is fully-saturated, there is only one point in which they can turn: with the green arrow.

Few things to note in the video: (1) it starts with the end of another leading phase, (2) the side-street is very quiet so it lags instead, and (3) the traffic signals are visible, but hard to see; you can see them change to red. There is a 1-second all-red phase.

Thank you for the time you took in making the video.  When thru traffic is too busy to allow left turn gaps during the thru phase - you correctly state that leading lefts have more capacity for left turns than lagging lefts.  But more capacity for left turns necessarily means less capacity for thru traffic.  You also correctly state that the reason the leading lefts have more time is because they essentially have two phases for making the left, at the beginning of the signal phase with the green arrow, and at the end when the light goes red before cross traffic gets green.  I will submit that this end phase turn is in fact a very brief unsignalled lagging left turn.  There is some danger involved with red light running, but essentially all who follow the rule of the road know that this is the time when left turners are to complete their turn.  For the two or three seconds it is equivalent to giving these left turners a simultaneous green arrow in both directions with a yellow arrow and then allowing cross traffic to proceed.

But is it fair to compare a 15 second lagging phase with a 15 second leading phase that also has a 3 second secret lagging phase?  It is not, because the leading phase has more overall time.  More left turners are being served, since more time is given to the left turners, and consequently less time is provided for thru traffic.

In our simplified model, we are ignoring a lot of factors, but just like my example earlier with the minor cross street, it is less efficient to provide multiple phases than a combined phase.  Similarly, it is less efficient to provide shorter signal cycles than longer signal cycles.

Simple intersection illustration.

two cycles, cycle length 60 sec

00-23 NS, 24-27 yellow, 28-29 all red; 30-53 EW, 54-57 yellow, 58-59 all red;
60-83 NS, 84-87 yellow, 88-89 all red;  90-113 EW, 114-117 yellow, 118-119 all red.

48 NS, 8 yellow NS, 48 EW, 8 yellow EW, 8 all red.


one cycle, cycle length 120 sec.

0-53 NS, 54-57 yellow, 58-59 all red; 60-113 EW, 114-117 yellow, 118-119 all red

54 NS, 4 yellow NS, 54 EW, 4 yellow EW, 4 all red

So we see that it is more efficient to have longer cycles with fewer phases.  There is more green time for each movement with the longer cycle length.  There is more combined green and yellow time for each movement with the longer cycle length.  This is why busier intersections tend to have longer cycle lengths.  A long cycle of course also means a long red, so the perceived delay to an individual driver may seem worse with a longer cycle, but the overall system is more efficient.


Again, to bring it all into perspective, there are reasons for preferring leading and there are reasons for preferring lagging.  For each intersection, the actual factors at play must be taken into account.  The most important benefits of leading signals is that it completely avoids yellow trap and it allows flexibility to allow extra thru time (in one direction) if one left gaps out early.  The most important benefits for lagging signals is that provides greater opportunity to avoid triggering the left turn signal in the first place if left turns are made during the thru phase, combines the protected phase with the clearance phase for left turns, and it minimizes danger to red light running and blocking cross street traffic.

Given this, in most circumstances, the lead-lead signal is better than lag-lag.  But if yellow trap is properly avoided AND [if red light running is a problem [higher speed roads], if LPIs are desired, if left turns in both directions tend to be more or less equal, or off-peak traffic usually provides significant gaps for turning during the thru phase] then lagging lefts are preferred.  Lagging lefts are also preferred if the opposing left is prohibited, like when the cross street is a one-way street or ends in a T.

In my experience, I come across far more lead-lead signals as in most cases they are better.  The lagging signals usually are special circumstance like with one-way cross streets.

Lagging signals can also be useful when dealing with a shared lane.  If there is no dedicated left turn lane, and there is a heavy left turn where some traffic turns and some traffic doesn't turn, then you have the problem that the person turning left will block those behind him who want to go straight.  FYAs are not available.  If the left turner can go during a gap, great.  If he can't, then he will have to go at the end of the cycle.  And what of the people who were waiting behind, they would want to go right away and not have to wait for the next green.  The ideal is a lagging signal with green orb and green arrow at the same time, but this is only safe if the opposing left turn is not also lagging and is otherwise prohibited/restricted with red arrow/controlled by FYA.

This type of thing is common in DC, but not the suburbs around.  Note the old use of 4 section signals b/c green arrow will appear with green orb at the end of the signal.  Yellow orb terminates green orb and green arrow simultaneously.  In DC seeing this type of signal is usually a lagging signal or a split-phase signal.

10th/Constitution: (opposing left prohibited due to T intersection)

https://www.google.com/maps/@38.8921628,-77.0261889,3a,75y,120.75h,76.14t/data=!3m6!1e1!3m4!1sbsVxW3KDhRj9fK0gQeuOXw!2e0!7i16384!8i8192

Georgia/Eastern: (opposing left restricted to leading with red arrow)

https://www.google.com/maps/@38.9847132,-77.0266792,3a,75y,7.3h,86.52t/data=!3m6!1e1!3m4!1s8qvJZVydu23hRLMhaTnPqQ!2e0!7i16384!8i8192

[tradephoric]

If the signal were leading left, the signal would provide the 2 or 3 cars with a green arrow at the beginning, even though in many circumstances, it is totally unnecessary, thereby delaying thru traffic.

There are a couple ways to prevent the leading-left turns from cycling during light traffic conditions.  You could cut the loop in the left turn lane about 50 feet back from the stop bar so that the left turn will only cycle if there are more than a few cars waiting.  Another option is for the controller to calculate the degree of saturation for thru traffic.  If the degree of saturation is low then it can force skip the left turn.   Drivers may expect the left-turn to cycle when they have been waiting patiently at the stop bar (especially when it seems to cycle for them during busy times) but if there are lots of gaps in opposing thru traffic they should get a gap to turn anyways.

But is it fair to compare a 15 second lagging phase with a 15 second leading phase that also has a 3 second secret lagging phase?  It is not, because the leading phase has more overall time.  More left turners are being served, since more time is given to the left turners, and consequently less time is provided for thru traffic.

Have you ever heard of the Pittsburg left?  According to Wikipedia, the Pittsburgh left is a colloquial term for the driving practice of the first left-turning vehicle taking precedence over vehicles going straight through an intersection, associated with the Pittsburgh, Pennsylvania area.  But whether a driver is performing a Pittsburg left at a lagging-left intersection, or squeezing through the gap in traffic at the end of the phase at a leading-left intersection... the thru traffic is getting the same amount of time. 

So we see that it is more efficient to have longer cycles with fewer phases.  There is more green time for each movement with the longer cycle length.  There is more combined green and yellow time for each movement with the longer cycle length.  This is why busier intersections tend to have longer cycle lengths.  A long cycle of course also means a long red, so the perceived delay to an individual driver may seem worse with a longer cycle, but the overall system is more efficient.

There has actually been a lot of research done regarding optimum cycle length.   While it's true that short cycle lengths lead to a higher percentage of "lost time"  during the cycle, it's also been proven that when a phase gets to be too long that the saturation flow rate through the intersection decreases significantly.  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 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.

[Amtrakprod]

What type of permissive-protected left turn (PPLT) do you prefer: leading or lagging? 

According to a recent survey, 83% of PPLTs in the US are leading while 11% are lagging.

I like lagging left turns, they just make sense especially for permissive lefts.


iPhone

[mrsman]

I have heard of the Pittsburgh left.  Outside of Pittsburgh and a few other areas, it is simply not done as it is dangerous.  I wouldn't assume in most places that I have been that there is any reserved right to make a leading left turn without the protection of an arrow.

I found this online.  Don't know when it was published, but it has a pretty good succinct table of the advantages and disadvantages of leading vs lagging.  It was done in the era before FYA was common.

https://www.in.gov/dot/div/contracts/standards/dm/2011/Part7/Ch77/figures/Fig77-5X.pdf

[paulthemapguy]

Leading.  Yellow trap is a phenomenon I really don't like, and a consistent use of leading left turns eradicates yellow trap from your system.   Though this Texas approach sounds like a cool idea now that I'm reading about it.

If the signal is always lagging, then there is no yellow trap.  The signal simply goes from green arrow to yellow arrow to red arrow, not different than a protected-only signal.  A yellow trap would only exist if the opposing traffic still has a green ball a la Dallas Phasing.  Many Metro Detroit signals are setup for lagging left turns rather than leading left turns, and they are setup in such a fashion as to lack a yellow trap.  I find I prefer them as one can enter the intersection, and if he/she cannot turn left, merely has to wait until the signal has a protected green arrow to complete the turn safely.  Leading PPLTs lead to having traffic block the intersection when the signal turns red.

If all the left turns are lagging, though, doesn't this mean that opposing approaches have to have the same amount of protected left turn time?  In other words, in order to avoid yellow trap, the green arrow phase for one approach has to match the same timing as the opposite approach's phase?  Because the phases would be:

1. NB and SB have green ball
2. NB and SB have yellow ball for 3-5 seconds
3. NB and SB have red ball for a second (all-red phase)
4. NB and SB have green left arrow at same time
5. NB and SB have yellow left arrow at same time
6. NB and SB have red left arrow at same time

[Brandon]

Leading.  Yellow trap is a phenomenon I really don't like, and a consistent use of leading left turns eradicates yellow trap from your system.   Though this Texas approach sounds like a cool idea now that I'm reading about it.

If the signal is always lagging, then there is no yellow trap.  The signal simply goes from green arrow to yellow arrow to red arrow, not different than a protected-only signal.  A yellow trap would only exist if the opposing traffic still has a green ball a la Dallas Phasing.  Many Metro Detroit signals are setup for lagging left turns rather than leading left turns, and they are setup in such a fashion as to lack a yellow trap.  I find I prefer them as one can enter the intersection, and if he/she cannot turn left, merely has to wait until the signal has a protected green arrow to complete the turn safely.  Leading PPLTs lead to having traffic block the intersection when the signal turns red.

If all the left turns are lagging, though, doesn't this mean that opposing approaches have to have the same amount of protected left turn time?  In other words, in order to avoid yellow trap, the green arrow phase for one approach has to match the same timing as the opposite approach's phase?  Because the phases would be:

1. NB and SB have green ball
2. NB and SB have yellow ball for 3-5 seconds
3. NB and SB have red ball for a second (all-red phase)
4. NB and SB have green left arrow at same time
5. NB and SB have yellow left arrow at same time
6. NB and SB have red left arrow at same time

That's exactly how they work for MDOT.

[mrsman]

Leading.  Yellow trap is a phenomenon I really don't like, and a consistent use of leading left turns eradicates yellow trap from your system.   Though this Texas approach sounds like a cool idea now that I'm reading about it.

If the signal is always lagging, then there is no yellow trap.  The signal simply goes from green arrow to yellow arrow to red arrow, not different than a protected-only signal.  A yellow trap would only exist if the opposing traffic still has a green ball a la Dallas Phasing.  Many Metro Detroit signals are setup for lagging left turns rather than leading left turns, and they are setup in such a fashion as to lack a yellow trap.  I find I prefer them as one can enter the intersection, and if he/she cannot turn left, merely has to wait until the signal has a protected green arrow to complete the turn safely.  Leading PPLTs lead to having traffic block the intersection when the signal turns red.

If all the left turns are lagging, though, doesn't this mean that opposing approaches have to have the same amount of protected left turn time?  In other words, in order to avoid yellow trap, the green arrow phase for one approach has to match the same timing as the opposite approach's phase?  Because the phases would be:

1. NB and SB have green ball
2. NB and SB have yellow ball for 3-5 seconds
3. NB and SB have red ball for a second (all-red phase)
4. NB and SB have green left arrow at same time
5. NB and SB have yellow left arrow at same time
6. NB and SB have red left arrow at same time

That's exactly how they work for MDOT.

This is the setup for a lag-lag.  Given the red left arrow, this is probably a protected only left turn signal, not a PPLT (protected/permissive).  The setup for PPLT, if using doghouses, is just like the above, except that phase 6 does not exist.  The arrows go dark and we have another brief all red before cross-traffic gets their green. 

If FYAs are used, there are two approaches.  First, there would be FYA during 1,2,and 3.  Then 4,5, and 6 would occur.  The alternate would have FYA and green orb during 1, solid yellow arrow and yellow orb during 2, red arrow and red orb during 3, and then 4, 5, and 6.

As trade mentioned earlier, a key down side is that the two opposing lefts have to be at exactly the same time, which is inefficient in cases where one direction tends to have a vastly different demand than the other.  However, the upside is that there is no yellow trap, and it addresses red light running issues since cars that are aware of the sequence will not try to take the turn on yellow knowing that a protected phase will be there soon after.  Another plus, is that because it follows the thru sequence, it is possible that every car wanting to turn left (in both directions) will have completed their turn during the thru phase and the left turn priority can be skipped entirely.

There aren't too many PPLT lag-lag signals in my area, but there are two that do stand out.  They are along GA Ave., near the Beltway.  This stretch has a reversible left turn lane (during rush hours, lefts are forbidden and it becomes an additional lane at peak direction).  BOth of the signals employ doghouses.  [MD doesn't have FYA, but they are beginning to use flashing red arrows in a similar manner at some intersections.]  Earlier tonight, I was at both intersections with the lag-lag signals.

At GA/Forest Glen, the typical non-rush hour signal sequence will have lag-lag after the thru phase, but it only will exist if it senses a car that is waiting in either lane (left NB or left SB).  Notice that due to the reversible lane setup further south, there are no left turn lanes here.  The left lane is an option straight or left lane.  This means that a left turner could block everyone behind him if he can't find a gap or they can't switch lanes.  Tonight, for the first time in memory, there was nobody waiting at the end of the cycle, so the left turn signal was skipped.

https://www.google.com/maps/@39.0155908,-77.0426176,3a,75y,354.83h,90t/data=!3m6!1e1!3m4!1sh0WdWSw2hpoMSsfxvCUuvg!2e0!7i16384!8i8192


GA/Seminary/Columbia, during off-peak times, has a center lane for left turns.  It also has a lag-lag signal.  I made the SB left from GA to Columbia.  During the green thru phase, there was no gap at all (typical for most times).  Fortunately, after yellow and red there was a protected green arrow.  Nobody going northbound stopped at all during the yellow phase, so if the lagging signal were not there, I would have to turn on red, while Columbia got the green.  [Seminary becomes Columbia when crossing GA, Seminary and Columbia are split-phased, westbound green and left is totally separate from eastbound green and left.  Each of these phases are relatively short.]  Now, I don't know if the drivers act this way because it is a busy corridor and they are all trying to make the light, or that they are aware that there is a lagging left [and no red light camera] so there is no incentive for them not to run the yellow because they know that I have my own protected green arrow coming.  Nevertheless, I felt safe just waiting for the light to change to green arrow and not try to guess when or if all of the cars in the opposing direction would deem it appropriate to stop for me.

https://www.google.com/maps/@39.0087084,-77.0402726,3a,75y,162.69h,92.55t/data=!3m6!1e1!3m4!1sBIeJhpIDjtogk-5rAPdVgQ!2e0!7i13312!8i6656

[wanderer2575]

Leading lefts can be beneficial when you have uneven queues.  Suppose a NBLT averages 20 vehicles in queue and the SBLT has only 3 vehicles in queue.  With leading lefts you can allocate 40 seconds for the left turn phase and allow the SBLT to gap out early.   If the SBLT suddenly gets heavy, it can soak up the full 40 seconds if it needs it.  You couldn't do this with lagging left turns (you could set up the lagging lefts to start non-simultaneous and run the SBLT short, but then it wouldn't be able to service a sudden rush of SBLT traffic). 

If the signal actually adjusts for that, I can accept that argument.  But in metro Detroit, regardless of all the pavement and video sensors, left turn signal phases seem pretty fixed regardless of the length of the queues.  It's not at all uncommon to see 20 vehicles in the NB queue, only a couple in the SB queue, and both get the same fixed-length signal.  So NB thru traffic sits longer at the red while the opposing LT signal is green for an empty lane, while only half the NBLT queue is able to proceed that cycle.

Oakland County MI is big on leading lefts for flashing yellow arrows and lagging lefts for fully-protected turns signals that still have flashing red balls; I don't know why the difference.  I hate the leading lefts because:
(1)  Opposing right turn traffic often turns at the same time, because they're not paying attention and think the cross street still has the green.
(2)  Right turn traffic from the cross street often turns right in front of oncoming thru traffic because they can't see when the leading left phase ends.
(3)  Too many people here still haven't figured out that a flashing yellow arrow means YOU CAN PULL INTO THE INTERSECTION AND THEN COMPLETE YOUR TURN WHEN TRAFFIC CLEARS OR THE LIGHT TURNS RED, same as if there were no turn signal at all.  I wish I had a nickel for every time I was stuck waiting an additional cycle because the person in front of me refused to cross the stop bar on a flashing arrow.

(Edited to fix what I meant, not what I said.)

[UCFKnights]

If the signal is actuated and the goal is to maximize throughput, assuming you don't need adjustments for nearby intersections, the fastest is definitely lead-lags. You want a lead in the direction that has more left turn traffic at that time period, to clear our the queue from the time that direction is red, and have a flow of cars into the lane to attempt to make the permissive lefts. On the direction that has less left turns, you want to try to see if you can skip the left turn phase entirely, by allowing them to make permissive lefts, and using a lagging left to clear out anyone who isn't able to make a permissive left. This should allow the phase to be skipped most frequently, and allow the shortest time when it does need to cycle to it. This format does require FYA's as it will lead to yellow trap with doghouses, so I know why it wasn't used in the past, but IMO should be the default with FYAs.