Feedback into deep dive into Light Rail at Grade Capacity for an existing operational environment

 
  santak003 Beginner

I'm wondering if anyone could weigh in on my assertion that for a particular study in Vancouver Canada that is
assessing which technology (BRT, LRT or metro) to use going from point A to point B, that LRT was dealt an uneven hand.

The fact that the study takes place in Vancouver is of little relevance.  I'm looking for feedback on my argument that the passengers per hour estimate is much higher than the 7200 pphpd and instead could be increased for this light rail at grade to 36000.  I'm looking for feedback on the technical argument.  The argument is a little deeper as it takes some operational characteristics of the environment the light rail is running in and goes through the Transit Capacity and Quality Service Operating Manuals light rail capacity at grade formula for calculating minimum achievable headways.

It's a long read and it goes through a lot of theory and practice and it's written by me: An inexperienced transit enthusiast.

I'm looking for any comments/feedback/suggestions you have as there are no other forums to illicit this type of feedback (and I don't work in transportation).

I suggest you read the link at the bottom first before the Jan 2019 to see the argument as the Jan 2019 report that I'm attacking, is long and contains many details that are not relevant.

Redefining maximum capacity of LRT at grade for Arbutus to UBC corridor: 36000 pphpd

Redefining maximum capacity of LRT at grade for Arbutus to UBC corridor: From 7200 to 36000 pphpd (and leaving LRT as a contender to skytrain): “Jan 2019 Rail Rapid Transit Study to UBC” (aka Slam the Tram).

The benefits of light rail run deep. Safety, Reliability, Comfort, Cost and Capacity.

“LRT is demand-responsive in that the length of trains and the service frequency can be easily adjusted when required”

In the Jan 2019 Rail Rapid Transit Study to UBC (aka “Slam the Tram”), McElhanney Consulting essentially knee-capped the LRT by denying the major pillar of “demand responsiveness” , by effectively limiting the LRT train to a theoretical maximum operating capacity at 7200 pphpd by limiting headways to 4 minutes and vehicle lengths to 2 train consists @ 80m total length with carrying capacity of 240 for each train unit for a max carrying capacity of 480 persons.

Jan 2019
McElhanney Consulting
"Rail to UBC Rapid Transit Study"
https://www.translink.ca/-/media/Documents/about_translink/governance_and_board/council_minutes_and_reports/2019/january/2019_01_24_technical_report_rail_to_ubc.pdf

The rest of the report eliminated the LRT at grade from consideration for Arbutus to UBC, all because of this max capacity limit of 7200 pphpd.

Using data from Vancouver’s operational environment, an argument is laid out that the actual maximum capacity that should have been used in the report is 36000 due to two factors: Vehicle Carrying Capacity should be adjusted to 1200 from 480 and minimum headway should be adjusted from 4 minutes to 2 minutes. The argument for this is laid out in three separate documents (backgrounders).

The backgrounders will illuminate certain concepts while using conservative estimates to arrive at results and most importantly how the operational capacity risk of implementing LRT at grade is LOW and sufficient for 2050 time horizons:

- How and when to trust the minimum headway formula
- How the minimum headway formula does not account for traffic signal priority
- How the minimum headway formula assumes that traffic congestion/saturation is at a reasonable level
- How the minimum headway formula incorporates the level of bunching you are designing for
- How, in a well run operating environment like Vancouver, the dwell time of the train and it's variation is the main element to achieve low minimum headway
- How runtime data from Vancouver streets shows that traffic in Vancouver is at a low level of saturation
- How traffic signal priority at low saturation levels of traffic can be applied in a preemptive way with no effects on cross traffic (Low Risk of implementation)
- How 98% of the westside has 160m block lengths and the two locations where it is not (120m at Macdonald and Westbrook) should trade off pedestrian access for block length
- How by changing the train vehicles, one can achieve a higher capacity for 160m block lengths


Start here:
https://docs.google.com/document/d/1r_f_yGevPLOpbX74MYN_PSYvHxjk40KjTddD6l8yigU/edit?usp=sharing

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  Valvegear Oliver Bullied, CME

Location: Norda Fittazroy
One look at the thread's heading was enough. It is meaningless jargon, so I don't hold out much hope for what follows.
  YM-Mundrabilla Minister for Railways

Location: Mundrabilla but I'd rather be in Narvik
One look at the thread's heading was enough. It is meaningless jargon, so I don't hold out much hope for what follows.
Valvegear
Don't you speak jargon and acronym?
Neither do I!
  allan Chief Commissioner

Yes, the natives here have sufficient difficulty with plain English: cant is a step too far.
  kitchgp Chief Commissioner

At a brief glance. A 1200-passenger tram would be about 180 metres long. Gold Coast trams are 43 m long and carry 300 pass. Sydney’s Lines 2 & 3 trams are 67 m (although they’re really 2 x coupled sets) and carry about 420 pass. You’d need either 4 x Gold Coast trams or 6 x Sydney trams (3 x coupled sets).

A 2-min headway in one direction would require a 2-min counter balancing headway in the other. Any at-grade crossing would have a tram cross every minute. Running at 40 km/h it would take a 180 m tram about 40 secs to cross, allowing for the traffic light sequence and possibly mini boom barriers. Trying to synchronise movements to reduce the occupancy time would be difficult, eg crossings would have to be the same distance apart, stops sufficient distance from crossings to allow trams to accelerate to a decent speed, etc.

It seems unworkable.
  santak003 Beginner

At a brief glance. A 1200-passenger tram would be about 180 metres long. Gold Coast trams are 43 m long and carry 300 pass. Sydney’s Lines 2 & 3 trams are 67 m (although they’re really 2 x coupled sets) and carry about 420 pass. You’d need either 4 x Gold Coast trams or 6 x Sydney trams (3 x coupled sets).

A 2-min headway in one direction would require a 2-min counter balancing headway in the other. Any at-grade crossing would have a tram cross every minute. Running at 40 km/h it would take a 180 m tram about 40 secs to cross, allowing for the traffic light sequence and possibly mini boom barriers. Trying to synchronise movements to reduce the occupancy time would be difficult, eg crossings would have to be the same distance apart, stops sufficient distance from crossings to allow trams to accelerate to a decent speed, etc.

It seems unworkable.
kitchgp

Thanks for the reply.  

I get about 18 seconds (@10 meters/second)  and not 40 seconds to cross at that unwieldy length (40km/h = 11 meters/second).  However your point is taken: Let's assume the length is the issue.

I see that there seems to be some consensus on light rail being able to push between 10,000 to 18,000 pphpd here: https://www.railpage.com.au/f-p1058337.htm

Assuming that priority is only in one direction and in the other direction the dwell time is exceedingly small I assume I can cut the train length roughly in half and keep the 2 minute headway?

I realize the length of the train is quite abnormal and I never realized that the time to pass the traffic light could be an issue and it does seem unworkable at that length no matter how you slice it.  The capacity at full length and shortest headway (2 minute) is 36000 pphpd as I mentioned, but the flaw seems to be the length of the train.  Given that somewhere around 10,000 to 15,000 is all that is needed to make the lrt case better, let me try now to rework the argument and maybe you can point out the flaw in the logic?

Let's simplify to a 80m tram @600 passengers with 3 minute headway or 2 minute headway (12000 pphpd @ 3minutes and 18000 pphpd @ 2 minutes).  Also the demand currently is heavy in one direction only and not the other.  Demand is high for 1.5 hours in the morning going West and 1.5 hours in the evening going east.  You can give priority in only one direction.

4 Major intersection separations are 1.1km, 1.4km, 2km, 2.4km spacing for a total one way travel length of approximately 7-8km.  Green time is 30 seconds and cycle time is 60 seconds.

There is a major commercial area as well.

Budapest manages priority traffic signalling for a 60m train @ 2 minutes (so 1 minute each way)

Budapest does this with 2 minute headways and a 60m tram achieving 10,000 pphpd.  Jerusalem is planning for up to 23000 pphpd with traffic signal priority and 3 minute headways and doubling it's current trains (length?).  How do they do it?  It seems impractical given that bi-directional headways are 1 minute and 1.5 minute, but it may entirely depend on the amount of traffic as they are giving full priority.  Are there operational tricks to make this workable as typically traffic is heavy in one direction and not the other, but the trains are limited in quantity.  The dwell time will be exceedingly small in the one direction so I suspect this is how it works, but maybe someone can shed some light on this other than just giving priority in one direction.:

Budapest:

"The large passenger transport capacity of this line can be characterised by the ability of the 36-strong vehicle Combino fleet to transport 10,600 passengers in one direction within 1 hour. Passenger count figures show that the number of passengers in peak hours exceeds 9,000. It takes 32-35 minutes to travel along the line in one direction, and the trams spend as little time as possible at terminal stations. The shortest headway between trams is 90 seconds, while the longest is seven minutes over the course of the day.
The vehicle consists of six segments, has a length of 53.99m and width of 2.4m, has a low-floor along its total length which allows for walking the complete length of the tram. It has eight doors with two wings on each side
The vehicle can accommodate 353 persons calculated with seated passengers and four standing passengers per square meter. It has 64 seats (six of which are folding seats)."

2006

https://www.intelligenttransport.com/transport-articles/832/combino-trams-prove-successful-for-budapest/

"Traffic lights along central Budapest’s outer ring road (Nagykörút) have been adjusted to give priority to trams, cutting journey time on lines 4 and 6 by two to three minutes.
...trams will also run more frequently from February; up from 28 to 30 trams per hour in peak periods.
The Municipality of Budapest initiative was implemented by BKK in order to cater for rising numbers of public transport passengers (already between 7,000 and 8,000 in peak hours compared to 3,000 individual vehicles).
Traffic lights at a further 68 junctions were reprogrammed to support 60-second intervals between trams (rather than the earlier 90-second intervals) and to cut journey time from 32 minutes to 28-30 minutes."
2012
https://www.eltis.org/discover/news/priority-trams-central-budapest-hungary-0


Jerusalem is another example with it's red line:

“Traffic signalization and arrangements at 99 intersections will be adjusted and linked to a central system in order to give priority to approaching LRT vehicles. “
“ A fleet of 23 trains, consisting of three LRVs each, will be needed to provide service for about 7,500 passengers in peak sections of the route. These low-floor vehicles will have a capacity of up to 155 passengers each, or up to 465 passengers per train. The concessionaire will have sufficient vehicles to provide base service with headways of 3 to 5 min during the morning peak (and not exceeding the maximum density of passengers per square meter). The peak periods will be 1½ h in the morning and 1½ h in the afternoon. Maximum LRT speed will be 30 kmph (18.5 mph) in the city center and 70 kmph (43.5 mph) on other sections.”
https://www.railwaygazette.com/jerusalem-light-rail-red-line-opens/36208.article

“The line’s impressive 95% availability, 98-99% punctuality, and zero operations-related accident”
“proposing to double the size of the existing fleet to serve the expected 250,000 daily passenger”
https://www.railjournal.com/in_depth/revolutionising-transport-in-the-holy-city

“Travel over the complete Red line is due to take 42 minutes from Pisgat Ze'ev at one end to Mount Herzl at the other (as of August 2012, the travel time is 46 minutes[19]). The line operates Sunday through Thursday, from 5:30 am to 11:30 pm, on Friday up to an hour before sundown and not during the Shabbat or Jewish holidays, resuming half an hour after Shabbat or the Holiday ends.[25] Commencing August 2, 2015, frequency will be every 3 minutes during rush hours and every 6 minutes in the daytime and at night. It is expected to carry up to 23,000 passengers an hour during peak morning rush hours.[32]

https://en.wikipedia.org/wiki/Jerusalem_Light_Rail
  kitchgp Chief Commissioner

On Melbourne’s Port Melbourne light rail, it takes about 30 secs to complete the closing and opening traffic light and booms cycle, ie from the time a tram approaches until it clears the intersection (much quicker than heavy rail). The C-class trams that use the line are 23m long.

Based on the timetable, Gold Coast’s trams average speed is about 27 km/h (stops, etc). Using a 2-minute headway, trams would be roughly 900m apart, assuming everything is running like clockwork. That doesn’t fit very well with intersection spacings of 1.1km, 1.4km, 2km and 2.4km.

Using Gold Coast’s average speed again, it would take 18 mins to run 8 km. Allowing 2 mins at each end to turnaround, that means a round trip of 40 mins or 20 trams to run a 2-minute headway. Those trams have to return at the same headway or you run out of trams after 40 mins. The only way to lengthen the return headway would be to have extra trams that only run in the peak direction during the particular 90-minute peak. Prioritising in one direction doesn’t reduce the round trip time. It just makes one direction’s time interval shorter and the other longer. Shorter headways reduce the capacity of the crossing roads.

It appears each design is location specific and needs detailed study. Traffic engineering seems to be like IT network engineering; more an art than a science.
  santak003 Beginner

On Melbourne’s Port Melbourne light rail, it takes about 30 secs to complete the closing and opening traffic light and booms cycle, ie from the time a tram approaches until it clears the intersection (much quicker than heavy rail). The C-class trams that use the line are 23m long.

Based on the timetable, Gold Coast’s trams average speed is about 27 km/h (stops, etc). Using a 2-minute headway, trams would be roughly 900m apart, assuming everything is running like clockwork. That doesn’t fit very well with intersection spacings of 1.1km, 1.4km, 2km and 2.4km.

Using Gold Coast’s average speed again, it would take 18 mins to run 8 km. Allowing 2 mins at each end to turnaround, that means a round trip of 40 mins or 20 trams to run a 2-minute headway. Those trams have to return at the same headway or you run out of trams after 40 mins. The only way to lengthen the return headway would be to have extra trams that only run in the peak direction during the particular 90-minute peak. Prioritising in one direction doesn’t reduce the round trip time. It just makes one direction’s time interval shorter and the other longer. Shorter headways reduce the capacity of the crossing roads.

It appears each design is location specific and needs detailed study. Traffic engineering seems to be like IT network engineering; more an art than a science.
kitchgp

Melbourne uses a loop based system.  For effective TSP, accurate vehicle arrival time is important

"An important principle of the Zurich system is knowing acurrately where the vehicles are.  They claim a knowledge within 1 second... On average vehicles are purported to get through lights within an average of 5-8 seconds"

(this is quite an insightful Australian authored document, see http://railknowledgebank.com/Presto/content/GetDoc.axd?ctID=MjE1ZTI4YzctZjc1YS00MzQ4LTkyY2UtMDJmNTgxYjg2ZDA5&rID=NDg2&pID=MTQ3Ng==&attchmnt=VHJ1ZQ==&uSesDM=False&rIdx=ODIxNQ==&rCFU=)


"Melbourne's tram network uses a loop detector system which relies on ... In other jurisdictions, road traffic systems are linked to a tram Automatic Vehicle Monitoring ..." (https://www.audit.vic.gov.au/report/using-ict-improve-traffic-management?section=31221--1-background-)


Also, the crossing roads are not as much an impact if there isn't much saturation.

http://railknowledgebank.com/Presto/content/GetDoc.axd?ctID=MjE1ZTI4YzctZjc1YS00MzQ4LTkyY2UtMDJmNTgxYjg2ZDA5&rID=NDg2&pID=MTQ3Ng==&attchmnt=VHJ1ZQ==&uSesDM=False&rIdx=ODIxNQ==&rCFU=



(I go over the amount of crossing traffic in a Vancouver's case in this document: https://docs.google.com/document/d/1jMKGniqr44gXYhtMAGvVoi67hb105ebt0VFv1sEgnis/edit)


I think the real reason people don't design for shorter headways with traffic is the amount of engineering that is required to get it right.  This risk, if not mitigated correctly based on how risky it is and what happens if failure occurs, can derail the project.  (For example: Let's design 2 minute headways with CBTC.OK .well what is the backup and what is the capacity of the backup situation.  Also, most projects fail...will your headway design fail and what is the backup and should you expect it to fail?)

People know how to build metros with CBTC technology where there is no traffic.  No one is daring to be creative for shorter headways for lrt.  It can be done.  Jerusalem is an example...I don't know how Alstom did it or how much traffic they have to deal with, but they have three minute headways and maybe most importantly Jerusalem transit authorities used a knowledgeable vendor (Alstom) where the vendor was operating in a "good environment".  In this case the environment could have been the fact that Alstrom was also implementing the traffic signal priority and the traffic saturation was known and the light rail vehicles were new and the equipment was supplied by ...  

https://www.railway-technology.com/projects/jerusalem/

“In common with other modern Alstom networks, the control centre is an integral part of the depot facility from where the route and vehicles will be monitored. Trams are driven under line of sight principles, with built-in priority at road intersections.”

“The line’s impressive 95% availability, 98-99% punctuality, and zero operations-related accident”

“proposing to double the size of the existing fleet to serve the expected 250,000 daily passenger”

In Canada, we use Thales for a lot of CBTC signalling (including our very first skytrain built in the 80's and our latest skytrain extension as we were the world's first CBTC signalling project implemented by home grown Thales Toronto talent), but Thales has never done an at-grade CBTC system using older light rail vehicles and were fired by the city of Edmonton for never delivering the capacity promised (as reduced headways) and in fact delivering a renovated system with much reduced capacity due to failures in signalling (It is mentioned that there are millions of lines of code for a CBTC solution). So maybe the risk of at-grade is the planning of the project itself in how to deal with the risk of "capacity" failure: There should be enough capacity slack on day 1 to allow for time to fix code issues, choosing the right vendor, choosing a (mix of) vendor(s) who has implemented an at grade solution with short headways, talking to other operational teams with short headways at grade and seeing the environment they operate in and the failures that are occurring.


https://edmontonjournal.com/news/local-news/thales-official-breaks-silence-to-say-not-all-metro-line-lrt-delay-is-on-them


Assuming you can get the traffic priority to work ok enough and little to no cross traffic impacts/delays...does it sound workable?

Also.any thoughts on what is too long for at grade lrt running in ROW?  There must be some safety or other practical considerations.  Usually it is fully segregated where train lengths can get quite long.  It's really a question of practical headway running because if you can get a fully automated system down to 60 seconds you can have shorter trains than if all you can achieve is 90 seconds etc..and this may come down to the system you are using in the field and all it's practical limitations that I wouldn't know about.  But when you come to at-grade..you may have other considerations as well which rule out running over certain sizes.  I'm just not sure what they would be.

So not sure if you have some feedback on size of train limitations when running at grade other than traffic signal priority length of time.  Can I run a 100m long train.  It is certainly less risky for capacity issues..when I can just have the flexibility of LRT and just add a unit to the end..instead of reducing headways on a busy corridor when I have already reduced the headways and ran into some side effects.  

The other question I would have is what about the 4 square meters vs 6 square meters.  Is that all just psychological?  I think that if a person always shows up at 8:30 and realizes that it will be 4 trains before they can get on..they may push there way to a 6 square meters capacity situation.  Is this "crush" capacity worth considering for a 15 minute cram time in the morning for students mostly?  I certainly think it is worth considering for a back-up situation in case your initial planning for headways is a little off until you can fix it in due time.
  santak003 Beginner

On Melbourne’s Port Melbourne light rail, it takes about 30 secs to complete the closing and opening traffic light and booms cycle, ie from the time a tram approaches until it clears the intersection (much quicker than heavy rail). The C-class trams that use the line are 23m long.

Based on the timetable, Gold Coast’s trams average speed is about 27 km/h (stops, etc). Using a 2-minute headway, trams would be roughly 900m apart, assuming everything is running like clockwork. That doesn’t fit very well with intersection spacings of 1.1km, 1.4km, 2km and 2.4km.

Using Gold Coast’s average speed again, it would take 18 mins to run 8 km. Allowing 2 mins at each end to turnaround, that means a round trip of 40 mins or 20 trams to run a 2-minute headway. Those trams have to return at the same headway or you run out of trams after 40 mins. The only way to lengthen the return headway would be to have extra trams that only run in the peak direction during the particular 90-minute peak. Prioritising in one direction doesn’t reduce the round trip time. It just makes one direction’s time interval shorter and the other longer. Shorter headways reduce the capacity of the crossing roads.

It appears each design is location specific and needs detailed study. Traffic engineering seems to be like IT network engineering; more an art than a science.
kitchgp


Given Vancouver’s operating environment has 160m block lengths, maybe the answer lies in less technology.  Can we use driver line of sight operations with no traffic signal priority (to start) and nice clean dwell times to allow for the occasional train bunching and the key factor is to have the platforms with two loading areas for extra capacity?.  I don’t know how difficult at-grade signalling is for moving block systems, but we can calculate how many buses per hour we can run at a high level of reliability and can accomplish the same via trains? If we add an additional loading area, can we not assume each additional loading area means 1.75 times more capacity, just like a bus?

From “the bible” = (Transit Capacity and Quality of Service Operation Manual or TCQSOM - third edition in the chapter on rail capacity from here: [color=#1155cc][size=2][font=Arial]http://onlinepubs.trb.org/onlinepubs/tcrp/tcrp_rpt_165ch-08.pdf[/font][/size][/color])

“  under less than ideal conditions, any of a number of other factors may control line capacity.
These include:
• Signaling systems designed for the minimum headways”

And again from the “the bible” we see that we can use bus capacity as a guide.

“Single streetcars in classic mixed-traffic operation can be treated as similar to buses with capacity determined from the procedures of Chapter 6, Bus Transit Capacity, with suitable modifications reflecting longer vehicle lengths and differences in dwell time variability. “

And again from “the bible” we see the argument that the capacity for trains is limited by the minimum sustainable headway, because the light rail line train approach the entire block length.  But if we go out of our way to limit the train size to 60m because of traffic signal priority and length of time it takes a train to travel through an intersection, then actually we can run as many trains as we want.  (below we see the argument for one train per traffic signal cycle. It's one train per cycle because the train is the entire block length potentially and also because dwell times can be longer than a green cycle time causing the train to wait an extra cycle...and so the minimum headway is 2 times the cycle time as a bare minimum).  But if we don’t use a train as the entire block and dwell variability is reduced than this requirement of a minimum headway of 2 times the cycle time is removed and essentially we have the same capacity considerations as a bus.

“Where, as is often the case, light rail train lengths approach the downtown street block lengths, then the maximum train throughput is simply one train per traffic signal cycle, provided the track area is restricted from other traffic. When other traffic, such as queuing left-turning vehicles, prevents a train from occupying a full block, throughput drops as not every train can proceed upon receiving a green indication at a traffic signal. Similarly, longer-than-normal dwell times can cause a train to be unable to proceed on green, requiring the train to wait an additional traffic signal cycle to proceed. Therefore, a common rule of thumb is that the minimum sustainable headway is double the longest traffic signal cycle on the on-street portions of the line. “

Basically the calculation of minimum headway of a bus is identical to a train, except that for a train it can be no better than 2 times the cycle length.

If we leave out traffic signal priority and focus just on block length and length of trains.  In Vancouver’s case the block length is 160m.  So the platform can have two berths.

Is that feasible to have multiple berths/loading areas of a train? If so, the multiplier of 1.75 times the capacity for an extra loading area applies (we will see this factor pointed out a bit later).

Assuming just line of sight driving and multiple berths and no traffic signal priority, we can use simple probability to see the maximum number that can be achieved by using the same calculation as buses  (this is all detailed in “the bible” - tcqsom - third edition [color=#1155cc][size=2][font=Verdana]http://onlinepubs.trb.org/onlinepubs/tcrp/tcrp_rpt_165ch-06.pdf[/font][/size][/color]) Known as Equation 6-6.  The most interesting thing is that tc or clearance time is much higher for a train than a bus and this reduces the number of trains/hour:

• The portion of time that the traffic signal permits bus movement is given by the g/C ratio, the ratio of the time the signal is effectively green for buses to the overall length of the traffic signal cycle. Multiplying the g/C ratio by 3,600 gives the number of seconds in an hour that buses are free to enter or leave the stop.
• Dwell time that occurs during the red phase does not impact capacity, as the bus would not have been able to enter or leave the stop during this time. Therefore, only the portion of the dwell time that occurs during green, on average, is used in calculating capacity.
Bt= 3,600(g/C) /  ( tc + td(g/C) + t0m )
Or
Bt= 3,600(g/C) /  ( tc + td(g/C) + Zcvtd )
Where
B, = loading area bus capacity (bus/h);  
3,600 = number of seconds in 1 hour;
g/C = green time ratio (the ratio of effective green time to total traffic signal cycle length, equals 1.0 for unsignalized streets and bus facilities);
t, = clearance time - [clearance time between trains, typically 15-20s + 5 s/train, for buses 10s]
td = mean dwell time
t0m = operating margin(s)
Z = standard normal variable corresponding to desired failure rate, from exhibit 6-56
Cv = coefficient of variation of dwell times (default 0.6 if dwell not measured and coefficient of variation not calculated from field measurements of individual dwell times)

where Z is from exhibit 6-56 and it relates to the probability of all berths on the platform being full.  Default values for downtown are 7.5 - 15% and for urban areas 2.5% - 7.5% (as given by “the bible” TCQSOM - third edition).  Failure rate bakes in our bunching level if you will.  A failure occurs when there is no available loading area when a train pulls up.  

Design Failure Rate Z
1 2.330
2.5 1.960
Etc.. etc…

Finally exhibit 6-63 in “the bible” (TCQSOM - third edition) suggests that the second berth is an effective 1.75 times capacity increase (instead of 2) for the extra loading area (based on world wide experience).

Using real world numbers (yes assumptions are made that these can become real with light rail) where skytrain dwell is 26.7 seconds and standard deviation is 2.5 seconds (yes Vancouver does know what it’s doing with dwells) and the cycle time is 60 seconds and the green time is 20 seconds (instead of 30 seconds) and we use a 1% failure rate which equates to a Z = 2.330 and multiply this all by the 1.75 for an extra loading area.

[Exhibit 8-16 from “the bible” (TCQSOM - third edition) we get the dwell time and standard deviation for skytrain system in chapter 8 on train capacity] ([color=#1155cc][size=2][font=Verdana]http://onlinepubs.trb.org/onlinepubs/tcrp/tcrp_rpt_165ch-08.pdf[/font][/size][/color])

=3600*0.333 / (40 + 26.7*0.333 + 2.330*(2.5/26.7)*26.7)

That’s 21 trains per hour without traffic signal priority measures and line of sight driving. So we don't care about 2 times the traffic signal cycle time and we have a 3 minute headway.  (Interestingly if a clearance time of 10 seconds instead of the 40 seconds for the train, which is typical of a bus time of pulling into a lane where there is not much traffic, you get 40 trains/hour.  Also if you use a g/C of 0.5 instead of 0.333 you get 60 trains per hour)

Since you have the extra loading area..it’s 21*1.75 or 36.75 trains per hour. That's more like headway of 2 minutes.

So with larger platform length and large trains...the capacity is achievable at low risk by adding an extra loading area.   So that seems low risk, no matter the signalling system in use?    Vancouver’s traffic saturation is less than 25% and that makes at grade crossings lower risk as well.

Basically I suspect that the capacity can be reached with at grade crossings in Vancouver. It works at low risk because even without advanced signalling and traffic signal priority and just by having slightly larger trains and two berths per platform you can achieve the capacity required.

Budapest has one minute headways and traffic signal priority for L4 and L6 (which is only one line with two different end points). It is the busiest tramway in Europe. So it is practical somehow and the formulas and logic drive us to the same conclusion.
  gunzel42 Locomotive Driver

During the construction of the South Road overpass on the Glenelg line, a temporary track was installed that was protected by traffic lights for the crossing of South Road.  Trams on approach activated the sequence immediately, traffic stopped, tram crossed, and traffic was on its way as soon as the tram cleared the crossing.  This significantly reduced the dwell time for road users at the crossing with minimal delay for the trams.

While there was a slight delay, this was the safest of crossings as ALL road traffic and tram traffic was stopped before the tram proceeded across the road.  If idiot motorist decided to run the red, tram driver was stopped and could see this and take preventative action.  In this instance there were no tram stops adjacent to the crossing, but if the tram stops were moved to the approach side rather than the departure side of the crossing with a similar set up to Greenhill Road and South Terrace where the tram stops and then moves to trigger the sequence, assuming the sequence activated immediately this would increase the safety of the tram crossing the road, reduce the dwell time for the road users, and have minimal if any impact on tram travel times.

This unfortunately still doesn't stop idiot motorist running into the side of the tram, but you can only protect those with Darwinism tendencies so far.  Grade separation is the only thing that prevents road traffic coming into contact with tram or rail traffic.
  tonyp Chief Commissioner

Location: Shoalhaven
I'd suggest that Prague has an even denser operation than Budapest, with trams during the day typically being at 1-4 minute headways in each direction, with some running at 30 second headways where routes come together, mostly on street. I can't provide any insights into the traffic management system, but on casual observation, the traffic light cycles are very quick, no green waves, just small amounts let through more regularly.
  Nightfire Minister for Railways

Location: Gippsland
I'd suggest that Prague has an even denser operation than Budapest, with trams during the day typically being at 1-4 minute headways in each direction, with some running at 30 second headways where routes come together, mostly on street. I can't provide any insights into the traffic management system, but on casual observation, the traffic light cycles are very quick, no green waves, just small amounts let through more regularly.
tonyp
The Praha tram system Is my most favorite trams system I have traveled on

Other European tram systems I have used

Paris
Milano
Roma
Wien
Berlin
Potsdam
Amsterdam (worst)
Rotterdam (how do you by a ticket)
Den Haag
Aarhus
Bussel
Blackpool
Zürich
Bern
Basel (second best)
München
Köln
Frankfurt Am Main
Dresden
Düsseldorf
Mannheim
Kraków
Stockholm
Göteborg
Oslo
Nürnberg

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