Saturday, August 22, 2009

47> Serial vs. Parallel

In my last post I brought up the idea of GRT as a way to get the first PRT track built because one of the problems with PRT is that it becomes less compelling with fewer stations. I think it is legitimate to ask, “At what point (in terms of scale) is PRT cost effective and profitable?” Is it worth building a mile of track with just a couple of stations?

This type of question got me to thinking about station design. Below (left) is a drawing showing the typical station usually associated with PRT. The vehicles wait in line for passengers, and then leave. In my example, they get off at one area and enter further down the line, cutting “turnaround” time. The problem with this design is that the whole station throughput is dependent on how fast the passengers enter the pods and seat themselves. In a very minimal system, this could limit the number of paying customers on the track.

On the right is a station with parallel berths for boarding, allowing the throughput of the station to be much higher. My original question was how minimal a system could be, and I will demonstrate my points with the following formula, where H is the headway between vehicles, T is the turnaround time, or the time I takes to enter a vehicle, get seated and get up to speed, and N is the number of stations.

Let’s consider the case, for example, of a system that could financially “break even” at 6 cars a minute, on (24 hr) average (10 second headway), but that means, for example, that the headways must be far closer during peak times, say, 2 seconds. Now let’s assume that the city wanted to start with only small triangle of track between 3 stations. If the stations were configured as in the left hand illustration, and the turnaround time (T) was, say, a minute, then it can be seen that H = 60secs divided by three, which is 20 seconds. Therefore the minimum headway is 20 seconds, or ten times as much as is required to break even. It can be shown that with the taxi-line style stations, it would take 30 stations to achieve the desired traffic throughput.

The second (right hand) illustration shows how parallel docking areas can be configured to allow multiple boardings at a time. In such a configuration the berths may be considered as separate stations, as far as the formula is concerned, but even with the additional berths the number of stations needed to break even is over 7. In a situation where the customer really only wants a 3 station loop, the stations had better be able to accommodate 10 berths each and the foot traffic had better be there to require them, or the project will lose money.

I think that there are important design implications to consider here, first and foremost being the importance of rapid boarding.

I, off-hand, do not recall seeing parallel boarding schemes in any illustrations other than the Mister System. Because of the slots that would be in the floor on most bottom track designs, I wonder how parallel boarding would even work, although two berths would be easy, because the elevator could be positioned between the tracks. In any case, designers should consider ways of speeding the boarding process as much as possible for limited system designs.


Anonymous said...

At neighborhood stations an in-line boarding method should be fine because volumes will be relatively low.

At high volume stations, I prefer the ULTRA-Heathrow method, where cars pull in to staggered docks/bays(similarly to what you've drawn, I think) & each car can pull out independently of the others.

This is particularly useful in the Heathrow Airport, where wrestling with baggage can significantly slow boarding for some people.

At really high volume stations, multiple bays on two sides of the station would provide even more service.

Anonymous said...

I second the "parallel" dead-end berths like ULTra has (at least in this rendering). It seems to be the best trade-off between space and resource efficiency and departure delay minimization. Alternatively, it might be possible to slide vehicles sideways into individual berths somehow, but this requires either wheels that can rotate 90 degrees or a plate or "fork" (as in forklift) that the vehicle can be pulled to the side on, and so is likely more expensive and/or technically challenging, though it could potentially save a bit more space.

Dead-end berths are still more resource-intensive than the simple queue style, so they should be reserved for higher-demand stations.

Anonymous said...

Rapid boarding is paramount for any PRT system. The ultimate experience is that of walking into an open elevator. That's probably the fastest it can become.

ULTra stations are parallel, multi-berth stations. A document by Peter Muller discussing this subject is here:

Anonymous said...

I mean here:

( Q: How to enter links in comments without having the tail cut off? )

Anonymous said...

About the question on when PRT becomes a good choice (over GRT).

It will be pleasant when this discussion is practical, based on concrete cases instead of hypothetical ones. But let's hypothize as that's what we currently can..

I think it comes down to how much expandability the customer is expecting, and planning for. Initially, GRT can be better, but it won't scale in area as nicely. Once "phase 2" and 3 and .. are implemented, PRT will gain more and more usefulness.

This is also the reason to make PRT cheap. The cheaper it (the track, the stations, the cabins) are, the broader networks can be built. The broad networks provide the benefit, and they do it exponentially. Just like Internet.

There's also cases such as tourist locations where a rather small, isolated track can be beneficial.

Personally, I envision PRT to be first implemented as local, rather small scale tracks. They would serve the local traffic and be feeders to existing subway etc. When, eventually, these islands get connected, the vitality of all of them is suddenly multiplied. You will notice you can do without the subway, and maybe even get there faster.

At this phase - some 20 years from now - the subway operators may see it a better alternative to use the tunnels for something else. Like letting PRTs run inside them.

That was the story - pleasant dreams. :)

David Maymudes said...

Unless I'm misreading your analysis, you seem to be assuming that in the "serial" system, only one vehicle at a time is being boarded. There's no reason you can't have 3-12 or even more vehicles being boarded at once.

The drawback to a serial system is that if somebody is slow to board they will hold other vehicles up; the question is whether this will happen often enough to justify the extra size of a parallel berth station.

The ULTra system at Heathrow where people will mostly be first-time riders with lots of baggage is the kind of situation that will tend to favor parallel systems; busy urban stations with lots of repeat commuters may be better served by large serial stations.

Dan said...

Dan The Blogger Responds-
Anonymous, resonance, thanks for pointing out the Ultra Station. Since Ultra essentially drives on a road, I have not really paid too much attention to them, other than I think it’s great to actually have a PRT in operation. The one-way design I posted may not end up comparing favorably with the “dock-and-backup” designs. I haven’t really worked through it. It requires some quick elevation changes to avoid pedestrian/moving vehicle interferences.

Akauppi, I’ll look into the link thing. I, personally, haven’t tried to post a link yet. Or perhaps, someone (resonance? cmfseattle?) could lend a hand your question.

David, you’re absolutely right. I was thinking about group boarding schemes since I posted this and am convinced there must be some reasonable way to do it. I suppose that they could load and depart in groups. I guess the science of people moving starts before they even get on board.

Nick said...

Blogger doesn't auto-linkify anything, so the only way to post a clickable, working link is to manually do the html tag...

So the tag for that link looks like:
<a href="
docs/PRTStationsMullerAPM09.pdf text</a>

...and it comes out looking like:

for more info:

cmfseattle said...

fire up your sketchup and make an animation for both scenarios:

if you have a stopwatch that can do multiple splits, the bus might be a good place to start studying how long it takes potential customers to do simple tasks. and self-checkouts at the grocery store.

Dan said...

Dan The Blogger Laments...
Ain't gonna happen, cmf.. too busy.

Hey, Akauppi, very fine link. I finely got to it...To those interested in my last post, this pdf is really worth a look.

Anonymous said...

One thing I noticed on your station drawings only now. They are way too long.

This is probably one of the many US vs. Europe issues, but for here, stations need to be mostly very compact. Similar in size to tram stations would in my mind be a good goal.

The size has to do with many things. Land prices, effect on rest of the traffic, ability to have _lots_ of such stations.

There is fundamentally nothing wrong with the layout, though. It's just that the way they are currently drawn stretches them to resemble train platforms. That's way too long.

Then a question.

How frequent do the people following this blog like stations to be? 500m apart? 200m apart?

I'd plan for twice as sparse as bus stops. I.e. 10 PRT stations would take over 20 existing bus stops.

cmfseattle said...

a few general thoughts on PRT:

ULTra PRT at Heathrow looks a lot like what was intended for Morgantown, except with batteries in the vehicles. even theirs has been called "bug-eyed" or "like a toaster." so it's going to be a very long time before any firms are going to stake their reputation on something like it (Masdar being the current exception).

i think most people aren't going to accept any guideway near their house. we might hope for something along the middle of arterial streets, because then it's at least 30 feet from front doors (and those houses are already bargains).

it's going to be very difficult to build political concensus, considering that most transit advocates are biased against PRT. also, note Marsden Burger's (he bought the rights to the Cabinentaxi design) comment regarding Boeing and small-vehicle transit. by the way, he wrote that a year before the DC Metro accident.

personally, i think don fichter's PRT design (pages 16 and 17) looks alright on a quiet residential street. but i'm biased like that.

Anonymous said...

It's like there are two worlds, when PRTs are discussed. Ours and the USA.

I really had to read your comment twice, cmfseattle, to see if I undestrood it right. "most transit advocates are biased against PRT". I've _never_ seen that. What I've seen - mostly at the Heathrow conference in April, which I covered in my blog - is rational, practical advancements that are almost "business as usual".

Granted, this area of business is still in its budding phase. But that does not prevent people (including companies outside of core PRT, s.a. architect offices and financial houses) to take it seriously, and to plan for it.

What I see in the discussions from USA (sans Peter Muller, who had good presentation in Heathrow, and a good paper I mentioned above), is having a completely different tone. Religious, in a way. "Us" vs. "them". I just fail to see that.

Maybe this is the small but loud crowd in the pub (or where-ever Americans would go...). Maybe cmfseattle you're part of that. Maybe you don't even realize it but your way of writing gives it up. USA still seems to be on a different planet, when PRTs are concerned.

Don't worry. China will introduce enough of these, eventually, to save the Planet. Then the rest of us can follow. :P

cmfseattle said...

akauppi, yes i'm guilty as charged. i've let the scoffers get to me. lashing out at the religious isn't productive.

and now, an on-topic thought:
David Maymudes said, "The drawback to a serial system is that if somebody is slow to board they will hold other vehicles up; the question is whether this will happen often enough to justify the extra size of a parallel berth station."

something perhaps not considered here is the circumstances under which this type of situation would occur. it would be during high-demand periods, when the main guideway would also be full of vehicles. so there would likely be an already-boarded vehicle or two, near the end of the station siding, waiting to enter the flow. in this case, it's really the average boarding time that matters.

Dan said...

Dan the Blogger Responds-(with a long-winded 2 part comment:o)

Akauppi, They’re long because they’re so damn fast! No, seriously, I didn’t really try to scale them. Obviously they would be as short as possible, but as fast and smooth as possible as well. Whatever physics dictates. As for land prices, there is generally, in the U.S. at least, a land “easement” which is owned by the city or utility companies adjacent to the street. In some cases, it is wide enough for future street widening, but is generally used for public sidewalks, streetlights and utilities. Length, therefore, is cheap, but width
costs a lot because then it’s a private property purchase. I have previously mentioned my worries about large radius turns because of the value of corner properties.

I wouldn’t want to set an arbitrary distance between stations. I think it would depend on the situation. Will stations detract from the neighborhood? What will the budget allow? Is it a health conscious culture? (In the U.S. that’s not really uniform across the country.) What is the projected usage per station? Is the local climate conducive to walking? Probably the most important factor is population density. (especially the density of potential riders, like around office buildings.) I wouldn’t think in terms of distance, but in terms of walking time. In the central business district waiting to cross streets slows walking. Slow walking plus many riders would justify closer stations. In suburbia longer distances would seem quite reasonable. At the edge of the system stations could be very far apart, with parking lots for people who live still further from town. The distance between stations is twice the furthest walk, and that long walk would presumably only affect the few who lived or worked near that center point between stations. Therefore a 12-minute walk between stations would translate into everyone being within 6, and most being within 4.

Dan said...

Dan continues into near infinity..

As per your comments with cmfseattle, yeah, it’s different all right. That’s why I wrote the post about trying to make a very limited system work. There doesn’t seem to be the courage in the US to try new things, especially on a big scale. There have been a lot of breaches of trust here, both in the public and private sectors. Also, one of our political parties preaches at every opportunity that government is inept and shouldn’t be trusted with any new responsibilities. After hearing that message for 25 years, it has sunk into everyone’s subconscious. Unfortunately government holds the purse strings with grants and matching funds for transportation initiatives.

Cmfseattle, I agree that Ultra won’t crack the US market. It does look like the result of some bizarre genetic experiment involving aliens and toasters. I have written some further thoughts to be (probably) posted later today, in which I criticize that big guideway…
I think PRT advocates and especially “wanna-be” providers have a blind spot toward the design deficiencies in their systems and even toward members of their own cause, which creates a perception of loss of objectivity. We need to be our own critics. BTW, thanks for the links, which led me to Jpods. Their “wheels inside the rail” design is practically identical to my own. (I’m still analyzing the rotary track switching scheme.) Not only that, but I had been drawing an elevator system where a track section, vehicle and all, could be raised and lowered just like one of their pictures. (Mine was designed for dense, multi-level automatic pallet warehousing, however, but still…)

As for your thoughts on David Maymude’s comments, I agree, although he was right about me not understanding the group boarding thing…The point of my post was to just see if a really simple layout, with no branches, could use PRT, or if GRT or other group boarded vehicles would be the clear winner. This was a hypothetical worst-case situation, where a city tells the PRT provider, “Yes, we want the “internet of transportation”. Build me a network of three stations on a loop and we’ll see how it works.” Anyway, My follow-up post (in the works) continues that line of inquiry.

cmfseattle said...

actually, i meant that ULTra or similar may be first installed here in the U.S., since it's more like automobiles than track-captive designs. i don't think it's a coincidence that "enclosed-golfcart PRT" is the only type making headway (sorry) with installations.

2getthere (supplying the Masdar vehicles) had a completely at-grade, automated parking lot shuttle with gates at the pedestrian/automobile crossings.

with more baby boomers retiring, there will be more demand for retirement communities (perhaps one of those "slow growth" areas the U.S. economy needs?). i've read about accidents where people were thrown from golf carts being used as Neighborhood Electric Vehicles on local streets.

maybe using a system like ULTra to link several retirement housing areas and local businesses would be a good first installation.

Dan said...

Sun City, Here we come! Seriously they are pretty big. You might have something there.

Bengt Gustafsson said...

Parallel back-out arrangement has a problem with taking up a lot of time while backing out. I don't think anyone has simulated this in full detail, except possibly ULTra internally.

Parallel ride-through as Dan indicated in his blog has a problem of knocking passengers over. I don't see how this can be worked around with one-berth tracks. As a large station with a few parallel tracks of several serial berths each it could work, but you would need to have a staircase and/or elevator between each pair of lines.

Ryan Baker said...

How about a feeder/departure lane?

(I would love to send a picture, but we'll try ASCII)

   /  \/   \/  \/  \/  \
   \  /\   /\  /\  /\  /

The middle line isn't the main track by the way, it's the deceleration/acceleration lane that of course is joined to the main track at both ends.

Few notes
Every / could hold an arriving vehicle. Some vehicles might skip this an go directly to the boarding/unboarding area if a spot is open. Priority to do so would be given to occupied vehicles over empties.

Vehicles could depart semi-autonomously. They would need to merge with other departing vehicles, but at that speed merging would be trivial compared to main line merging.

No back-out.

Lead-in track could be much shorter because deceleration can occur on the center track. If it's too short then the most rearward berth might not be accessible without some mainline deceleration, but this may be possible often enough that with proper balancing the rear berths still gets nearly full utilization.

Ryan Baker said...


     --   --  --   --  --
    /  \/  \/  \/  \/  \
    \   /\  /\  /\  /\  /
     --   --  --   --  --

The change in this idea.. The entire diversion curve is used for boarding mini-platoons. Maybe 3 vehicles, maybe more depending on length of --.

By eliminating the other connections it makes it possible for boarders to walk to the \ or / positions, even for supported systems.