Here's a little word problem for you to chew on:
Suppose you're a commuter rail operator.
Suppose you'd like to run a peak of 9 trains per hour (tph) per direction.
Suppose your express trains can run the line in 60 minutes.
Suppose your non-express trains can run the line in 70 minutes.
Suppose your non-express trains have at least a couple of different stopping patterns.
Suppose signals allow a minimum headway of 3 minutes.
Construct a working timetable entirely without overtakes.
Winner gets the big red suspension bridge I've been unable to sell!
29 March 2010
A Timetable Puzzler
Subscribe to: Post Comments (Atom)
An "express" train that cannot overtake a local train really isn't an "express". It's just a "limited-stop" train.ReplyDelete
With a single track each way, all train service is constrained by the slowest train on the track. This is just like being stuck behind a RV that you can't pass on a narrow road. Poor, poor Caltrain riders....
Clem, I take it this what you think is in store for us when the SF-SJ Alternatives Analysis comes out?ReplyDelete
I'm getting a feeling of dread about this upcoming CHSRA meeting.
All of CHSRA station designs are way overbuilt. So most likely they will plan for overtake at Millbrae Intergalactic, or Palo Alto Pan-galactic.ReplyDelete
Assuming your locals are either skip-stop locals or front-loaded and back-loaded locals with express portions (for example a northbound local/express that stops at all southern peninsula stations and then runs express to TTC, and a companion that skips most southern peninsula stations and then hits all stops on the northern portion) then you could:ReplyDelete
send your expresses on the :00,:20,:40, followed on :03, :23 and :43 by the back-loaded (northern peninsula all-stop on a northbound line, or the skip-stop local that skips the first stop), and then the front-loaded local (or the skip stop local that hits the first stop) on the :06, :26 and :46.
Your first express would arrive on the :00, your two locals on :13 and :16, and your next express four minutes later on the :20, one minute shy of your 3-minute headway.
I still foresee Caltrain running their express trains using HSR trainsets (or trainsets compatible with HSR in terms of speed and platform heights, etc).ReplyDelete
Can't answer the question. Do the trains run on one track? (The answer is "impossible" if you want bidirectional service) or two tracks or three tracks or four tracks or...ReplyDelete
AndyDuncan, you noticed your proposal is the opposite of the way Caltrain does it now? If the express-then-local follows the local-then-express, riders can still get from any station to any station, if they're willing to change trains. (Wonder how many people are?)ReplyDelete
@Tim: That would certainly be a preferable stopping pattern, but given the parameters of this little exercise, you wouldn't be able to do that because it wouldn't fit into the 9TPH requirement without overtakes.ReplyDelete
To be clear: I'm not advocating this stopping pattern, or this set of constraints, I'm just trying to answer clem's puzzler.
It sounds like you're using diesels for express and emu for non-express. Shouldn't express go faster than the 57 minute baby bullet time today? I guess that's when the problem starts to get interesting.ReplyDelete
The 60 minute and 70 minute times don't really excite me.
I agree with Peter. I think they will keep the locals on the two tracks only, then use the equipment for express trains on the HSR tracks.ReplyDelete
Even easier would be to simply sell tickets for the HSR locals under Caltrain.ReplyDelete
How perfectly ... 1950s Chicago of our World's Finest Transportation Engineering Professionals.
And pristine segregated tracks for the PB Wonder Train.
How perfectly ... 1960s San Francisco of our World's Finest Transportation Engineering Professionals.
Where on earth do they find these people?
What next? On board fission reactors? Gyrocopter parking?
Yesterday's Tomorrows: relive them in the Inbred Backwater that Cost Containment Forgot!
@Andy: you can't have trains following within 3 minutes of each other. If the train ahead makes a station stop, the train behind has to slow down as well and wait until the train ahead has departed the station. So even if your signal system theoretically allows 3 minute headways, your practical limit is about 5 minutes.ReplyDelete
@Adirondacker: two tracks, thank you. I must have another smaller bridge somewhere to thank you.
@Tim: yes. This ping-pong arrangement would cost another 10 minutes per cycle and limit throughput to 6 tph or less.
@Martin: the speed of the trains, the length of the line, or how quickly they accelerate is irrelevant to the problem. EMU vs. diesel won't affect the throughput in tph; the signal headway and the stopping pattern (and resulting average speed difference) entirely determine the throughput.
@Peter & Eric: I said no overtakes.
@Samsonian: yes. Me too.
"you can't have trains following within 3 minutes of each other. If the train ahead makes a station stop, the train behind has to slow down as well and wait until the train ahead has departed the station. So even if your signal system theoretically allows 3 minute headways, your practical limit is about 5 minutes."ReplyDelete
Well, it's only 3 minutes as they leave the first station. The trains in the skip-stop strategy would be 3 minutes plus one-station segment's worth of time ahead which gets you nearer to 5 minutes, the front-loaded locals and back-loaded locals would be even further apart, only coming back to 3 minutes apart at the terminal station.
They might get too close near the end though.
Now try it with two centerline transfer overtakes (which is four structures total). Is it any easier?ReplyDelete
More to the point, where should those overtakes be?
If it's only got two tracks it's not going to be the one that will be built on the Peninsula. The easy solution on the Peninsula is to run the express trains on the express tracks.....ReplyDelete
Bad Adirondacker, bad! I said NO overtakes and only two tracks. You persist in trying to wiggle out of the bounds of the problem.ReplyDelete
There may indeed be two other tracks built on the peninsula, but as far as we know, they will be tied up with 9 tph of nose-to-tail HSR. You can't count on any of that capacity being re-allocated to or shared with express commuter trains.
For any of you who think this particular problem doesn't overlap with reality, please hold your criticism until April 8th.
What if you just allow each train to dwell in each station only 1 minute max. With trains coming approximately every 6 minutes, if you miss one, the next is not far behind. Run it like a subway. EMU's accelerate faster and stop quicker than the current system. That's 25 minutes sitting at stations and 35 minutes for travel. Try to average 70 mph between stops, and all trains arrive in 1 hour from SJ to SF and vice versa. And with the new system suppose to allow 125 max, even better. All trains, all stations, one hour.ReplyDelete
oops, average 80-90 mphReplyDelete
Clem, I think the practical headway is still 3 minutes if the train that's behind is slower than the train that's ahead. At least that's how it works on the TGV, where locals depart the Gare du Nord 3 minutes after expresses.ReplyDelete
In that case, you could do a 20-minute takt with express trains leaving SJ at :00, intermediate trains leaving SJ at :03, and locals leaving SJ at :06. As long as the intermediate trains' first stop in each direction is strictly between the expresses' and the locals', it should be fine.
On the other hand, "should be fine" is conditioned on strict schedule adherence. San Francisco is not Berlin and it's not Tokyo, which means this plan working is a counterfactual.
Eric, your proposed stop time is impossible. The reason is that you need to take into account acceleration and deceleration, not just dwells. Subway EMUs lose about 40 seconds per stop, from a much lower top speed.ReplyDelete
You persist in trying to wiggle out of the bounds of the problem.ReplyDelete
It's not my fault you didn't define it adequately. :-)
On the hour a super express leaves the terminal bound for the other terminal and gets there in 55 minutes since it doesn't make any stops until it gets to the other terminal.
3 minute headways you said?
at :03 the Very Limited Stop leaves
and then another at :06
at :09 an all Limited Stop train leaves followed by another at :12
at :15 the locals start to run every three minutes until :24 when they close the terminal station for 30 minutes.
Ya didn't say the schedule had to make sense, just that it works. Ask some in Central New Jersey what "the 40 minute gap" is.
If you want to alternate locals and expresses you can only have one of each every 13 minutes and more than two tracks at each end.
:00 express of some sort
It's kinda heavy on expresses because the train leaving at the top of the next hour has to also be an express. But then you didn't define a service pattern. And there's that pesky four track section at each end. Oh well I guess that isn't it.
Try to average 70 mph between stops... oops, average 80-90 mphReplyDelete
That's not possible with steel wheel on steel rail technology with the stops being spaced as closely as they are. Not even with the best EMUs.
Ask some in Central New Jersey what "the 40 minute gap" is.
I'm with you... here in San Carlos I have my own 40 minute gap every morning.
I don't see why Andy Duncan's original solution doesn't work under the criteria provided. Particularly if it were done as a skip stop.ReplyDelete
consider hypothetical line with stations:
express goes directly from 0 to 9 at :00
next is evens only going 0-2-4-6-8-9 and leaves at :03, arrives at :13+1
next is odds only going 0-1-3-5-7-9 and leaves at :06, arrives at :16+1
the two skip stops will both be stopped at stations simultaneously, but 1 station apart, except for the final station (9) where they both arrive, but separated by 3 minutes, no need for one train to slow for the other, no need for overtakes, worst case you have the :06 leave at :07 if there is an extra minute needed for dwell time at station 9.
As far as I can tell, AndyDuncan's plan is copacetic given the rules provided in the puzzler.
What if I want to go from station #1 to station #4?ReplyDelete
@ Clem -ReplyDelete
Why insist on formulating a fictitious problem? If it wants to, Caltrain can run a regional high-speed service on the HSR tracks and separate local trains on the legacy tracks.
Or else, it can strike a deal with CHSRA requiring whoever ends up operating the HSR trains to operate a regional high-speed service on its behalf, e.g. by having to offer Caltrain blocks of discounted seats to resell.
The notion that a rail service provider must own and operate all of its own equipment and infrastructure is a 19th century notion. Change the business model!
"The notion that a rail service provider must own and operate all of its own equipment and infrastructure is a 19th century notion. Change the business model!"ReplyDelete
Clem shows every sign of being aware of this development already. It's the World's Finest Transportation Planning Professionals at the Peninsula Rail Program and CHSRA who are a century or two out of touch.
@Alon, The rider takes the reverse direction train to stop 1, then gets the skip-stop that will take them to station 4. Certainly not ideal (and that's not even the worst case, imagine going from 4-5!), but every station is accessible from every other station, and there are much worse situations, but there are no stipulations in the rules regarding convenience. As far as I can tell, according to the given rules, AndyDuncan's plan wins the bridge.ReplyDelete
Perhaps the rules need some clarification.
I meant reverse to stop 0 from stop 1.ReplyDelete
The requirements don't say how many expresses you need either.ReplyDelete
A two express timetable with the front-and-back-loaded locals (which of course don't have to be pure express on the front or back portions, they just have to hit less stops on one side of the transfer station than the other), which I think are preferable to skip-stop trains could have expresses leave on the :00 and the :30, with back-loaded locals on the :03, :14, :33 and :44 and front-loaded locals on the :06, :17, :36 and :47. Still far from perfect but it gets you 10tph and twice an hour the pattern allows someone from a front-loaded local to transfer with a 3-minute wait to a back-loaded local if they need to transfer from one low-traffic station to another on the other side of the line.
With a one-express pattern you could run even more locals.
I think the point of this exercise is that there's a number of crappy timetables you could construct around this particular set of constraints, but that something as simple as four caltrain-compatible platform tracks at Redwood City would make a world of difference.
A two express timetable with the front-and-back-loaded localsReplyDelete
There's also the option of turning trains at Redwood City during the peak. The specs don't say that there's only two terminals or that all trains must run between San Francisco and San Jose.
"There's also the option of turning trains at Redwood City during the peak."ReplyDelete
Why would any train turn at Redwood City? Have you ever visited the Bay Area by any chance? Just wondering.
Regardless, good luck turning trains operating under FRA freight-trains-are-us commuter railroading rules with commuter railroading Amtrak crews on a two track only forever commuter railroading line running at five minute headways. Commuter railroading CBOSS (the "C" is for "Commuter"!) or commuter railroading speed signals: it doesn't matter.
No need for that anyway. Bob Doty's Baby Bullet today. Bob Doty's Baby Bullet tomorrow. Bob Doty's Baby Bullet forever. All praise the Baby Bullet. All praise Bob Doty. All praise the skipping and the stopping and the skip-stopping.
Get used to it, because that's all we're ever going to get. It's all we deserve, as commuter railroad patrons of a commuter railroad line.
buck up Anon, At least there's skip stop and a baby bullet, BART can't even figure out how to do that!ReplyDelete
Anon, railroads in the U.S. working under full blown FRA rules, turn trains in the middle of the line. Makes a lot of sense to turn trains at Redwood City. They run local or semi-express between there and San Francisco and the trains south of Redwood City run express between Redwood City and San Francisco. Depending on the time of day the trains that run south of Redwood City run express to stops near San Jose, some sort of limited service or make all local stops. . . just like long commuter lines all over the world do. . .ReplyDelete
Since the schedule is in English and the fares are denominated in U.S. dollars might I suggest looking at the Metro North, Shore Line Express and Amtrak schedules - both to Boston and Springfield because there is a small contingent of commuter traffic on the Springfield line. I'm sure that there's a lot of kibbitzing that could be done over the schedules but they work reasonably well.
I'm not getting the comments.ReplyDelete
The World's Finest Railroading Professionals are freely, of their own volition, by explicit choice, deciding to SHOOT US IN THE HEAD FOR NO REASON AT ALL and you're coming up with rich and fulfilling life experiences we can expect to experience afterwards?
Yeah lemons from lemonade and all that, but at some point you can't even pretend any longer that rational, ethical, numerate humans and that class of individual inhabit the same world.
BTW Adirondacker12800: yes, it's possible to turn around US commuter trains. I read somewhere on the intertubes that maybe even Caltrain does it 80 times a day or so. But as somebody who has ridden through San Mateo County a couple thousand times, I'm missing your point about turning trains in Redwood City ... and that's ignoring the operational unreality of doing so given the headways and complete lack of infrastructure under discussion.
Why insist on formulating a fictitious problem?ReplyDelete
Who said it was fictitious?
Caltrain can run a regional high-speed service on the HSR tracks
With a separate incompatible sub-fleet? Different platform height? Different train control system? That would be downright stupid. Who would pay for extra (and under-utilized) platforms and extra land at express stations other than the two peninsula HSR stops? What use is an express that makes only two intermediate stops? If this express service consumes HSR track capacity, why not let Caltrain consume the same HSR track capacity to do overtakes?
If you're going to go down that incompetent path, just forget Caltrain commuter service and put in BART. I'm not joking.
Ok - a new puzzler.ReplyDelete
1) Instead of putting a 80' x 40' electrical substation outside of the ROW in an industrial area, change the plans to put it in the ROW in exactly the right place to make as many residents as upset as possible.
2) Then later try and fit four tracks through the remaining 60' of ROW when High Speed Rail gets added
This just came out in new Caltrain Final EIR http://www.scribd.com/doc/29263066
If you're going to go down that incompetent path, just forget Caltrain commuter service and put in BART. I'm not joking.ReplyDelete
Oh, that's EXACTLY what PB and its incompetent/corrupt collaborators want to do eventually. BART-to-San Jose will take at least a few decades to build at enormous cost, but they want to have the Peninsula path prepped for building BART around the Bay!!! A useless functional goal, but transportation functionality is not what this is about. Follow the money...
it's possible to turn around US commuter trains. I read somewhere on the intertubes that maybe even Caltrain does it 80 times a day or so.ReplyDelete
Anon was claiming that the FRA would never allow it in the middle of the line. Commuter railroads all over the Northeast do it. Go examine the schedules for SLE and Metro North at Stamford some time.
I'm missing your point about turning trains in Redwood City.
You don't have to but you could.
Off the top of my head, like at Stamford, Mineola, Croton, Matawan, Jersey Ave, SEPTA does it on most of the lines. I'm sure there are more. I'm sure there are others in places where I've never had to examine a train schedule before buying a ticket.
Run local from San Francisco to Redwood City and express from San Francisco to Redwood City. The local terminates and the express then runs local between Redwood City and San Jose. Means the people south of Redwood City get a faster ride to San Francisco. I know this is horrific but the few dozen people an hour at peak whose trip can't be arranged with the peak hour(s) limited service can step off the train and make a timed transfer to a local. I vaguely remember that it's called Taktverkehr in some places.
and that's ignoring the operational unreality of doing so given the headways and complete lack of infrastructure under discussion.
Clem didn't define infrastructure beyond "two tracks" and then only after being asked. The assumption seems to be the four track system between San Jose and San Francisco. I'm going to assume the signal system is going to be something more sophisticated than telegraphs and train orders from the mention of three minute headways. They are probably going to do things like install platforms and TVMs and station lighting, so I'm reasonably sure they are going to install switches here and there.
Switches that allow the train that that runs local between San Jose and Redwood City to switch to the express tracks, hold onto your hat here, and run express between Redwood City and San Francisco. Unfortunately that's outside of the scope of the definitions.
With a separate incompatible sub-fleet? Different platform height? Different train control system?
Well the whole fleet could, hold onto your hats again, be compatible with HSR...
Clem: You never mentioned the number of express vs local trains. It looks possible if you only have one express though (I haven't done a detailed analysis but 5 minute intervals gives you 12 slots per hour, and the express effectively takes up three slots).ReplyDelete
Ad12800 proposes "turning" trains at Redwood City, as RRs do "at Stamford, Mineola, Croton, Matawan, Jersey Ave". Do trains actually "turn" at those places, or do they just terminate and pull into the coachyards, eventually to re-emerge? If they are sitting on the main line while they turn, how long do they sit, and do they do it during peak hour?ReplyDelete
They do turn, at least at some of those stations. For example, at Jersey Avenue they pull into the northbound local track, terminate, and sit there until they turn back. All the trains that go further south run express, and traffic on this section is low enough that the locals' crossing over doesn't cause capacity problems.ReplyDelete
Jersey Ave is odd. There are two platforms, both of them on the southbound side. Southbound trains that are going to the Morrisville yard use a platform at the NEC's southbound local track, where you would expect it to be. It's only used to discharge passengers. Trains that are going to be turned leave the NEC and go to a platform that is off on what used to be a branch line. Whether that platform is a southbound platform or a northbound platform depends on your direction of travel. All northbound passengers use it though. You can't get to Jersey Ave from stations south of there, there is no platform on the northbound side.ReplyDelete
Tim they could turn trains on the main local track. Probably not too wise, there are many other options they could use. Those options are outside of Clem's specs though.
Very bad news from Caltrain CEO Scanlon at today's JPB meeting:ReplyDelete
Caltrain goes broke; huge service cuts loom; survival in doubt
Major shutdown was inevitable anyway, once the major HSR construction starts.ReplyDelete
On that wide ROW? Absolutely not. Some disruptions, timetable changes, weekend shutdowns yes, but total shutdownd is absolutely unnecessary.ReplyDelete
Caltrain sets the bar really low for shutdowns. They did weekend shutdown for 2 years just for minor signal and track improvement project.ReplyDelete
But that's not the way American Railroading is done.ReplyDelete
Thats the way Californian railroading is done, there is life including railroading, some of it 24/7 passenger carrying railroading, east of the Sierra Nevada.
"there is life including railroading, some of it 24/7 passenger carrying railroading, east of the Sierra Nevada."ReplyDelete
More than one of us writing here experienced the North East Corridor Improvement Program first hand and now visit often enough to be exposed the full wonder of SEPTA/LIRR/MNCRR/MBTA/Amtrak technical prowess and track-km throughput rates and station rebuilding timescales.
Sorry, but it's American Railroading, just like at Caltrain. (Well yes, Amtrak has the one futuristic track relaying and undercutting machine. That's something.)
It would be nice if it weren't the case, but honestly what is the incentive to change or improve?
....those dastardly Northeastern railroads and Metra. Running electric trains to level boarding platforms, some of them for over a century. Terrible the way the LIRR runs 24/7 and Metro North and NJTransit almost 24/7. All of them having all those horrific connections to other modes of transportation. Particularly annoying when they do maintenance without taking all of the tracks out of service. It's awful.ReplyDelete
Well yes, Amtrak has the one futuristic track relaying and undercutting machine. That's something.
Amtrak owns a few hundred miles of right of way, with a few thousands of miles of track, how many do they need?
I suspect the railroads that have thousands of miles of ROW have more than one. Search for "loram" on YouTube. The foamers love to go out and video the automated MOW equipment in action. Lots of it in North American on railroads like UP and BNSF. Mostly east of the Sierra Nevada but that's where most of the railroad tracks and people in the US live.
The track repairs, brought about by the overweight trains, take out tracks all the time in the Northeast. Back when I traveled to New Haven regularly, I'd see the local track out of service all the time; there would be extenders connecting the platform with the express track. It's just less disruptive because most mainlines here are four-tracked.ReplyDelete
(To be fair, the compliant EMUs aren't that overweight - the single-level M7 weighs a little less than a European bilevel EMU, and a little more than a Japanese bilevel. But it still weighs 50-100% more than comparable single-level EMUs. And the single-level Metra Electric cars weigh more than any non-US bilevel.)