Timetable Padding Practices
Two weeks ago, the Wall Street Journal wrote this piece about our Northeast Corridor report. Much of it was based on a series of interviews William Boston did with me, explaining what the main needs on the corridor are. One element stands out since the MTA responded to what I was saying about schedule padding – I talk about how Amtrak and Metro-North both pad the timetables on the Northeast Corridor by about 25%, turning a technical travel time of an hour into 1:15 (best practices are 7%), and in response, the MTA said that they pad their schedules 10% and not 7%. This is an incorrect understanding of timetable padding, which speaks poorly to the competence of the schedule planners and managers at Metro-North.
The article says,
Aaron Donovan, a spokesman for the Metropolitan Transportation Authority, says the extra time built into Metro-North schedules generally averages 10%, depending on destination and length of trips, and takes into account routine track maintenance and capital work that can increase runtime. Metro-North continually reviews models, signal timing, equipment, and other elements of operation to improve travel times and reliability for customers, he says.
This is, to be clear, incorrect. Metro-North routinely recovers longer delays than 10%; delay recovery on the New Haven Line can reach well over 20 minutes out of a nominally two-hour trip, around 25% of the unpadded trip length. The reason this is incorrect isn’t that Donovan is dishonest or incompetent (he is neither of these two things), but almost certainly that the planners he spoke with genuinely believe they only pad 10%, because they, like all American railroaders, do not know how modern rail scheduling is done.
Modern rail scheduling practices in the higher-reliability parts of Europe and Japan start with the technical timetable, based on the actual speed zones and trains’ performance characteristics. This includes temporary speed restrictions. The ideal maintenance regime does not use them, instead relying on regular nighttime maintenance windows during which all tracks are out of service. However, temporary restrictions may exist if a line is taken out of service and trains are rerouted along a slower route, which is regrettably common in Germany. Modern signaling systems are capable of incorporating temporary speed restrictions – this is in fact a core requirement for American positive train control (PTC), since American maintenance practices rely on extensive temporary restrictions for work zones and one-off slowdowns. If the signal system knows the exact speed zones on each section of track, then so can the schedule planners.
The schedule contingency figure is computed relative to the best technical schedule. It is not computed relative to any assumption of additional delays due to dispatch holds or train congestion. The 7% figure used in Switzerland, Sweden, and the Netherlands takes care of the high levels of congestion on key urban segments.
The core urban networks in these countries stack favorably with Metro-North in track utilization. The Hirschengraben Tunnel in Zurich runs 18 S-Bahn trains per hour in each direction most of the day and 20 at rush hour with some extra S20 runs, and the Weinberg Tunnel runs 8 S-Bahn trains per hour and if I understand the network graphic right 7.5 additional intercities per hour. I urge people to go look at the graphic and try tracking down the lines just to see how extensively branched and reverse-branched they are; this is not a simple network, and delays would propagate. The reason the Swiss rail network is so punctual is that, unlike American rail planning, it integrates infrastructure and timetable development. This means many things, but what is relevant here is that it analyzes where delays originate and how they propagate, and focuses investments on these sections, grade-separating problematic flat junctions if possible and adding pocket tracks if not.
Were I to only take timetable padding into account relative to an already more tolerant schedule incorporating congestion and signaling limitations, I would cite much lower figures for timetable padding. Switzerland speaks of a uniform 7% pad, but in Sweden the figures include two components, a percentage (taking care of, among other things, suboptimal driver behavior) and a fixed number of minutes per 100 km, which at current intercity speeds resolve to 7% as in Switzerland. But relative to the technical trip time, the pad factors based on both observed timetable recovery and actual calculations on current speed zones are in the 20-30% range, and not 10%.
Of course, at no point do I suggest that Metro-North and Amtrak could achieve 7% right now, through just writing more aggressive timetables. To achieve Swiss, Dutch, and Swedish results, they would need Swiss, Dutch, or Swedish planning quality, which is sorely lacking at both railroads. They would need to write better timetables – not just more aggressive ones but also simpler ones: Metro-North’s 13 different stopping patterns on New Haven Line trains out of 16 main line peak trains per hour should be consolidated to 2. This is key to the plan – the only way Northern Europe makes anything work is with fairly rigid clockface timetables, so that one hour or half-hour is repeated all day, and conflicts can be localized to be at the same place every time.
Then they would need to invest based on reliability. Right now, the investment plans do not incorporate the timetable, and one generally forward-thinking planner found it odd that the NEC report included both high-level infrastructure proposals and proposed timetables to the minute. In the United States, that’s not the normal practice – high-level plans only discuss high-level issues, and scheduling is considered a low-level issue to be done only after the concrete is completed. In Northern European countries with competently-run railways and also in Germany, the integration of the timetable and infrastructure is so complete that draft network graphics indicating complete timetables of every train to the minute are included in the proposal phase, before funding is committed. In Switzerland, such a timetable is available before the associated infrastructure investments go to referendum.
Under current American planning, the priorities for Metro-North are in situ bridge replacements in Connecticut because their maintenance costs are high even by Metro-North’s already very expensive standards. But under good planning, the priority must be grade-separating Shell Interlocking (CP 216) just south of New Rochelle, currently a flat junction between trains bound for Grand Central and ones bound for Penn Station. The flat junctions to the branches in Connecticut need to be evaluated for grade-separation as well, and I believe the innermost, to the New Canaan Branch, needs to be grade-separated due to its high traffic while the ones to the two farther out branches can be kept flat.
None of this is free, but all of this is cheap by the standards of what the MTA is already spending on Penn Station Access for Metro-North. The rewards are substantial: 1:17 trip times from New Haven to Grand Central making off-peak express stops, down from 2 hours today. The big ask isn’t money – the entire point of the report is to figure out how to build high-speed rail on a tight budget. Rather, the big ask is changing the entire planning paradigm of intercity and commuter rail in the United States from reactive to proactive, from incremental to comfortable with groun-up redesigns, from stuck in the 1950s to ready for the transportation needs of the 21st century.
Pedestrian Observations 
So… what happened here? Are the “before-padding” schedules generated from incorrect train performance data (such that average drivers under average conditions reliably exceed them)? Is the American process so opaque to its own practitioners that it manages to include a padding step twice (under two different names/justifications) without anyone realizing that it does? (“No, that’s not the machine spirit, that’s just some steam.”)
Separately, I have a toy train network R^3->R where iteratively optimizing along one variable at a time does/doesn’t converge to the same optimum as could be reached by using all three together (phrased this way to acknowledge that the latter may find a local, not the global optimum), is there a name for the property it has/lacks?
American timetabling is based on past performance. So they look at their on-time trains and add 10%, or they look at a certain percentile of lateness and use that as a schedule.
What do you mean by iteratively optimizing a toy train network?
Because their customers live on Planet Earth not Planet Railfan and want to know what time the train will be there most of the time. Not what time it could be there when all the stars align, the weather is good and no … incidents.. happen. What the trainspotters in New Jersey call Shirley time. The on-time performance was awful so the then current head of NJ Transit, Shirley Delibero, had the schedules rejiggered so the slow trains were on time.
Which is what is useful to people on Planet Earth. Knowing when the train will likely arrive. Not when the train could arrive if everything everywhere, including that the the past two governors funded things, went well.
Because their customers live on Planet Earth not Planet Railfan and want to know what time the train will be there most of the time.
The passengers in Switzerland, Netherlands and Sweden also want to know when their train arrives, just like other customers, however their trains, planned as Alon describes, are more likely to arrive when the schedule says than the trains planned the way Metro-North/NJT does it.
Which is what is useful to people on Planet Earth.
As mentioned, the people in the countries planning Alon’s way get more of that useful knowledge than American people. But there is another thing that is useful to people, which is shorter trips. Saving 43 minutes riding from New Haven to NY would be useful to a lot of people. Doing what Alon advocates gives them that, as well as the knowledge of when the train will come.
It’s a pity Metro North isn’t in Switzerland. But it’s not. It’s a pity Nixon administration didn’t fund the stuff the Johnson Administration proposed either. Or Saint Ronnie of Reagan. …. though the dastardly evil Bill Clinton made the Republican walk the talk and got the Federal government funded. No matter how hard you clap today, it doesn’t allocate money in 1999 so the bridge is replaced in 2003. But here we are.
People don’t want to know what Alon waving magic wands, you clapping and ruby slippers all around could do, in 2040. They want to know when the train will arrive in Grand Central on Tuesday, the day after Labor Day, 2025. They are delighted when it arrives 6 minutes early. They are unconcerned that the schedules are fudged to make them look good. Unaware they are not arranged as in Switzerland. Because they aren’t on a train in Switzerland. And are blissfully unaware it offends your obsessive compulsive sensibilities. Just too too bad. But they get to where they are going. Which isn’t in Switzerland.
None of that changes that replacing a decrepit bridge is a separate project from replacing a different decrepit bridge or grade separating the Hell Gate branch line from the New Haven main line is a different project. None of your yearning for Switzerland changes that grade separating the Hell Gate line from the New Haven main line is something that would be nice to have. A failed bridge means the trains don’t run at all.
Whether or not the bridge is decrepit enough to need replacing is separate issue from how much it will cost to replace. Or how much it costs for the white collar circle jerks that lead up to having construction start.
Why are you even here?
I see, it’s the pearl oyster school of schedule design.
By iterative optimization I mean that if I have an f=|a-b|+0.1a+0.1b and I can only take steps parallel to either a or b (every step must get me a lower f), I get stuck, whereas if I can step in arbitrary directions I run down the diagonal talweg. This is what I’m reminded of by American (and Hungarian) infrastructure (from “high-level” issues to e.g. level-boarding platforms) and rolling stock planning being done with at best some vague sense of “this should be faster”, or not even that, and without reference to each other, and schedules adjusting to the material changes “out of step”. (I don’t have a good sense for how to express discrete optimization, but luckily, takts aren’t used by American railroads, and are still giving some indigestion to MÁV and/or the ministry.)
They work with what they have. Not what railfans think they should have done.
Something to take into account in the Netherlands and Switzerland is the waiting for connections because of the taktfahrplan. Places where the infrastructure didn’t need to be upgraded to be “as fast as necessary” often have quite some leeway in the timetable, that’s not used to pad travel time excessively, but to make dwell times longer, making transfers easier. But this does prevent delays from propagating beyond one of these extended dwell stations.
An example is the The Hague – Nijmegen intercity service. At Leiden, it dwells for 5 minutes, at Amsterdam Zuid 5 minutes, at Utrecht Centraal 5 minutes and at Arnhem 5 minutes (turnaround, so could be 4 at best). At these stations, some IC services that use the same double decker non-level boarding stock only dwell for 2 minutes.
In these countries, shorter services often don’t make these extended stops, but have frequent turnarounds to prevent delay propagation. Other than that there are maybe a handful of services that are optimally planned, such as IC5 in Switzerland that doesn’t dwell longer than 3 minutes on the 2 hour Lausanne – Zürich stretch (but at Zürich it does wait longer). Whereas IC1 does have a 5 minute dwell at Bern.
Sweden seems different, with no long dwells on X2 services, and maybe Sweden is the best analogy for the NEC since it’s just some linear corridors with some branches, for timetabling purposes.
Ah, that’s what’s going on! I recently moved to Leiden from the US and had wondered why some intercity trains seemed to have a five-minute dwell time at Leiden Centraal, since that seemed like a fairly excessive amount of padding at an intermediate station. I take it these dwells are either for transfers from the line east to Utrecht or between the Oude Lijn to Amsterdam via Haarlem and the Schipollijn?
Yep, it’s about the cross-platform transfers from Haarlem/Schiphol to Den Haag Centraal / Rotterdam and vice versa. And because IC trains run 4tph around Haarlem and 6tph around Schiphol, and then 4tph to Den Haag Centraal and 6tph towards Rotterdam, some of the dwells/transfers don’t neatly line up.
The Amsterdam Zuid dwell is because the schedules on the Leiden corridors and the Utrecht – Amsterdam corridor don’t line up correctly. That might not get fixed until they make the step from 6tph to 8tph on the main intercity corridors. But maybe it gets fixed when frequency increases on the Almere – Schiphol corridor and frequency on the high speed line increases, not sure about that one.
The Utrecht dwell is because there are cross platform transfers between trains that run 3 minutes behind each other on the same tracks between Amsterdam and Utrecht. That one can only be fixed if frequency increases to 8tph per corridor in the future and they accept that trains don’t have cross-platform transfers to each other, but you have to wait a bit for the next train.
The Arnhem dwell is to move from a 10 minute spread at Utrecht Centraal to a 15 minute spread at Nijmegen, while also serving the intermediate stops of Driebergen-Zeist and Veenendaal de Klomp interchangeably, and thread between the Zwolle/Zutphen – Nijmegen/Roosendaal trains. The other train has a longer dwell at 7 minutes because of this. Maybe these dwells get shorter when the additional island platform at Nijmegen is built.
Once you get to 8tph, surely you don’t need timed transfers any more (since the maximum transfer time would be 7.5min anyway), so at that point you can get rid of the extended dwells for the intercity trains.
The flip side of this is that when Switzerland builds high-cost infrastructure, it does so on the “only as fast as necessary” principle as well, which means that the target trip time is just less than an integer or half-integer multiple of the hour. No additional padding beyond the 7% is done on these connections, like Zurich-Bern, because that would require spending more money on high- and medium-speed lines with extensive tunneling to get the technical travel time even lower.
I believe the best case real world padding scenario is the British who do 45 second stops on local services and 2 minute stops on long distance services with approximately 10% padding over the technical time.
I have less information on the Japanese but my impression is that in reality they do something similar. Certainly some of their departures from Tokyo were pretty relaxed when I was looking from my hotel overlooking the railway – and it is highly doubtful the padding is therefore only 4%.
If the Swiss or Dutch instead have very long dwells at some stops then probably in reality it works out pretty similar to the British at around 10%.
Chiltern has a whole series of different stopping patterns, definitely closer to each hourly train having its own with more at peak, but it still maintains 90.5% on time within 3 minutes with 30 year old diesel rolling stock. So yes simpler stopping patterns help but aren’t essential.
Yes the Nozomi on the Tokaido Shinkansen has 1 stopping pattern, but the Hikari has at least 4 depending on how generous I want to be and the Kodama has 1-2.
On the Sanyo Shinkansen the Nozomi trains have 5 patterns, the Mizuho has 4, the Sakara has at least 5 I think?
Give your Tokyo visit hotel window “data” a rest, for God’s sake.
As I snarked last time you were at this (in a brief pause between Chiltern, Chiltern, and Chiltern)
Now back to Chiltern! Something JR East, along with the entire rest of the world, clearly still has a great deal to learn from.
There is tonnes to learn from the Japanese and they do things very well, but you aren’t using 25% of your padding in the first mile of a 300 mile trip for the half dozen trains I looked at over a couple of days and maintaining 99% on time performance or whatever. The relaxed departure times were also a feature of all the Shinkansen trains I rode in Japan.
I’d suspect one major detail you may be missing in your anecdote is that Japanese trains aren’t necessarily scheduled to depart precisely on the minute; Shinkansen trains for example can depart 0 seconds, 15 seconds, 30 seconds, or 45 seconds into the minute but that information is always hidden from the public timetable. Your claims of trains regularly leaving “1-2 minutes late” from Tokyo is incompatible with the arrival punctuality that you don’t contest, given that there’s a scheduled all-trains stop just 6 minutes down the line at Shinagawa – there isn’t much room to make up delays and it would also block arriving Shinkansens operating under identical time constraints at the switches. Such chaos would surely be noticed by more than just you.
The only citation I have on Japanese padding is from California HSR docs, which put north-of-Tokyo Shinkansen padding in the 3-5% range.
As per Wikipedia from Omiya to Utsunomiya the line speed is 275km/h and north of Utsunomiya it is 320km/h. The technical time for both is 16.95 minutes and 40.575 minutes. With 3 minutes for acceleration and braking that is 60 minutes. The fastest non stop service takes 66 minutes and 68 is typical.
You’re working under faulty assumptions, missing at least a major slow section near Sendai, and engaging in a bit of “creative” rounding as well. If we assume acceleration and deceleration happens uniformly at the max acceleration spec (which likely leads to an underestimate of time lost since e.g. the real acceleration curve is slower) that amounts to 3.1 minutes lost, which summed with your max line speed times adds up to 60.6 minutes. Then there’s the aforementioned slow section leading up to Sendai where the Shinkansen has to navigate tight curves while following the conventional line for a decent stretch. With the speculated speed limit of 100 km/h there, even after accounting for acceleration distance that adds at least another minute lost.
Alon what I can find is that general practice for Japanese timetable padding (“yoyuujifun”- 余裕時分) is said to be 2~3% for double track lines*, and 5~7% for single track lines. This is for railways in general, not shinkansen-specific. Each line has its operating peculiarities, and I reckon the urban stretch of the Tohoku/Joetsu/Hokuriku shinkansen line between Tokyo and Omiya has operating restraints due to bottlenecks which may require more padding than the above number.
*taken from this ancient document (pg. 5):
https://orsj.org/wp-content/or-archives50/pdf/bul/Vol.32_11_709.pdf
Back in the 1980s they would have achieved those figures by speeding for sure.
It’s only in the past 25 years that commercial drivers have been under pressure not to speed. Bus schedules effectively required it to stay to time historically.
Most of the time you can’t juggle more than one concept at time. They above mishmash has three. Perhaps four?
Replacing bridges, that are over a century old and need to be replaced, are separate projects from whatever New Rochelle fantasy you are having. Having trains cross over opposite direction tracks limits service. It doesn’t stop it. Like a bridge failure would.
What is past it’s service life and needs to be replaced, what would speed up service, what would be nice but not necessary are separate issues as how overpriced things are. And it’s not just rail projects that are overpriced, highway projects are too. Even the private ones managed by the valiant captains of industry who are going t squeeze every nickel until the buffalo shits.
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Alon I don’t think you explained this one as well as you could.
While you talked about what the Americans don’t do at length, you didn’t really say what they do do.
Are those delays arrived at theoretically, or empirically? This sentence is a bit vague, but I gather what the Americans are doing is an empirical rather than theoretical method, which is saying the nth percentile travel time is 10% less than the schedule. Is that right?
The Americans are wrong about this, but you might take some time to explain why it leaves slop on the table.
I see one of two possible answers:
I would like to know which one it is!
The biggest obstacle to getting this conversation even in the right ballpark seems to be a lack of high level coordination between the planning entities, namely the MTA, Amtrak, and CTDOT. In CT it appears that CTDOT just does whatever they want, maintaining the tracks at their convenience, with the MTA dispatching trains between New Haven and New Rochelle without regard to schedule optimization, and dropping slow orders like it’s hot. In fact, Amtrak’s Host Railroad Report Card is highly revealing.
This is for July 2025:
https://www.amtrak.com/content/dam/projects/dotcom/english/public/documents/corporate/HostRailroadReports/July-2025-Amtrak-Host-Railroad-Report.pdf
MNRR clocked 1,559 min / 10k Amtrak service miles of delay for Acela and 1,238 min for NER in July 2025 alone. The track over which these delays are occurring isn’t explicitly called out, but it’s 56 route miles, which conveniently is the exact length between New Haven and New Rochelle, which CTDOT owns. The primary causes are DSR (slow orders) and CTI (commuter train interference). CT’s 2022-2026 State Rail Plan itself notes slow orders as the main cause of slowdowns on the corridor.
Now, slow orders because of construction is kind of understandable–the bridges have to get replaced sometime, and (I have no evidence of this) snooty Fairfield County residents probably don’t want work occurring at night–but what I don’t get is why Amtrak isn’t being dispatched favorably over Metro-North trains. It’s a four-track mainline, assuming all four tracks are in service (they probably aren’t, but I can’t see a recent source which tells me). Why are NER and Acelas trundling behind M8s? Inquiring minds want to know, so they can pester state legislators.
There should be an interstate authority which controls all scheduling and owns all infrastructure from Washington to Boston. There is a Northeast Corridor Commission, but its charter is to allocate costs and prepare planning documents. It can’t force compliance.
In fact, the Connect NEC 2037 report is here:
http://nec-commission.com/app/uploads/2023/11/C37-Full-Report-Nov-23.pdf
Nary a word about scheduling coordination. Lots about creating jobs and spending money. That’s not the goal here! The goal is to move the most people as fast and efficiently as possible! The goal should be up front and in plain English: for $X, passengers will get Y minutes faster. Shaking my damn head…
I’ll bite. Which schedule are you coordinating with what?
Nope. Go away, troll.
Happy to engage with anyone except you.
I’m sure by 2037 Penn Station Access will have been up and running for months. Which means this schedule will have even more trains on it.
https://www.mta.info/schedules/metro-north/new-haven
What’s going to connect with what? Why wouldn’t competent adults consult it and select an intercity train that gets them to their suburban station expeditiously?
What’s going to connect with what: trains north of New Rochelle can run either local or express; trains south of New Rochelle can run to either Grand Central or Penn. It would be good if New Rochelle allowed timed transfers (cross-platform like pre-ESA Jamaica, if rebuilt).
Focus. Also juggle more than one concept at a time.
What connections the commuter railroads are making internally is outside of the scope of an Amtrak study on intercity travel.
The LIRR makes cross platform transfers all day long at Jamaica. I’m not in the mood to see how long Grand Central shuts down at night. Or Brooklyn. You can’t make cross platform transfers between Grand Central, Penn Station and Brooklyn. Nor or I in the mood to check all the branch schedules to see how many transfers they schedule in Nassau and Suffolk. They do.
Metro North is aware of the concept because they do it with the branch lines. And these days with the trains from Springfield or New London. It’s possible to make cross platform transfers outbound at the island platform at New Rochelle. It’s not possible to make them inbound because there is a side platform. Which will be difficult to reconfigure because they went and built a parking garage right at the far edge of the platform. I’m sure people pointed out that was an unwise decision but they went and fucked things up anyway. There is plenty of space for two islands in Larchmont. There is an argument to be made to put the intercity station in Rye. Which is closer to all the corporate offices along the Cross Westchester/I-287. Which could have dedicated ramps from the highways to the parking garages in the wasteland between the ramps and the tracks. Which doesn’t stop them from building island platforms at both Larchmont and Rye. Focusing on intercity, if great big thundering herds of intercity passengers are going to be to and fro’ing in Westchester the enormous parking garages need to be someplace. Downtown New Rochelle wouldn’t be my first choice.
Just like you can’t make cross platform transfers between Grand Central, Penn Station and Brooklyn, in Jamaica, you can’t make cross platform transfers between intercity trains and the local from Grand Central to Stamford and the express from Penn Station to New Haven, in New Rochelle. Keep in mind there is a side platform on the inbound side and you can’t make cross platform transfers at all.
Fretting about connections is clueless railfannery because competent adults will check the schedules. Or trust the trip planner. And even if they don’t whatever train they are hoping to connect to will be there “soon” most of the day. And I’m still not sure which connections either of you is imagining. And after very very briefly skimming through the Amtrak study I noticed that they want to spend billions to make the trains as fast as they were after the Metroliners arrived half a century ago. Nah, clueless railfans want to know when the Danbury train is going to meet the Acela. In 2040.
I believe the European approach is that you do a 2 week closure sometime to do this and work 24/7 to get it done.
I did also have a quick look at the timetable and there are a lot of overtakes where the British would timetable the slower train to depart after the faster one, that means you need all four tracks and switching between them to do the timetable. For example does train 1431 really need to pass 1433?
The point of having four tracks is that the express train can pass the local train. Without switching tracks.
I’m going to hazard a guess that the very clever people who use South Norwalk arrange themselves to use the train that leaves at 7:59 and arrives in Grand Central at 9:00. Instead of taking the train that leaves at 7:51, makes more stops and doesn’t get to Grand Central until 9:02. Saving themselves 10 minutes. Which frees up seats on the train that leaves at 7:51 for the people at the stops the 7:51 does make. Stops the 7:59 doesn’t make. Because it is an express from the point of view of those stations. On tracks they can’t get to from their platforms.
Shell Interlocking/CP 216 Improvement | Would it be viable to reduce the Main Line track between Pelham and New Rochelle from four to two tracks, reconfigure New Rochelle station with two island platform (one for GC trains and one for Penn trains), and construct a underpass in the area between Petersville Rd overpass and Larchmont Station?
https://www.google.com/maps/d/u/0/edit?mid=1LSqM-M2jRMHviANf-oEW5WJVL3uSQgo&usp=sharing
Why would you want to reduce the Pelham-New Rochelle section to two tracks?
Operationally reducing the tracks from four to two between Pelham and New Rochelle [All the tracks would physically remain for maintenance/track outages] and constructing a track underpass for Metro North trains in the area between Petersville Rd overpass and Larchmont Station would eliminate all conflict points with Amtrak’s merging Hell Gate line that limit speeds at the existing interlocking for intercity travel. Penn Station Access would reduce the # of Metro North trains going to Grand Central.
One has to take care comparing observed vs. policy recovery time. Observed recovery time, on average, is generally going to be greater than the recovery time mandated by policy because the integer nature of vehicles / trains requires rounding up the cycle time to a multiple of the headway; the extra that is forced by rounding is what I call schedule slack. For instance, if the minimum technical cycle time is 100 minutes, headway is 30 minutes, and the minimum recovery standard is 10%, a cycle time of 110 minutes is allowable by policy, but in practice 10 minutes of schedule slack will also be added, resulting in an observed recovery time of 20 minutes, because unless interlining can be used to reduce schedule slack, the cycle length will have to 120 minutes (a multiple of 30 minutes). In my grad school research on bus route headways, I saw that average layover in practice was a good deal larger than the minimum layover policy due to this need for rounding.
That’s true when, and only when, the turnaround time is not itself used for the additional recovery based on the cycle time. On American commuter rail, the practice is to park trains for long periods of time at the city terminal between the peaks, and not to run on any clockface schedule that requires a compatible cycle time. It’s different with bus routes, because American towns do run these on a consistent cycle time in order to pulse in town center.