# Quick Note: High Speed 2 and Euston

There was reporting in the Sun, since officially denied, that Britain is planning to cut Euston from its high-speed rail project and run trains only as far a Old Oak Common, a future development site west of Central London. I assume given the source and lack of any other confirmation that the plans are to run to Euston as planned. But what if the story is not completely fake news, and there are plans to cut on construction at Euston? I can see a cut being positive value engineering, using space at the station more efficiently.

What’s the issue with High Speed 2?

High Speed 2 is an extremely expensive line. Among proper intercity high-speed rail lines (as opposed to suburban lines running at medium speed), it is the most expensive in our database per kilometer. The projected cost as of 2019-20 is about the same as that of all lines built to date in Germany and France combined; Germany has about 1,000 km of newly-built high-speed lines and France 2,500, whereas HS2 is planned to be 530 km.

The high costs are related to some massive scope creep, including tunnels in relatively flat terrain through the Chilterns, dug essentially because the area has rich NIMBYs and the British state decided not to fight them. Those are already in advanced enough construction that I don’t think descoping them and building the line at-grade with compulsory purchase of land is viable. However, some of the scope is new stations, which British defenders of the system insist are necessary. Birmingham is to get an entirely new station at Curzon Street, and London Euston is to get a substantial increase in size, with additional tracks and approaches. This is said to be necessary for capacity reasons.

Are new stations necessary for capacity?

No. Euston today has 16 platform tracks; it had 18 before HS2 construction started. The S-Bahn-quality Watford DC line can use two; the remaining slow services at the station amount to around 10-12 trains per hour, which S-Bahn-quality terminals like Saint-Lazare on the RER E and Catalunya on the Barcelona Rodalies network can comfortably turn on four tracks; those two comparisons turn 16 and 24 trains per hour on four tracks, respectively. The services out of Euston branch more than the RER and Rodalies, but this is mostly a mix of stopping patterns, largely on the same legacy line.

Then there’s HS2 itself. The line is expected to get very high ridership, justifiably: all cities along the line are larger than their comparison cases on the LGV Sud-Est, often substantially, and the projection is that very high capacity is required, on the order of 16 trains per hour. This stretches high-speed rail to its limit: the Shinkansen, which mixes local and express trains on double track, peaks around 14-15 trains per hour, and the complexly branched TGV around 12. HS2 expects to do better perhaps through better signals but also through having a simpler stopping pattern on its most congested section, between London and the bifurcation at Birmingham Interchange, on which trains are to run nonstop.

However, 16 trains per hour can still turn on about six platform tracks. This is not easy: the Tohoku Shinkansen turns 14 on four tracks, but this is a limit case, famous not just in rail media but also in business media as successful optimization of infrastructure. Nonetheless, given how constrained the site is, it’s useful to learn from the best and not the average. If it’s possible to descope the plans to add new tracks to Euston, this should be done; present plans for Euston cost billions.

Is this happening?

Maybe. Britain is aware of the situation at Tokyo Station, although it seems more interested in looking for reasons not to learn than in learning. Perhaps very high costs are leading to a reevaluation, in which Euston can be made smaller than in current plans and trains can turn more efficiently.

But again, the ultimate source on this said nothing of this sort, and is unreliable. So who knows?

# Paris-Berlin Trains, But no Infrastructure

Yesterday, Bloomberg reported that Macron and Scholz announced new train service between Paris and Berlin to debut next year, as intercity rail demand in Europe is steadily rising and people want to travel not just within countries but also between them. Currently, there is no direct rail service, and passengers who wish to travel on this city pair have to change trains in Frankfurt or Cologne. There’s just one problem: the train will not have any supportive infrastructure and therefore take the same eight hours that trains take today with a transfer.

This is especially frustrating, since Germany is already investing in improving its intercity rail. Unfortunately, the investments are halting and partial – right now the longest city pair connected entirely by high-speed rail is Cologne-Frankfurt, a distance of 180 km, and ongoing plans are going to close some low-speed gaps elsewhere in the system but still not create any long-range continuous high-speed rail corridor connecting major cities. With ongoing plans, Cologne-Stuttgart is going to be entirely fast, but not that fast – Frankfurt-Mannheim is supposed to be sped up to 29 minutes over about 75 km.

Berlin-Paris is a good axis for such investment. This includes the following sections:

• Berlin-Halle is currently medium-speed, trains taking 1:08-1:16 to do 162 km, but the flat, low-density terrain is easy for high-speed rail, which could speed this up to 40-45 minutes at fairly low cost since no tunnels and little bridging would be required.
• Halle-Erfurt is already fast, thanks to investments in the Berlin-Munich axis.
• Erfurt-Frankfurt is currently slow, but there are plans to build high-speed rail from Erfurt to Fulda and thence Hanau. The trip times leave a lot to be desired, but newer 300 km/h trains like the Velaro Novo, and perhaps a commitment to push the line not just to Hanau but closer to Frankfurt itself, could do this section in an hour.
• Frankfurt-Saarbrücken is very slow. Saarbrücken is at the western margin of Germany and is not significant enough by itself to merit any high-speed rail investment. Between it and Frankfurt, the terrain is rolling and some tunneling is needed, and the only significant intermediate stops are Mainz (close enough to Frankfurt it’s a mere stop of opportunity) and Kaiserslautern. Nonetheless, fast trains could get from Frankfurt to the border in 45 minutes, whereas today they take two hours.

Unfortunately, they’re not talking about any pan-European infrastructure here. Building things is too difficult, so instead the plan is to run night trains – this despite the fact that Frankfurt-Saarbrücken with a connection to the LGV Est would make a great joint project.

# Midwestern Urban Geography and High-Speed Rail

I’ve been uploading videos about high-speed rail lately, of which the most recent, from a week ago, is a return to my attempt at producing a high-speed rail map proposal for the eastern half of the United States. I streamed and then blogged a map here with followup here, but having looked at the model more, I’d like to do a refinement – both to introduce a slightly bigger map and explain why it is so, and talk about the issue of connecting low-speed lines. Along the way, I feel like I must talk about an issue mentioned in comments occasionally about the politics of only connecting major metropolitan areas, especially since this map still has fewer lines than various state wishlists stapled by Amtrak; this is especially important because one of the motivations for this post is a criticism of current plans by Matt Yglesias.

The map

A full-size (6 MB) version of the map can be found here. This is not intended as a comprehensive map of all desirable low-speed connections – I made no effort to include the Northeastern ones, which I wrote about in the context of New England and Upstate New York, and which Ben She has done good work on in the context of eastern Pennsylvania and the mid-Atlantic. Rather, I want to focus on the Midwest.

But first, to explain a little more about why this map includes more red (high-speed) lines than previously, the reason has to do with my spreadsheet for computing ridership density based on Metcalfe’s law. The original posts computed everything by hand, which meant that some low-ridership city pairs I just rounded to zero; the spreadsheet does include them, making every line look much stronger. This, in particular, makes St. Louis-Kansas City and Atlanta-Birmingham, omitted last year, and Nashville-Memphis, suggested last year as a maybe, solid propositions.

A note of caution is still advised. Those weak city pairs that aggregate to sufficient ridership for significant return on investment are often at long distance, such as Kansas City-New York. The ridership model is trained on Shinkansen data out of Tokyo and sanity-checked with some French, German, and Spanish data, but the same model overpredicts Shinkansen ridership on inter-island trips for which planes are a convenient alternative, like Tokyo-Fukuoka or Tokyo-Hakodate. This makes me reluctant to add a Kansas City-Dallas connection, which the spreadsheet thinks generates a bit more than \$1 million in annual operating profit per km of new construction: the extra ridership out of Kansas City-Dallas includes some very long-distance trips like Dallas-Detroit, for which the model is likely an overprediction.

The truth is likely between the spreadsheet and the handmade version of the model; while the Shinkansen is not competitive with planes when trains take five hours, European high-speed trains are, for example Paris-Nice. This leads to the inclusion of the new sections, but the exclusion of Kansas City-Dallas. Note also that I did look at Birmingham-New Orleans and Memphis-Little Rock, and both were weak even in the spreadsheet (though I did not attempt Birmingham-New Orleans-Houston) – the Deep South is too low-density and rural to support as expansive a system.

But the topic of this post is not the South, but the Midwest.

Midwestern urban geography

The United States is usually a country of fewer, bigger metropolitan areas, like rich Asia and unlike Europe; unlike both Europe and Asia, American cities are very decentralized, and the exceptions are in the Northeast and West, not the Midwest. In particular, naive comparisons of Midwestern to French high-speed rail corridors are unwarranted: while Chicago is of the same approximate size as Paris, and secondary Midwestern metropolitan areas like Detroit and St. Louis are substantially larger than French ones like Lyon and Marseille, Lyon and Marseille are ringed by many small metropolitan areas with their own TGV service, whereas at the same radius, St. Louis has only its suburbs.

However, this phenomenon of fewer, bigger metro areas has exceptions. Michigan, in particular, has a slightly more European geography. Using the smaller numbers produced by the metropolitan statistical area (MSA) calculation rather than the broader combined statistical area (CSA), Metro Detroit has 43% of Michigan’s population as of the 2020 census. The median Michigander lives in the Grand Rapids MSA, with 1.1 million people, fewer than the US-wide median of 1.6-1.7 million. Michigan is a fairly urban state, and below Grand Rapids is a succession of six-figure metropolitan areas: Ann Arbor, Lansing, Flint, Kalamazoo, Battle Creek, Saginaw.

Ohio is similar to Michigan. Its three main metro areas, excluding Cincinnati’s out-of-state suburbs, have just a hair less than half the state’s population; the median Buckeye therefore lives in Dayton, MSA population 800,000. Moreover, the southern half of Michigan has fairly high population density, as does Ohio – nothing as dense as the Northeast or Germany, but they’re comparable to France.

This geography lends itself to an expansive intercity rail network: the cities are relatively close to one another, and there are many of them meriting a connection. In Ohio, this happens to take the form of an entirely high-speed network, since Cleveland, Columbus, Dayton, and Cincinnati all lie on one line, and then the most natural east-west route between the Northeast and the Midwest passes through Cleveland and Toledo. Ohio, in this case, is a state with fairly good geography for low-speed intercity rail that just happens to also have good geography for high-speed rail due to its location. Michigan, in contrast, is not on the way between much, and thus should get a low-speed rail network, including both connections to Chicago (such as to Grand Rapids) and an intra-state network.

Wisconsin has many, smaller cities as well: the median resident is in an MSA of around 200,000 people, currently Racine. Fortunately, many of those cities lie on just one line between Chicago and Minneapolis, plus a low-speed branch up to Green Bay. Unfortunately, coverage is lacking by the standards of Ohio, Michigan, or much more big city-dominated Illinois and Minnesota.

Getting low-speed rail right

I am happy to report that in Michigan and Ohio at least, good projects for low-speed rail are pursued. When I streamed my video, I was told in Twitch chat that Michigan is looking into funding a Detroit-Lansing-Grand Rapids intercity train. Ohio likewise has long had ideas for a statewide network, beginning with the Cleveland-Cincinnati spine.

It is unfortunate that these projects are not planned well. In a future post, I should write more about the concept of the wrong project versus the right project done poorly; I obliquely pointed this out when writing about leakage in the context of urban transit, where some American cities have poor project prioritization (such as Los Angeles) whereas others choose more or less the right projects but execute them poorly (such as New York and San Francisco). In this schema, the current plans for low-speed rail are often the right project, done wrong.

What I mean by this is that there’s a set of best industry practices for getting low-speed (that is, legacy) rail right, emanating out of Germany and surrounding countries, especially Switzerland. These include,

• Integration of timetable planning and infrastructure, to minimize construction costs – if higher costs are acceptable, just build high-speed rail.
• A clockface all-day schedule with a minimum of one train every two hours, and ideally a train every hour if the distances are shorter or the cities are bigger.
• Timed connections at major nodes to both other intercity trains within the same network and regional mass transit (such as regional trains or connecting buses).
• Reliability-centric planning, in which sources of delays are to be proactively eliminated – on a system this tightly coordinated, delays on one line propagate across the entire system.
• An average speed of around 100-130 km/h – the higher numbers are more appropriate in flat terrain.

Marco Chitti has an excellent post that I must revisit in the future giving more detailed guidelines, mostly at regional level but also with an eye toward national intercity rail planning.

The upshot is that trying to incrementally build up ridership for a few trains per day does not work. The US has a few trains per day on a few corridors now, such as Chicago-Detroit, and daily trains on most others, and this hasn’t built up ridership. The low-speed, low-frequency intercity trains Europe had before the introduction of the TGV in France and the high-frequency, tightly-linked InterCity network in Germany were rapidly losing market share to cars and planes. To build such a network now would be like to build infrastructures wired telephones in a developing country rather than just skipping straight to cellphones as developing countries have.

Politics and Matt Yglesias’s post

Matt likes pointing out that current transportation plans in the United States are deficient, and to link to my posts as a better alternative. There was a lot of dunking on Matt’s post about this (as there is on anything that Matt writes) by left-identified people who, in effect, think daily or twice-daily trains between small cities are a great investment. This dunking usually takes the form of “how dare Matt, a lifelong East Coaster, tell people in [insert Midwestern town] that they don’t deserve trains?”. In a less abrasive form, some people in comments here, like Pharisee, have made the point that these expansive maps proposing daily trains to many places have good geographic coverage whereas what I propose does not. Let me explain why this line of thinking is wrong.

The issue is that the United States is, again, a country that for the most part has fewer, larger metropolitan areas than Europe. The map I made above hits MSAs with a large majority of the country’s population. Of the top 50 as of the 2020 census, the only misses are Denver, Oklahoma City, Salt Lake City, and New Orleans. Denver and Salt Lake City are far from everything else, and the other two are in theory on routes from Texas to the rest of the country but there’s too little population on the way for a connection in the geography of 2022.

Moreover, within the Midwest, coverage is ample. The Midwest is a highly (sub-)urbanized region, much of which has fairly high population density, and the biggest exception to the high density, Minnesota, has a large enough city to justify a line to Chicago by itself (and Milwaukee is on the way, too). The areas that are usually most moralized as Real America – Michigan, Ohio, Pennsylvania – are on the way. This shouldn’t be too surprising: the Real America moralization centers areas with a past industrial history, evoking feelings of nostalgia for midcentury American industrial dominance, and those areas remain major cities today, just relatively poorer than they were in the 1960s. This way, in the Midwest, every state has a large majority of its population in an MSA with a high- or low-speed train station on my map, except Iowa, which is unusually rural.

This is not even out of any consciously political desire to serve these areas. I draw maps out of a ridership model. It just so happens that metropolitan areas of 4 million people situated in dense geographies scream “build high-speed trains to me,” and those include Detroit.

The problem – the reason Matt is so negative on current plans – is that current plans are bad. They are low- and not high-speed rail, which by itself is not horrible, but they’re also bad low-speed rail. Daily trains are just not good. But this does not mean the Midwest can’t or shouldn’t get a good intercity rail network: it should, combining high- and low-speed trains as appropriate.

# Philadelphia and High-Speed Rail Bypasses (Hoisted from Social Media)

I’d like to discuss a bypass of Philadelphia, as a followup from my previous post, about high-speed rail and passenger traffic density. To be clear, this is not a bypass on Northeast Corridor trains: every train between New York and Washington must continue to stop in Philadelphia at 30th Street Station or, if an in my opinion unadvised Center City tunnel is built, within the tunnel in Center City. Rather, this is about trains between New York and points west of Philadelphia, including Harrisburg, Pittsburgh, and the entire Midwest. Whether the bypass makes sense depends on traffic, and so it’s an example of a good investment for later, but only after more of the network is built. This has analogs in Germany as well, with a number of important cities whose train stations are terminals (Frankfurt, Leipzig) or de facto terminals (Cologne, where nearly all traffic goes east, not west).

Philadelphia historically has three mainlines on the Pennsylvania Railroad, going to north to New York, south to Washington, and west to Harrisburg and Pittsburgh. The first two together form the southern half of the Northeast Corridor; the third is locally called the Main Line, as it was the PRR’s first line.

Trains can run through from New York to Washington or from Harrisburg to Washington. The triangle junction northwest of the station, Zoo Junction, permits trains from New York to run through to Harrisburg and points west, but they then have to skip Philadelphia. Historically, the fastest PRR trains did this, serving the city at North Philadelphia with a connection to the subway, but this was in the context of overnight trains of many classes. Today’s Keystone trains between New York and Harrisburg do no such thing: they go from New York to Philadelphia, reverse direction, and then go onward to Harrisburg. This is a good practice in the current situation – the Keystones run less than hourly, and skipping Philadelphia would split frequencies between New York and Philadelphia to the point of making the service much less useful.

The advantage of skipping Philadelphia are that trains from New York to Harrisburg (and points west) do not have to reverse direction and are therefore faster. On the margin, it’s also beneficial for passengers to face forward the entire trip (as is typical on American and Japanese intercity trains, but not European ones). The disadvantage is that it means trains from Harrisburg can serve New York or Philadelphia but not both, cutting frequency to each East Coast destination. The effect on reliability and capacity is unclear – at very high throughput, having more complex track sharing arrangements reduces reliability, but then having more express trains that do not make the same stop on the same line past New York and Newark does allow trains to be scheduled closer to each other.

The relative sizes of New York, Philadelphia, and Washington are such that traffic from Harrisburg is split fairly evenly between New York on the other hand and Philadelphia and Washington on the other hand. So this really means halving frequency to each of New York and Philadelphia; Washington gets more service with split service, since if trains keep reversing direction, there shouldn’t be direct Washington-Harrisburg trains and instead passengers should transfer at 30th Street.

The impact of frequency is really about the headway relative to the trip time. Half-hourly frequencies are unconscionable for urban rail and very convenient for long-distance intercity rail. The headway should be much less than the one-way trip time, ideally less than half the time: for reference, the average unlinked New York City Subway trip was 13 minutes in 2019, and those 10- and 12-minute off-peak frequencies were a chore – six-minute frequencies are better for this.

The current trip time is around 1:20 New York-Philadelphia and 1:50 Philadelphia-Harrisburg, and there are 14 roundtrips to Harrisburg a day, for slightly worse than hourly service. It takes 10 minutes to reverse direction at 30th Street, plus around five minutes of low-speed running in the station throat. Cutting frequency in half to a train every two hours would effectively add an hour to what is a less than a two-hour trip to Philadelphia, even net of the shorter trip time, making it less viable. It would eat into ridership to New York as well as the headway rose well above half the end-to-end trip, and much more than that for intermediate trips to points such as Trenton and Newark. Thus, the current practice of reversing direction is good and should continue, as is common at German terminals.

The presence of a high-speed rail network has two opposed effects on the question of Philadelphia. On the one hand, shorter end-to-end trip times make high frequencies even more important, making the case for skipping Philadelphia even weaker. In practice, high speeds also entail speeding up trains through station throats and improving operations to the point that trains can change directions much faster (in Germany it’s about four minutes), which weakens the case for skipping Philadelphia as well if the impact is reduced from 15 minutes to perhaps seven. On the other hand, heavier traffic means that the base frequency becomes much higher, so that cutting it in half is less onerous and the case for skipping Philadelphia strengthens. Already, a handful of express trains in Germany skip Leipzig on their way between Berlin and Munich, and as intercity traffic grows, it is expected that more trains will so split, with an hourly train skipping Leipzig and another serving it.

With high-speed rail, New York-Philadelphia trip times fall to about 45 minutes in the example route I drew for a post from 2020. I have not done such detailed work outside the Northeast Corridor, and am going to assume a uniform average speed of 240 km/h in the Northeast (which is common in France and Spain) and 270 km/h in the flatter Midwest (which is about the fastest in Europe and is common in China). This means trip times out of New York, including the reversal at 30th Street, are approximately as follows:

Harrisburg: 1:30
Pittsburgh: 2:40
Cleveland: 3:15
Toledo: 3:55
Detroit: 4:20
Chicago: 5:20

Out of both New York and Philadelphia, my gravity model predicts that the strongest connection among these cities is by Pittsburgh, then Cleveland, then Chicago, then Detroit, then Harrisburg. So it’s best to balance the frequency around the trip time to Pittsburgh or perhaps Cleveland. In this case, even hourly trains are not too bad, and half-hourly trains are practically show-up-and-go frequency. The model also predicts that if trains only run on the Northeast Corridor and as far as Pittsburgh then traffic fills about two hourly trains; in that case, without the weight of longer trips, the frequency impact of skipping Philadelphia and having one hourly train run to New York and Boston and another to Philadelphia and Washington is likely higher than the benefit of reducing trip times on New York-Harrisburg by about seven minutes.

In contrast, the more of the network is built out, the higher the base frequency is. With the Northeast Corridor, the spine going beyond Pittsburgh to Detroit and Chicago, a line through Upstate New York (carrying Boston-Cleveland traffic), and perhaps a line through the South from Washington to the Piedmont and beyond, traffic rises to fill about six trains per hour per the model. Skipping Philadelphia on New York-Pittsburgh trains cuts frequency from every 10 minutes to every 20 minutes, which is largely imperceptible, and adds direct service from Pittsburgh and the Midwest to Washington.

Building a longer bypass

So far, we’ve discussed using Zoo Junction. But if there’s sufficient traffic that skipping Philadelphia shouldn’t be an onerous imposition, it’s possible to speed up New York-Harrisburg trains further. There’s a freight bypass from Trenton to Paoli, roughly following I-276; a bypass using partly that right-of-way and, where it curves, that of the freeway, would require about 70 km of high-speed rail construction, for maybe \$2 billion. This would cut about 15 km from the trip via 30th Street or 10 km via the Zoo Junction bypass, but the tracks in the city are slow even with extensive work. I believe this should cut another seven or eight minutes from the trip time, for a total of 15 minutes relative to stopping in Philadelphia.

I’m not going to model the benefits of this bypass. The model can spit out an answer, which is around \$120 million a year in additional revenue from faster trips relative to not skipping Philadelphia, without netting out the impact of frequency, or around \$60 million relative to skipping via Zoo, for a 3% financial ROI; the ROI grows if one includes more lines in the network, but by very little (the Cleveland-Cincinnati corridor adds maybe 0.5% ROI). But this figure has a large error bar and I’m not comfortable using a gravity model for second-order decisions like this.

# High-Speed Rail Doesn’t Depend on Megaregions

On my Discord channel, I was reminded of the late-2000s work by some institutional American urbanists about the concept of megaregions. Wikipedia has a good summary of the late-2000s discourse on the subject. In short, there are linear ties across the East Coast from Boston to Washington (“BosWash”), with more or less continuous suburban development in between, and some urbanists tried to generalize this concept to other agglomerations of metropolitan areas, not usually successfully. The American work on this carved most of the country’s population into 10 or 11 megaregions, sometimes annexing portions of Canada, as in the Regional Plan Association’s America 2050 program:

There is a lot to critique about this map. Canada has a strong self-conception as a distinct entity from the United States; while there’s a case for lumping Vancouver with Seattle and Portland as the Pacific Northwest, lumping Toronto with the Midwest is irresponsible. The Hampton Roads region is not meaningfully a periphery of the Northeast, but is rather Southern (for example, it is heavily militarized, and the South has consistently higher enlistment rates than the Northeast). The Rio Grande Valley is not especially connected with New Orleans.

But the core of the program is to propose this as the basis of high-speed rail investment, and that’s where it fails the most visibly. When one of my Discord channel participants posted the map in the channel about high-speed rail, I started talking about my gravity model, and pointed out some patterns that emerge.

For this, consult a table of ridership between any pair of American or Canadian cities in the main connected component of my proposed map:

The table omits Texas, California, and the Pacific Northwest. But it includes lines that I initially considered and rejected, going to Kansas City and Birmingham; the reason is that when I calculated it by hand I omitted very weak long-range connections such as between Boston and the Midwest, whereas the table can automatically calculate them and add them in, producing an estimate of 5 million annual riders between Boston and the entire Midwest region. These extra connections make weak lines like those to Birmingham and Kansas City appear stronger, so those lines are included; it’s plausible they could even justify a connection to Texas via both New Orleans and and Tulsa, but those are not included (and would at any case not impact the analysis below).

The following table includes some connections between two adjacent cities in the table, with their total projected passenger counts. Those are very high numbers, higher than you’d expect; this is because they lump in a great many city pairs – for example, New York-Philadelphia includes all connections from New York, Boston, and Albany to Philadelphia and points south and west, and those sum to a much higher number than just the internal trips on the Northeast Corridor, let alone just trips originating in New York and ending in Philadelphia or the reverse. Also, as a note of caution, there may be small inaccuracies if I mistakenly tabulated very weak markets like Chicago-Charlotte as going via the wrong path; they do not change the main conclusion.

Some observations jump from this (partial) table:

• New York-Boston is much weaker than a lot of segments that are by themselves far weaker than the Northeast Corridor. The reason for this is that a full 31.1 million annual riders on New York-Boston are internal to the Northeast Corridor, whereas the other city pairs require large swaths of the network to be built to have such high traffic.
• From Philadelphia to points west, traffic density is fairly consistent. There’s no separation between a Northeastern and Midwestern megaregion evident in the data: Cleveland has about the same traffic density going east and west, as does Pittsburgh. Rather, it’s the connections between the East Coast and the Midwest, chiefly Philadelphia-Pittsburgh-Cleveland but also the Empire corridor between Albany and Cleveland, that create high ridership.
• Washington-Atlanta is a tail gradually weakening with distance from the Northeast Corridor, rather than an independent corridor.

Outside the US, the same observation about the irrelevance of megaregions to high-speed rail is true. The European attempt to describe a megaregion, the so-called Blue Banana, was constructed explicitly to exclude France – but the highest-traffic density intercity rail link in Europe is between Paris and the bifurcation splitting toward Lyon and Dijon. Frankfurt-Mannheim is a close second, but French intercity trains average around 220 km/h and German ones around 130 km/h depending on the line, and the actually existing high-speed rail network gets higher peak traffic density than the medium-speed one.

Ultimately, high-speed rail as a mode of transportation is a means of connecting metropolitan areas. Whether they fall into megaregions or not is immaterial – some strong links connect distinct regions, like Northeast-Midwest, with higher demand for traffic than some of the internal connections.

# When Different Capital Investments Compete and When They Don’t

Advocates for mass transit often have to confront the issue of competing priorities for investment. These include some long-term tensions: maintenance versus expansion, bus versus rail, tram versus subway and commuter rail, high-speed rail versus upgraded legacy rail, electronics versus concrete. In some cases, they genuinely compete in the sense that building one side of the debate makes the other side weaker. But in others, they don’t, and instead they reinforce each other: once one investment is done, the one that is said to compete with it becomes stronger through network effects.

Urban rail capacity

Capacity is an example of when priorities genuinely compete. If your trains are at capacity, then different ways to relieve crowding are in competition: once the worst crowding is relieved, capacity is no longer a pressing concern.

This competition can include different relief lines. Big cities often have different lines that can be used to provide service to a particular area, and smaller ones that have to build a new line can have different plausible alignments for it. If one line is built or extended, the case for parallel ones weakens; only the strongest travel markets can justify multiple parallel lines.

But it can also include the conflict between building relief lines and providing extra capacity by other means, such as better signaling. The combination of conventional fixed block signaling and conventional operations is capable of moving maybe 24 trains per hour at the peak, and some systems struggle even with less – Berlin moves 18 trains per hour on the Stadtbahn, and has to turn additional peak trains at Ostbahnhof and make passengers going toward city center transfer. Even more modern signals struggle in combination with too complex branching, as in New York and some London lines, capping throughput at the same 24 trains per hour. In contrast, top-of-line driverless train signaling on captive metro lines can squeeze 42 trains per hour in Paris; with drivers, the highest I know of is 39 in Moscow, 38 on M13 in Paris, and 36 in London. Put another way, near-best-practice signaling and operations are equivalent in capacity gain to building half a line for every existing line.

Reach and convenience

In contrast with questions of capacity, questions of system convenience, accessibility, reliability, and reach show complementarity rather than competition. A rail network that is faster, more reliable, more comfortable to ride, and easier to access will attract more riders – and this generates demand for extensions, because potential passengers would be likelier to ride in such case.

In that sense, systematic improvements in signaling, network design, and accessibility do not compete with physical system expansion in the long run. A subway system with an elevator at every station, platform edge doors, and modern (ideally driverless) signaling enabling reliable operations and high average speeds is one that people want to ride. The biggest drawback of such a system is that it doesn’t go everywhere, and therefore, expansion is valuable. Expansion is even more valuable if it’s done in multiple directions – just as two parallel lines compete, lines that cross (such as a radial and a circumferential) reinforce each other through network effects.

This is equally true of buses. Interventions like bus shelter interact negatively with higher frequency (if there’s bus shelter, then the impact of wait times on ridership is reduced), but interact positively with everything else by encouraging more people to ride the bus.

The interaction between bus and rail investments is positive as well, not negative. Buses and trains don’t really compete anywhere with even quarter-decent urban rail. Instead, in such cities, buses feed trains. Bus shelter means passengers are likelier to want to ride the bus to connect the train, and this increases the effective radius of a train station, making the case for rail extensions stronger. The same is true of other operating treatments for buses, such as bus lanes and all-door boarding – bus lanes can’t make the bus fast enough to replace the subway, but do make it fast enough to extend the subway’s range.

Mainline rail investments

The biggest question in mainline rail is whether to build high-speed lines connecting the largest cities on the French or Japanese model, or to invest in more medium-speed lines to smaller cities on the German or especially Swiss model. German rail advocates assert the superiority of Germany to France as a reason why high-speed rail would detract from investments in everywhere-to-everywhere rail transport.

But in fact, those two kinds of investment complement each other. The TGV network connects most secondary cities to Paris, and this makes regional rail investments feeding those train stations stronger – passengers have more places to get to, through network effects. Conversely, if there is a regional rail network connecting smaller cities to bigger ones, then speeding up the core links gives people in those smaller cities more places to get to within two, three, four, five hours.

This is also seen when it comes to reliability. When trains of different speed classes can use different sets of track, it’s less likely that fast trains will get stuck behind slow ones, improving reliability; already Germany has to pad the intercity lines 20-25% (France: 10-14%; Switzerland: 7%). A system of passenger-dedicated lines connecting the largest cities is not in conflict with investments in systemwide reliability, but rather reinforces such reliability by removing some of the worst timetable conflicts on a typical intercity rail system in which single-speed class trains never run so often as to saturate a line.

Recommendation: invest against type

The implication of complementarity between some investment types is that a system that has prioritized one kind of investment should give complements a serious look.

For example, Berlin has barely expanded the U-Bahn in the last 30 years, but has built orbital tramways, optimized timed connections (for example, at Wittenbergplatz), and installed elevators at nearly all stations. All of these investments are good and also make the case for U-Bahn expansion stronger to places like Märkisches Viertel and Tegel.

In intercity rail, Germany has invested in medium-speed and regional rail everywhere but built little high-speed rail, while France has done the opposite. Those two countries should swap planners, figuratively and perhaps even literally. Germany should complete its network of 300 km/h lines to enable all-high-speed trips between the major cities, while France should set up frequent clockface timetables on regional trains anchored by timed connections to the TGV.

# Deutsche Bahn’s Meltdown and High-Speed Rail

A seven-hour rail trip from Munich to Berlin – four and a half on the timetable plus two and a half of sitting at and just outside Nuremberg – has forced me to think a lot more about the ongoing collapse of the German intercity rail network. Ridership has fully recovered to pre-corona levels – in May it was 5% above 2019 levels, and that was just before the nine-euro monthly ticket was introduced, encouraging people to shift their trips to June, July, and August to take advantage of what is, among other things, free transit outside one’s city of residence. But at the same time, punctuality has steadily eroded this year:

It’s notable that the June introduction of the 9€ ticket is invisible in the graphic for intercity rail; it did coincide with deterioration in regional rail punctuality, but the worst problems are for the intercity trains. My own train was delayed by a mechanical failure, and then after an hour of failed attempts to restart it we were put on a replacement train, which spent around an hour sitting just outside Nuremberg, and even though it skipped Leipzig (saving 40 minutes in the process), it arrived at Berlin an hour and a half behind its schedule and two and a half behind ours.

Sometimes, those delays cascade. It’s not that high ridership by itself produces delays. The ICEs are fairly good at access and egress, and even a full train unloads quickly. Rather, it’s that if a train is canceled, then the passengers can’t get on the next one because it’s full beyond standing capacity; standing tickets are permitted in Germany, but there are sensors to ensure the train’s mass does not exceed a maximum level, which can be reached on unusually crowded trains, and so a train’s ability to absorb passengers on canceled trains as standees is limited.

But it’s not the short-term delays that I’m most worried about. One bad summer does not destroy a rail network; riders can understand a few bad months provided the problem is relieved. The problem is that there isn’t enough investment, and what investment there is is severely mistargeted.

Within German discourse, it’s common to assert superiority to France and Southern Europe in every possible way. France is currently undergoing an energy crisis, because the heat wave is such that river water cannot safely cool down its nuclear power plants; German politicians have oscillated between using this to argue that nuclear power is unreliable and the three remaining German plants should be shut down and using this to argue that Germany should keep its plants open as a gesture of magnanimity to bail out France.

Rail transport features a similar set of problems. France has a connected network of high-speed lines, nearly all of which are used to get between Paris and secondary cities. Germany does not – it has high-speed lines but the longest connection between major cities allowing more than 200 km/h throughout is Cologne-Frankfurt, a distance of 180 km.

The natural response of most German rail advocates is to sneer at the idea of high-speed rail; France has genuine problems with punctuality, neglect of legacy rail lines, and poor interconnections between lines (it has nothing like the hourly or two-hour clockface timetables of German intercity rail), and those are all held as reasons why Germany has little to learn from France. Instead, those advocates argue, Germany should be investing in network-wide punctuality, because reliability matters more than speed.

The problem is that the sneering at France is completely unjustified. A French government investigation into punctuality in 2019-20 found that yes, French intercity trains suffered from extensive delays – but in 2019 intercity trains were on-time at the terminus 77.4% of the time, compared with 73.8% in Germany. Germany did better in 2020 when nobody was riding, but went back to 75% in 2021 as ridership began to recover. High-speed trains were the most punctual in Spain and the Netherlands, where they do not run on classical lines for significant stretches, unlike in France, Germany, or Italy.

Moreover, German trains are extremely padded. Der Spiegel has long been a critic of poor planning in German railways, and in 2019 it published a comparison of the TGV and ICE. The selected ICE connections were padded more than 20%; only Berlin-Munich was less, at 18%. The TGV comparisons were padded 11-14%; these are all lines running almost exclusively on LGVs, like Paris-Bordeaux, rather than the tardier lines running for significant distances on slow lines, like Paris-Nice. And even 11-14% is high; Swiss planning is 7% on congested urban approaches, with reliability as the center of the country’s design approach, while JR East suggested 4% for Shinkansen-style entirely dedicated track in its peer review of California High-Speed Rail.

Thus, completing a German high-speed rail network is not an opposed goal to reliability. Quite to the contrary, creating a separate network running only or almost only ICEs to connect Berlin, Hamburg, Hanover, Bremen, the main cities of the Rhine-Ruhr, Frankfurt, Munich, and Stuttgart means that there is less opportunity for delays to propagate. A delayed regional train would not slow down an intercity train, permitting not just running at high punctuality but also doing so while shrinking the pad from 25% to 7%, which offers free speed.

Cutting the pad to 7% interacts especially well with some of the individual lines Germany is planning. Hanover-Bielefeld, a distance of 100 km, can be so done in 27-28 minutes; this can be obtained from looking at the real performance specs of the Velaro Novo, but also from a Japanese sanity check, as the Nagoya-Kyoto distance is not much larger and taking the difference into account is easy. But the current plan is to do this in 31 minutes, just more than half an hour rather than just less, complicating the plan for regular timed connections on the half-hour.

German rail traffic is not collapsing – quite to the contrary. DB still expects to double intercity ridership by the mid-2030s. This requires investments in capacity, connectivity, speed, and reliability – and completing the high-speed network, far from prioritizing speed at the expense of the other needs, fulfills all needs at once. Half-hourly trains could ply every connection, averaging more than 200 km/h between major cities, and without cascading delays they would leave the ongoing summer of hell in the past. But this requires committing to building those lines rather than looking for excuses for why Germany should not have what France has.

# Quick Note: Why Not Fly?

I was asked a deceptively simple question on Twitter: why would people bother with taking a train when flying is available? In my (admittedly primitive) modeling for high-speed rail ridership in the US, I’m including some nontrivial ridership and revenue coming from cities at a distance that people do fly, like Boston-Washington, New York-Cleveland, and so on. What gives?

The simplest answer is that evidently people do take trains at such distances. Statista has some examples, all with more rail than air travel; an Air2Rail paper by Arie Bleijenberg has some numbers within Europe in Annex B. The main factor is rail travel time, with a malus for markets with poor rail connectivity (such as anything crossing the Channel). When trains take four hours, as on Paris-Toulon, they have a small majority of the travel market (source, p. 14 – look at the 2009 numbers, the 2023 numbers being a speculation); Paris-Nice manages to have respectable modal split even at 5.5 hours.

But that answer is frustrating. Why do people take trains for 4-5 hours when it’s possible to fly in an hour?

The first answer is door-to-door travel time. This includes all of the following features:

• Airports are far from city centers whereas train stations are almost universally within them; even taking into account that most people don’t live in city center, they tend to have easier access to the train station than to the airport, and then destinations are massively centralized in the city.
• Trains have no security theater to delay passengers, and passengers can get from the station entrance to the platform in 10 minutes if the station is exceptionally labyrinthine and they’re unfamiliar with its layout and two minutes if it’s not or they are.
• Passengers with luggage can take it on the train and don’t have to be further delayed for baggage claim.

All of these features work to make trains more pleasant than planes even when the door-to-door trip times are equal. The sequential queuing for security and then boarding on a plane is a hassle in addition to extra time; of note, in the Air2Rail link, the most glaring underperformance in high-speed rail modal split relative to trip times is for routes crossing the Channel, because they have such queuing courtesy of British paranoia about terrorism in the Chunnel and also charge higher fares.

The advantages of planes over trains are elsewhere. First, planes are faster airport-to-airport than trains are station-to-station, and as a result, a longer distances they are much faster door-to-door and therefore dominant. And second, trains travel in lines whereas planes travel point-to-point; it’s not hard to come up with city pairs that have no reason to have an even semi-direct high-speed railway between them even though they are at rail-appropriate range, for example Nice-Geneva (290 km) or Cincinnati-Charlotte (540 km).

But once the lines exist, they should get substantial passenger traffic – and the modal split with air is very well-documented in the literature and the overall traffic is still fairly well-modeled as well.

# How Many Tracks Do Train Stations Need?

A brief discussion on Reddit about my post criticizing Penn Station expansion plans led me to write a very long comment, which I’d like to hoist to a full post explaining how big an urban train station needs to be to serve regional and intercity rail traffic. The main principles are,

• Good operations can substitute for station size, and it’s always cheaper to get the system to be more reliable than to build more tracks in city center.
• Through-running reduces the required station footprint, and this is one of the reasons it is popular for urban commuter rail systems.
• The simpler and more local the system is, the fewer tracks are needed: an urban commuter rail system running on captive tracks with no sharing tracks with other traffic and with limited branching an get away with smaller stations than an intercity rail station featuring trains from hundreds of kilometers away in any direction.

On subways, where usually the rush hour crunches are the worst, trains in large cities run extremely frequently, brushing up against the physical limitation of the tracks. The limit is dictated by the brick wall rule, which states that the signal system must at any point assume that the train ahead can turn into a brick wall and stop moving and the current train must be able to brake in time before it reaches it. Cars, for that matter, follow the same rule, but their emergency braking rate is much faster, so on a freeway they can follow two seconds apart. A metro train in theory could do the same with headways of 15 seconds, but in practice there are stations on the tracks and dealing with them requires a different formula.

With metro-style stations, without extra tracks, the governing formula is,

$\mbox{headway } = \mbox{stopping time } + \mbox{dwell time } + \mbox{platform clearing time }$

Platform clearing time is how long it takes the train to clear its own length; the idea of the formula is that per the brick wall rule, the train we’re on needs to begin braking to enter the next station only after the train ahead of ours has cleared the station.

But all of this is in theory. In practice, there are uncertainties. The uncertainties are almost never in the stopping or platform clearing time, and even the dwell time is controllable. Rather, the schedule itself is uncertain: our train can be a minute late, which for our purpose as passengers may be unimportant, but for the scheduler and dispatcher on a congested line means that all the trains behind ours have to also be delayed by a minute.

What this means that more space is required between train slots to make schedules recoverable. Moreover, the more complex the line’s operations are, the more space is needed. On a metro train running on captive tracks, if all trains are delayed by a minute, it’s really not a big deal even to the control tower; all the trains substitute for one another, so the recovery can be done at the terminal. On a mainline train running on a national network in which our segment can host trains to Budapest, Vienna, Prague, Leipzig, Munich, Zurich, Stuttgart, Frankfurt, and Paris, trains cannot substitute for one another – and, moreover, a train can be easily delayed 15 minutes and need a later slot. Empty-looking space in the track timetable is unavoidable – if the schedule can’t survive contact with the passengers, it’s not a schedule but crayon.

How to improve operations

In one word: reliability.

In two words: more reliability.

Because the main limit to rail frequency on congested track comes from the variation in the schedule, the best way to increase capacity is to reduce the variation in the schedule. This, in turn, has two aspects: reducing the likelihood of a delay, and reducing the ability of a delay to propagate.

Reducing delays

The central insight about delays is that they may occur anywhere on the line, roughly in proportion to either trip time or ridership. This means that on a branched mainline railway network, delays almost never originate at the city center train station or its approaches, not because that part of the system is uniquely reliable, but because the train might spend five minutes there out of a one-hour trip. The upshot is that to make a congested central segment more reliable, it is necessary to invest in reliability on the entire network, most of which consists of branch segments that by themselves do not have capacity crunches.

The biggest required investments for this are electrification and level boarding. Both have many benefits other than schedule reliability, and are underrated in Europe and even more underrated in the United States.

Electrification is the subject of a TransitMatters report from last year. As far as reliability is concerned, the LIRR and Metro-North’s diesel locomotives average about 20 times the mechanical failure rate of electric multiple units (source, PDF-pp. 36 and 151). It is bad enough that Germany is keeping some outer regional rail branches in the exurbs of Berlin and Munich unwired; that New York has not fully electrified is unconscionable.

Level boarding is comparable in its importance. It not only reduces dwell time, but also reduces variability in dwell time. With about a meter of vertical gap between platform and train floor, Mansfield has four-minute rush hour dwell times; this is the busiest suburban Boston commuter rail station at rush hour, but it’s still just about 2,000 weekday boardings, whereas RER and S-Bahn stations with 10 time the traffic hold to a 30-second standard. This also interacts positively with accessibility: it permits passengers in wheelchairs to board unaided, which both improves accessibility and ensures that a wheelchair user doesn’t delay the entire train by a minute. It is fortunate that the LIRR and (with one peripheral exception) Metro-North are entirely high-platform, and unfortunate that New Jersey Transit is not.

Reducing delay propagation

Even with reliable mechanical and civil engineering, delays are inevitable. The real innovations in Switzerland giving it Europe’s most reliable and highest-use railway network are not about preventing delays from happening (it is fully electrified but a laggard on level boarding). They’re about ensuring delays do not propagate across the network. This is especially notable as the network relies on timed connections and overtakes, both of which require schedule discipline. Achieving such discipline requires the following operations and capital treatments:

• Uniform timetable padding of about 7%, applied throughout the line roughly on a one minute in 15 basis.
• Clear, non-discriminatory rules about train priority, including a rule that a train that’s more than 30 minutes loses all priority and may not delay other trains at junctions or on shared tracks.
• A rigid clockface schedule or Takt, where the problem sections (overtakes, meets, etc.) are predictable and can receive investment. With the Takt system, even urban commuter lines can be left partly single-track, as long as the timetable is such that trains in opposite directions meet away from the bottleneck.
• Data-oriented planning that focuses on tracing the sources of major delays and feeding the information to capital planning so that problem sections can, again, receive capital investment.
• Especial concern for railway junctions, which are to be grade-separated or consistently scheduled around. In sensitive cases where traffic is heavy and grade separation is too expensive, Switzerland builds pocket tracks at-grade, so that a late train can wait for a slot without delaying cross-traffic.

So, how big do train stations need to be?

A multi-station urban commuter rail trunk can get away with metro-style operations, with a single station track per approach track. However, the limiting factor to capacity will be station dwell times. In cases with an unusually busy city center station, or on a highly-interlinked regional or intercity network, this may force compromises on capacity.

In contrast, with good operations, a train station with through-running should never need more than two station tracks per approach track. Moreover, the two station tracks that each approach track splits into should serve the same platform, so that if there is an unplanned rescheduling of the train, passengers should be able to use the usual platform at least. Berlin Hauptbahnhof’s deep tracks are organized this way, and so is the under-construction Stuttgart 21.

Why two? First, because it is the maximum number that can serve the same platform; if they serve different platforms, it may require lengthening dwell times during unscheduled diversions to deal with passenger confusion. And second, because every additional platform track permits, in theory, an increase in the dwell time equal to the minimum headway. The minimum headway in practice is going to be about 120 seconds; at rush hour Paris pushes 32 trains per hour on the shared RER B and D trunk, which is not quite mainline but is extensively branched, but the reliability is legendarily poor. With a two-minute headway, the two-platform track system permits a straightforward 2.5-minute dwell time, which is more than any regional railway needs; the Zurich S-Bahn has 60-second dwells at Hauptbahnhof, and the Paris RER’s single-level trains keep to about 60 seconds at rush hour in city center as well.

All of this is more complicated at a terminal. In theory the required number of tracks is the minimum turn time divided by the headway, but in practice the turn time has a variance. Tokyo has been able to push station footprint to a minimum, with two tracks at Tokyo Station on the Chuo Line (with 28 peak trains per hour) and, before the through-line opened, four tracks on the Tokaido Main Line (with 24). But elsewhere the results are less optimistic; Paris is limited to 16-18 trains per hour at the four-track RER E terminal at Saint-Lazare.

At Paris’s levels of efficiency, which are well below global best practices, an unexpanded Penn Station without through-running would still need two permanent tracks for Amtrak, leaving 19 tracks for commuter traffic. With the Gateway tunnel built, there would be four two-track approaches, two from each direction. The approaches that share tracks with Amtrak (North River Tunnels, southern pair of East River Tunnels) would get four tracks each, enough to terminate around 18 trains per hour at rush hour, and the approaches that don’t would get five, enough for maybe 20 or 22. The worst bottleneck in the system, the New Jersey approach, would be improved from today’s 21 trains per hour to 38-40.

A Penn Station with through-running does not have the 38-40 trains per hour limit. Rather, the approach tracks would become the primary bottleneck, and it would take an expansion to eight approach tracks on each side for the station itself to be at all a limit.

# Intercity Rail Frequency and the Perils of Market Segmentation

SNCF loves market segmentation. Run by airline execs, the company loves to create different trains for different classes of people. Not only do individual trains have opaque pricing run on the basis of yield management, in which similar seats on the same train at the same time of day and day of week may have different fares, but also there are separately-branded trains for separate fare classes, the higher-fare InOui and the lower-fare OuiGo. On international trains, SNCF takes it to the limit and thus Eurostar and Thalys charge premium fares (both about twice as high as domestic TGVs per passenger-km) and don’t through-ticket with domestic TGVs. This has gotten so bad that in Belgium, some advocates have proposed a lower-priced service on the legacy Paris-Brussels line, which would have to be subsidized owing to the high cost of low-speed intercity rail service.

But why is market segmentation on rail so bad? The answer has to do with frequency and cost structures that differ from those of airlines. Both ensure that the deadweight loss from market segmentation exceed any gains that could be made from extracting consumer surplus.

The issue of frequency

A segmented market like that of domestic TGVs reduces frequency on each segment. To maintain segmentation, SNCF has to make the segments as difficult to substitute for each other as possible. OuiGo serves Marne-la-Vallée instead of Gare de Lyon and forcing passengers onto a 20-minute RER connection, or even longer if they’re arriving in Paris and the wave of 1,000 TGV riders creates long lines at the ticketing machines; on other LGVs it serves the traditional Parisian station and thus the segments are more substitutable.

The situation of Eurostar and Thalys reduces frequency as well: the high fares discourage ridership and send much of it to intercity buses or suppress travel. Fewer riders, or fewer riders per segment as in the case of domestic TGVs, lead to fewer trains. What’s the impact of this on ridership?

The literature on high-speed rail ridership elasticities has some frequency estimates. In Couto’s thesis (PDF-p. 225), it is stated that passenger rail ridership has an elasticity of 0.53 with respective to overall service provision. There are also multiple papers estimating the elasticity with respect to travel time: in Cascetta-Coppola the elasticity ranges from -1.6 to -2.2, in Börjesson it is -1.12, and in a Civity report it is stated based on other work that it is -0.8 to -2. The lowest values in Börjesson are associated with the premium-fare AVE, while the range for the original TGV, priced at the same level as the slower trains it replaced, is -1.3 to -1.6. The upshot is that halving frequency through market segmentation reduces ridership by a factor of 2^0.53 = 1.44, which is far more than the benefit yield management is claimed to have, which is a 4% increase in revenue per SNCF’s American proposals from 2009.

Why are trains different?

Planes and buses happily use yield management. High-speed trains do not, except for those run by SNCF or RENFE – and ridership in France isn’t really higher than in fixed-fare Northern Europe or East Asia while ridership in Spain is much lower. Why the difference?

The reason has to do with the ratio of waiting time to trip time. Thalys connects Paris and Brussels in 1.5 hours, every half hour at rush hour and every 2 hours midday. At rush hour, frequency is sort of noticeable; off-peak, it dominates travel time. This is nothing like planes – even short-distance trips involve hours of access, waiting, and egress time, and therefore trips are not usually spontaneous, and day trips are rare except for business travelers.

Buses, finally, are so small that a market like New York-Philadelphia supports multiple competitors each running frequently, and passenger behavior is such that different companies are substitutable, so that the effective frequency is multiple buses per hour.