# Stuttgart 21’s Impending Capacity Problems and Timed Connections

The largest single transportation project in Germany today is a new underground main station for Stuttgart, dubbed Stuttgart 21. Built at a cost of €8.2 billion, it will soon replace Stuttgart’s surface terminal with a through-station, fed in four directions by separate tunnels. The project attracted considerable controversy at the beginning of this decade due to its cost overruns and surface disruption. It’s had a long-term effect on German politics as well: it catapulted the Green Party into its first ever premiership of a German state, and the Green minister-president of the state, Winfried Krestchmann, has remained very popular and played a role in mainstreaming the party and moving it in a more moderate direction.

But the interesting thing about Stuttgart 21 now is not the high cost, but a new problem: capacity. The new station will face capacity constraints worse than those of the surface station, particularly because Germany is transitioning toward timed connections (“Deutschlandtakt”) on the model of Switzerland. Since Stuttgart is closing the surface station and selling the land for redevelopment, a second underground station will need to be built just to add enough capacity. It’s a good example of how different models of train scheduling require radically different kinds of infrastructure, and how even when all the technical details are right, the big picture may still go wrong.

What is the Stuttgart 21 infrastructure?

The following diagram (via Wikipedia) shows what the project entails.

The existing tunnel, oriented in a northeast-southwest direction, is used exclusively by S-Bahn trains. Longer-distance regional trains (“RegionalBahn“) and intercity trains terminate on the surface, and if they continue onward, they must reverse direction.

The new tunnel infrastructure consists of four independent two-track tunnels, two coming in from the northwest and two from the southeast, with full through-service. In addition, an underground loop is to be constructed on the south in order to let trains from points south (Singen) enter Stuttgart via the Filder tunnel while serving the airport at Filder Station without reversing direction. The total double-track tunnel length is 30 kilometers.

Stuttgart 21’s station infrastructure will consist of eight tracks, four in each direction:

The two tracks facing each platform are generally paired with the same approach track, so that in case of service changes, passengers will not be inconvenienced by having to go to a different platform. The interlocking permits trains from each of the two eastern approaches to go to either of the western ones without conflict and vice versa, and the switches are constructed to modern standards, with none of the onerous speed restrictions of American station throats.

So what is the problem?

First of all, the four approach tunnels are not symmetric. The Feuerbach tunnel leads to Mannheim, Frankfurt, Würzburg, and points north, and the Filder tunnel leads to Ulm and points east, including Munich; both are planned to be heavily used by intercity trains. In contrast, the other two tunnels lead to nothing in particular. The Obertürkheim tunnel leads to the current line toward Ulm, but the under-construction high-speed line to Ulm feeds Filder instead, leaving Obertürkheim with just a handful of suburbs.

On the Deutschlandtakt diagram for Baden-Württemberg, every hour there are planned to be 12 trains entering Stuttgart from the Feuerbach tunnel, 10.5 from the Filder tunnel, 5.5 from the Bad Cannstatt tunnel, and 6 from the Obertürkheim tunnel. For the most part, they’re arranged to match the two busier approaches with each other – the track layout permits a pair of trains in either matching to cross with no at-grade conflict, but only if trains from Feuerbach match with Filder and trains from Bad Cannstatt match with Obertürkheim are both station tracks facing the same platform available without conflict.

A train every five minutes through a single approach tunnel feeding two station tracks is not normally a problem. The S-Bahn, depicted on the same map in black, runs 18 trains per hour in each direction through the tunnel; bigger cities, including Paris and Munich, run even more frequent trains on the RER or S-Bahn with just a single station platform per approach track, as on any metro network.

However, the high single-track, single-direction frequency is more suitable on urban rail than on intercity rail. On a metro, trains rarely have their own identity – they run on the same line as a closed system, perhaps with some branching – so if a train is delayed, it’s possible to space trains slightly further apart, so the nominal 30 trains per hour system ends up running 28 trains if need be. On an S-Bahn this is more complicated, but there is still generally a high degree of separation between the system and other trains, and it’s usually plausible to rearrange trains through the central tunnel. On intercity rail, trains have their own identity, so rearrangement is possible but more difficult if for example two trains on the same line, one express and one local, arrive in quick succession. As a result, one platform track per approach track is unsuitable – two is a minimum, and if more tracks are affordable then they should be built.

How do you intend to run the trains?

If the paradigm for intercity rail service is to imitate shorter-range regional trains, then through-tunnels are both easier and more desirable. A relatively closed system with very high frequency between a pair of stations calls for infrastructure that minimizes turnarounds and lets trains just run in the same sequence.

The Shinkansen works this way, leveraging three key features: its near-total isolation from the legacy train network, running on a different gauge; the very high demand for trains along individual corridors on specific city pairs; and the generally high punctuality of Japanese trains even on more complex systems. As it happens, Tokyo is a terminal, with trains going north and south but not through, as a legacy of the history of breaking up Japan National Railway before the Shinkansen reached Tokyo from the north, with different daughter companies running in each direction. However, Shin-Osaka is a through-station, fitting through-trains as well as terminating trains on just eight tracks.

In the developed world’s second busiest intercity rail network, that of Switzerland, the paradigm is different. In a country whose entire population is somewhat less than that of Tokyo without any of its suburbs, no single corridor is as strong as the Shinkansen corridors. Trains form a mesh with timed connections every hour, sometimes every half hour. Intercity trains are arranged to arrive at Zurich, Bern, and Basel a few minutes before the hour every 30 minutes and depart a few minutes later. In that case, more approach tracks and more platform tracks are needed. Conversely, the value of through-tracks is diminished, since passengers can transfer between trains more easily if they can walk between platforms without changing grade.

Infrastructure-timetable integration

Germany aims to integrate the infrastructure and timetable, as Switzerland does. However, Stuttgart 21 is a failure of such integration. The Deutschlandtakt service paradigm calls for many trains entering and leaving the station within the span of a few minutes. Today there are four effective approaches with two tracks each, same as under the Stuttgart 21 plan, but they are better-distributed.

The idea of Stuttgart 21, and similar proposals for Frankfurt and Munich, is solid provided that the intention is to run trains the Japanese way. It Stuttgart were designed to be the junction of two consistently high-intensity lines, then it would work without additional infrastructure. But it is not: its approach tunnels are supposed to support such design, but the service pattern will not look this way because of how the tunnels are placed relative to Germany’s population distribution. Even highly competent engineering can produce incompetent results if the details do not match the big picture.

# S-Bahn and RegionalBahn

The American rail activist term regional rail refers to any mainline rail service short of intercity, which lumps two distinct service patterns. In some German cities, these patterns are called S-Bahn and RegionalBahn, with S-Bahn referring to urban rail running on mainline tracks and RegionalBahn to longer-range service in the 50-100 km range and sometimes even beyond. It’s useful to distinguish the two whenever a city wishes to invest in its regional rail network, because the key infrastructure for the two patterns is different.

As with many this-or-that posts of mine, the distinction is not always clear in practice. For one, in smaller cities, systems that are labeled S-Bahns often work more like RegionalBahn, for example in Hanover. Moreover, some systems have hybrid features, like the Zurich S-Bahn – and what I’ve advocated in American contexts is a hybrid as well. That said, it’s worth understanding the two different ends of this spectrum to figure out what the priority for rail service should be in each given city.

S-Bahn as urban rail

The key feature of the S-Bahn (or the Paris RER) is that it has a trunk that acts like a conventional urban rapid transit line. There are 6-14 stations on the trunks in the examples to keep in mind, often spaced toward the high end for rapid transit so as to provide express service through city center, and all trains make all stops, running every 3-5 minutes all day. Even if the individual branches run on a clockface schedule, people do not use the trunk as a scheduled railroad but rather show up and go continuously.

Moreover, the network layout is usually complementary with existing urban rail. The Munich S-Bahn was built simultaneously with the U-Bahn, and there is only one missed connection between them, The Berlin S-Bahn and U-Bahn were built separately as patchworks, but they too have one true missed connection and one possible miss that depends on which side of the station one considers the crossing point to be on. The RER has more missed connections with the Metro, especially on the RER B, but the RER A’s station choice was designed to maximize connections to the most important lines while maintaining the desired express stop spacing.

Urban rail lines rarely terminate at city center, and the same is true for S-Bahn lines. In cities whose rail stations are terminals, such as Paris, Munich, Frankfurt, and Stuttgart, there are dedicated tunnels for through-service; London is building such a tunnel in Crossrail, and built one for Thameslink, which has the characteristics of a hybrid. In Japan, too, the first priority for through-running is the most local S-Bahn-like lines – when there were only six tracks between Tokyo and Ueno, the Yamanote and Keihin-Tohoku Lines ran through, as did the Shinkansen, whereas the longer-range regional lines terminated at the two ends until the recent through-line opened.

The difference between an S-Bahn and a subway is merely that the subway is self-contained, whereas the S-Bahn connects to suburban branches. In Tokyo even this distinction is blurred, as most subway lines connect to commuter rail lines at their ends, often branching out.

RegionalBahn as intercity rail

Many regional lines descend from intercity lines that retooled to serve local traffic. Nearly every trunk line entering London from the north was built as a long-range intercity line, most commuter rail mainlines in New York are inner segments of lines that go to other cities or used to (even the LIRR was originally built to go to Boston, with a ferry connection), and so on.

In Germany, it’s quite common for such lines to maintain an intercity characteristic. The metropolitan layout of Germany is different from that of the English-speaking world or France. Single-core metro regions are rather small, except for Berlin. Instead, there are networks of independent metropolitan cores, of which the largest, the Rhine-Ruhr, forms an urban complex almost as large as the built-up areas of Paris and London. Even nominally single-core metro regions often have significant independent centers with long separate histories. I blogged about the Rhine-Neckar six months ago as one such example; Frankfurt is another, as the city is ringed by old cities including Darmstadt and Mainz.

But this is not a purely German situation. Caltrain connects what used to be two independent urban areas in San Francisco and San Jose, and many outer ends of Northeastern American commuter lines are sizable cities, such as New Haven, Trenton, Providence, and Worcester.

The intercity characteristic of such lines means that there is less need to make them into useful urban rail; going express within the city is more justifiable if people are traveling from 100 km away, and through-running is a lower priority. Frequency can be lower as well, since the impact of frequency is less if the in-vehicle travel time is longer; an hourly or half-hourly takt can work.

S-Bahn and RegionalBahn combinations

The S-Bahn and RegionalBahn concepts are distinct in history and service plan, but they do not have to be distinct in branding. In Paris, the distinction between Transilien and the RER is about whether there is through-running, and thus some lines that are RegionalBahn-like are branded as RER, for example the entire RER C. Moreover, with future extension plans, the RER brand will eventually take over increasingly long-distance regional service, for example going east to Meaux. Building additional tunnels to relieve the worst bottlenecks in the city’s transport network could open the door to connecting every Transilien line to the RER.

Zurich maintains separate brands for the S-Bahn and longer-distance regional trains, but as in Paris, the distinction is largely about whether trains terminate on the surface or run through either of the tunnels underneath Hauptbahnhof. Individual S-Bahn branches run every half hour, making extensive use of interlining to provide high frequency to urban stations like Oerlikon, and many of these branches go quite far out of the city. It’s not the same as the RER A and B or most of the Berlin S-Bahn, with their 10- and 15-minute branch frequencies and focus on the city and innermost suburbs.

But perhaps the best example of a regional rail network that really takes on lines of both types is that of Tokyo. In branding, the JR East network is considered a single Kanto-area commuter rail network, without distinctions between shorter- and longer-range lines. And yet, the rapid transit services running on the Yamanote, Keihin-Tohoku, and Chuo-Sobu Lines are not the same as the highly-branched network of faster, longer-range lines like Chuo Rapid, Yokosuka, Sobu Rapid, and so on.

The upshot is that cities do not need to neatly separate their commuter rail networks into two separate brands as Berlin does. The distinction is not one of branding for passengers, but one of planning: should a specific piece of infrastructure be S-Bahn or RegionalBahn?

Highest and best use for infrastructure

Ordinarily, the two sides of the spectrum – an S-Bahn stopping every kilometer within the city, and a RegionalBahn connecting Berlin with Magdeburg or New York with New Haven – are so different that there’s no real tradeoff between them, just as there is no tradeoff between building subways and light rail in a city and building intercity rail. However, they have one key characteristic leading to conflict: they run on mainline track. This means that transportation planners have to decide whether to use existing mainline tracks for S-Bahn or RegionalBahn service.

Using different language, I talked about this dilemma in Boston’s context in 2012. The situation of Boston is instructive even in other cities, even outside the United States, purely because its commuter rail service is so bad that it can almost be viewed as blank slate service on existing infrastructure. On each of the different lines in Boston, it’s worth asking what the highest and best use for the line is. This really boils down to two questions:

1. Would the line fill a service need for intra-urban travel?
2. Does the line connect to important outlying destinations for which high speed would be especially beneficial?

In Boston, the answer to question 1 is for the most part no. Thirty to forty years ago the answer would have been yes for a number of lines, but since then the state has built subway lines in the same rights-of-way, ignorant of the development of the S-Bahn concept across the Pond. The biggest exceptions are the Fairmount Line through Dorchester and the inner Fitchburg Line through suburbs of Cambridge toward Brandeis.

On the Fairmount Line the answer to question 2 is negative as well, as the line terminates within Boston, which helps explain why the state is trying to invest in making it a useful S-Bahn with more stops, just without electrification, high frequency, fare integration, or through-service north of Downtown Boston. But on the Fitchburg Line the answer to question 2 is positive, as there is quite a lot of demand from suburbs farther northwest and a decent anchor in Fitchburg itself.

The opposite situation to that of Fairmount is that of the Providence Line. Downtown Providence is the largest job center served by the MBTA outside Boston; the city ranks third in New England in number of jobs, behind Boston and Cambridge and ahead of Worcester and Hartford. Fast service between Providence and Boston is obligatory. However, Providence benefits from lying on the Northeast Corridor, which can provide such service if the regional trains are somewhat slower; this is the main justification for adding a handful of infill stops on the Providence Line.

In New York, the situation is the most complicated, befitting the city’s large size and constrained location. On most lines, the answers to both questions is yes: there is an urban rail service need, either because there is no subway service (as in New Jersey) or because there is subway service and it’s overcrowded (as on the 4/5 trains paralleling the Metro-North trunk and on the Queens Boulevard trains paralleling the LIRR trunk); but at the same time, there are key stations located quite far from the dense city, which can be either suburban centers 40 km out or, in the case of New Haven, an independent city more than 100 km out.

Normally, in a situation like New York’s, the solution should be to interline the local lines and keep the express lines at surface terminals; London is implementing this approach line by line with the Crossrail concept. Unfortunately, New York’s surface terminals are all outside Manhattan, with the exception of Grand Central. Penn Station has the infrastructure for through-running because already in the 1880s and 90s, the ferry transfers out of New Jersey and Brooklyn were onerous, so the Pennsylvania Railroad invested in building a Manhattan station fed by east-west tunnels.

I call for complete through-running in New York, sometimes with the exception of East Side Access, because of the island geography, which makes terminating at the equivalent of Gare du Nord or Gare de Lyon too inconvenient. In other cities, I might come to different conclusions – for example, I don’t think through-running intercity trains in Chicago is a priority. But in New York, this is the only way to guarantee good regional rail service; anything else would involve short- and long-range trains getting in each other’s way at Penn Station.

# Deutschlandtakt and Country Size

Does the absolute size of a country matter for public transport planning? Usually it does not – construction costs do not seem to be sensitive to absolute size, and the basics of rail planning do not either. That Europe’s most intensely used mainline rail networks are those of Switzerland and the Netherlands, two geographically small countries, is not really about the inherent benefits of small size, but about the fact that most countries in Europe are small, so we should expect the very best as well as the very worst to be small.

But now Germany is copying Swiss and Dutch ideas of nationally integrated rail planning, in a way that showcases where size does matter. For decades Switzerland has had a national clockface schedule in which all trains are coordinated for maximum convenience of interchange between trains at key stations. For example, at Zurich, trains regularly arrive just before :00 and :30 every hour and leave just after, so passengers can connect with minimum wait. Germany is planning to implement the same scheme by 2030 but on a much bigger scale, dubbed Deutschlandtakt. This plan is for the most part good, but has some serious problems that come from overlearning from small countries rather than from similar-size France.

In accordance with best industry practices, there is integration of infrastructure and timetable planning. I encourage readers to go to the Ministry of Transport (BMVI) and look at some line maps – there are links to line maps by region as well as a national map for intercity trains. The intercity train map is especially instructive when it comes to scale-variance: it features multihour trips that would be a lot shorter if Germany made a serious attempt to build high-speed rail like France.

Before I go on and give details, I want to make a caveat: Germany is not the United States. BMVI makes a lot of errors in planning and Deutsche Bahn is plagued by delays; these are still basically professional organizations, unlike the American amateur hour of federal and state transportation departments, Amtrak, and sundry officials who are not even aware Germany has regional trains. As in London and Paris, the decisions here are defensible, just often incorrect.

Run as fast as necessary

Switzerland has no high-speed rail. It plans rail infrastructure using the maxim, run trains as fast as necessary, not as fast as possible. Zurich, Basel, and Bern are around 100 km from one another by rail, so the federal government invested in speeding up the trains so as to serve each city pair in just less than an hour. At the time of this writing, Zurich-Bern is 56 minutes one-way and the other two pairs are 53 each. Trains run twice an hour, leaving each of these three cities a little after :00 and :30 and and arriving a little before, enabling passengers to connect to onward trains nationwide.

There is little benefit in speeding up Switzerland’s domestic trains further. If SBB increases the average speed to 140 km/h, comparable to the fastest legacy lines in Sweden and Britain, it will be able to reduce trip times to about 42 minutes. Direct passengers would benefit from faster trips, but interchange passengers would simply trade 10 minutes on a moving train for 10 minutes waiting for a connection. Moreover, drivers would trade 10 minutes working on a moving train for 10 minutes of turnaround, and the equipment itself would simply idle 10 minutes longer as well, and thus there would not be any savings in operating costs. A speedup can only fit into the national takt schedule if trains connect each city pair in just less than half an hour, but that would require average speeds near the high end of European high-speed rail, which are only achieved with hundreds of kilometers of nonstop 300 km/h running.

Instead of investing in high-speed rail like France, Switzerland incrementally invests in various interregional and intercity rail connections in order to improve the national takt. To oversimplify a complex situation, if a city pair is connected in 1:10, Switzerland will invest in reducing it to 55 minutes, in order to allow trains to fit into the hourly takt. This may involve high average speeds, depending on the length of the link. Bern is farther from Zurich and Basel than Zurich and Basel are from each other, so in 1996-2004, SBB built a 200 km/h line between Bern and Olten; it has more than 200 trains per day of various speed classes, so in 2007 it became the first railroad in the world to be equipped with ETCS Level 2 signaling.

With this systemwide thinking, Switzerland has built Europe’s strongest rail network by passenger traffic density, punctuality, and mode share. It is this approach that Germany seeks to imitate. Thus, the Deutschlandtakt sets up control cities served by trains on a clockface schedule every 30 minutes or every hour. For example, Erfurt is to have four trains per hour, two arriving just before :30 and leaving just after and two arriving just before :00 and leaving just after; passengers can transfer in all directions, going north toward Berlin via either Leipzig or Halle, south toward Munich, or west toward Frankfurt.

Flight-level zero airlines

Richard Mlynarik likes to mock the idea of high-speed rail as conceived in California as a flight-level zero airline. The mockery is about a bunch of features that imitate airlines even when they are inappropriate for trains. The TGV network has many flight-level zero airline features: tickets are sold using an opaque yield management system; trains mostly run nonstop between cities, so for example Paris-Marseille trains do not stop at Lyon and Paris-Lyon trains do not continue to Marseille; frequency is haphazard; transfers to regional trains are sporadic, and occasionally (as at Nice) TGVs are timed to just miss regional connections.

And yet, with all of these bad features, SNCF has higher long-distance ridership than DB, because at the end of the day the TGVs connect most major French cities to Paris at an average speed in the 200-250 km/h range, whereas the fastest German intercity trains average about 170 and most are in the 120-150 range. The ICE network in Germany is not conceived as complete lines between pairs of cities, but rather as a series of bypasses around bottlenecks or slow sections, some with a maximum speed of 250 and some with a maximum speed of 300. For example, between Berlin and Munich, only the segments between Ingolstadt and Nuremberg and between Halle and north of Bamberg are on new 300 km/h lines, and the rest are on upgraded legacy track.

Even though the maximum speed on some connections in Germany is the same as in France, there are long slow segments on urban approaches, even in cities with ample space for bypass tracks, like Berlin. The LGV Sud-Est diverges from the classical line 9 kilometers outside Paris and permits 270 km/h 20 kilometers out; on its way between Paris and Lyon, the TGV spends practically the entire way running at 270-300 km/h. No high-speed lines get this close to Berlin or Munich, even though in both cities, the built-up urban area gives way to farms within 15-20 kilometers of the train station.

The importance of absolute size

Switzerland and the Netherlands make do with very little high-speed rail. Large-scale speedups are of limited use in both countries, Switzerland because of the difficulty of getting Zurich-Basel trip times below half an hour and the Netherlands because all of its major cities are within regional rail distance of one another.

But Germany is much bigger. Today, ICE trains go between Berlin and Munich, a distance of about 600 kilometers, in just less than four hours. The Deutschlandtakt plan calls for a few minutes’ speedup to 3:49. At TGV speed, trains would run about an hour faster, which would fit well with timed transfers at both ends. Erfurt is somewhat to the north of the midpoint, but could still keep a timed transfer between trains to Munich, Frankfurt, and Berlin if everything were sped up.

Elsewhere, DB is currently investing in improving the line between Stuttgart and Munich. Trains today run on curvy track, taking about 2:13 to do 250 km. There are plans to build 250 km/h high-speed rail for part of the way, targeting a trip time of 1:30; the Deutschlandtakt map is somewhat less ambitious, calling for 1:36, with much of the speedup coming from Stuttgart21 making the intercity approach to Stuttgart much easier. But with a straight line distance of 200 km, even passing via Ulm and Augsburg, trains could do this trip in less than an hour at TGV speeds, which would fit well into a national takt as well. No timed transfers are planned at Augsburg or Ulm. The Baden-Württemberg map even shows regional trains (in blue) at Ulm timed to just miss the intercity trains to Munich. Likewise, the Bavaria map shows regional trains at Augsburg timed to just miss the intercity trains to Stuttgart.

The same principle applies elsewhere in Germany. The Deutschlandtakt tightly fits trains between Munich and Frankfurt, doing the trip in 2:43 via Stuttgart or 2:46 via Nuremberg. But getting Munich-Stuttgart to just under an hour, together with Stuttgart21 and a planned bypass of the congested Frankfurt-Mannheim mainline, would get Munich-Frankfurt to around two hours flat. Via Nuremberg, a new line to Frankfurt could connect Munich and Frankfurt in about an hour and a half at TGV speed; even allowing for some loose scheduling and extra stops like Würzburg, it can be done in 1:46 instead of 2:46, which fits into the same integrated plan at the two ends.

The value of a tightly integrated schedule is at its highest on regional rail networks, on which trains run hourly or half-hourly and have one-way trip times of half an hour to two hours. On metro networks the value is much lower, partly because passengers can make untimed transfers if trains come every five minutes, and partly because when the trains come every five minutes and a one-way trip takes 40 minutes, there are so many trains circulating at once that the run-as-fast-as-necessary principle makes the difference between 17 and 18 trainsets rather than that between two and three. In a large country in which trains run hourly or half-hourly and take several hours to connect major cities, timed transfers remain valuable, but running as fast as necessary is less useful than in Switzerland.

The way forward for Germany

Germany needs to synthesize the two different rail paradigms of its neighbors – the integrated timetables of Switzerland and the Netherlands, and the high-speed rail network of France.

High investment levels in rail transport are of particular importance in Germany. For too long, planning in Germany has assumed the country would be demographically stagnant, even declining. There is less justification for investment in infrastructure in a country with the population growth rate of Italy or of last decade’s Germany than in one with the population growth rate of France, let alone one with that of Australia or Canada. However, the combination of refugee resettlement and a very strong economy attracting European and non-European work migration is changing this calculation. Even as the Ruhr and the former East Germany depopulate, we see strong population growth in the rich cities of the south and southwest as well as in Berlin.

The increased concentration of German population in the big cities also tilts the best planning in favor of the metropolitan-centric paradigm of France. Fast trains between Berlin, Frankfurt, and Munich gain value if these three cities grow in population whereas the smaller towns between them that the trains would bypass do not.

The Deutschlandtakt’s fundamental idea of a national integrated timed transfer schedule is good. However, a country the size and complexity of Germany needs to go beyond imitating what works in Switzerland and the Netherlands, and innovate in adapting best practices for its particular situation. People keep flying domestically since the trains take too long, or they take buses if the trains are too expensive and not much faster. Domestic flights are not a real factor in the Netherlands, and barely at all in Switzerland; in Germany they are, so trains must compete with them as well as with flexible but slow cars.

The fact that Germany already has a functional passenger rail network argues in favor of more aggressive investment in high-speed rail. The United States should probably do more than just copy Switzerland, but with nonexistent intercity rail outside the Northeast Corridor and planners who barely know that Switzerland has trains, it should imitate rather than innovating. Germany has professional planners who know exactly how Germany falls short of its neighbors, and will be leaving too many benefits on the table if it decides that an average speed of about 150 km/h is good enough.

Germany can and should demand more: BMVI should enact a program with a budget in the tens of billions of euros to develop high-speed rail averaging 200-250 km/h connecting all of its major cities, and redo the Deutschlandtakt plans in support of such a network. Wedding French success in high-speed rail and Swiss and Dutch success in systemwide rail integration requires some innovative planning, but Germany is capable of it and should lead in infrastructure construction.

# Massachusetts Sandbags Rail Electrification

In the last year, Massachusetts has been studying something called the Rail Vision, listing several alternatives for commuter rail modernization. This has been independent of the North-South Rail Link study, and one of the options that the Rail Vision considered was full electrification. Unfortunately, the report released yesterday severely sandbags electrification, positing absurdly high costs. The state may well understand how bad its report is – at least as of the time of this writing, it’s been scrubbed from the public Internet, forcing me to rely on screencaps.

In short: the alternative that recommends full system electrification was sandbagged so as to cost \$23 billion. This is for electrification, systems, and new equipment; the NSRL tunnel is not included. All itemized costs cost a large multiple of their international cost. The Americans in my feed are even starting to make concessions to extremely expensive projects like the Caltrain electrification, since the proposed MBTA electrification is even costlier than that.

But the telltale sign is not the cost of the wires, but rolling stock. The report asserts that running electrified service requires 1,450 cars’ worth of electric multiple units (“EMUs”), to be procured at a cost of \$10 billion. More reasonable figures are 800 and \$2 billion respectively.

Why 1,450 cars?

The all-electric option assumes that every line in the system will get a train every 15 minutes, peak and off-peak. What counts as a line is not clear, since some of the MBTA’s commuter lines have branches – for example, the Providence and Stoughton Lines share a trunk for 24 km, up to Canton Junction. However, we can make reasonable assumptions about which branches are far enough out; overall rolling stock needs are not too sensitive to these assumptions, as most lines are more straightforward.

The MBTA is capable of turning trains in 10 minutes today. In making schedules, I’ve mostly stuck to this assumption rather than trying to go for 5-minute turnarounds, which happen in Germany all the time (and on some non-mainline American subways); occasionally trains steal 1-2 minutes’ worth of turnaround time, if there’s a longer turn at the other end. Thus, if the one-way trip time is up to 50 minutes, then 8 trainsets provide 15-minute service.

To me, high-frequency regional rail for Boston means the following peak frequencies:

Providence/Stoughton: a train every 15 minutes on each branch. Service south of Providence is spun off to a Rhode Island state service, making more stops and running shorter trains as demand is weaker than commuter volumes to Boston. With this assumption, the Providence Line requires 7-8 trainsets. The Stoughton Line, with the South Coast Rail expansion to New Bedford and Fall River, each served every half hour, requires around 9-10. Say 18 sets total.

Worcester: the big question is whether to exploit the fast acceleration of EMUs to run all-local service or mix local and express trains on tracks in Newton that will never be quadrupled unless cars are banned. The all-local option has trains doing Boston-Worcester in just under an hour, so 9-10 trainsets are required. The mixed option, with a train every 15 minutes in each pattern, and local trains only going as far as Framingham, requires 14 sets, 8 express and 6 local.

Franklin/Fairmount: a train every 15 minutes on the Franklin Line, entering city center via the Fairmount Line, would do the trip in around 50 minutes. It may be prudent to run another train every 15 minutes on the Fairmount Line to Readville, a roughly 17-minute trip by EMU (current scheduled time with diesel locomotives: 30 minutes). Overall this is around 12 trainsets.

Old Colony Lines: there are three lines, serving very low-density suburbs. The only destinations that are interesting for more than tidal commuter rail are Plymouth, Brockton, Bridgewater State, and maybe an extension to Cape Cod. Each branch should get a train every 30 minutes, interlining to a train every 10 from Quincy Center to the north. About 10-12 trainsets are needed (2 more if there’s an hourly train out to Cape Cod); this is inefficient because with three branches, it’s not possible to have all of them depart South Station at :05 and :35 and arrive :25 and :55, so even if there’s a train every 15 minutes per branch, the requirement doesn’t double.

Fitchburg Line: a local train to Wachusett every 15 minutes would require around 12 sets (75 minutes one-way). The number may change a little if there’s an overlay providing service every 7.5 minutes to Brandeis, or if trains beyond South Acton only run every half hour.

Lowell Line: an EMU to Lowell would take about 27 minutes, depending on the stop pattern; 5 trainsets provide 15-minute frequency.

Haverhill Line: an EMU to Haverhill running the current route (not via the Wildcat Branch) would take about 40 minutes, so 7 trainsets provide a train every 15 minutes.

Eastern Lines: like the Old Colony Lines, this system has very low-density outer branches, with only one semi-reasonable outer anchor in Newburyport. Trains should run to Beverly every 10 minutes, and then one third should turn, one third should go to Rockport, and one third should go to Newburyport. With the same inherent inefficiency in running this service on a symmetric schedule as the Old Colony, around 10-12 sets are needed.

This is about 90 sets total. At eight cars per set, and with a spare ratio of 11%, the actual requirement is 800 cars, and not 1,450. The difference with the state’s assumption is likely that I’m assuming trains can run at the acceleration rates of modern EMUs; perhaps the state thinks that EMUs are as slow and unreliable as diesel locomotives, so a larger fleet is necessary to provide the same service.

Rolling stock costs

Reducing the cost of infrastructure is complicated, because it depends on local factors. But reducing the cost of industrial equipment is easy, since there are international vendors that make modular products. Factories all over Europe, Japan, and South Korea make this kind of equipment, and the European factories barely require any modifications to produce for the American market under current federal regulations.

It is not hard to go to Railway Gazette and search for recent orders for EMUs; names of trainsets include Talent, FLIRT, Mireo (cost information here) and Coradia. The linked Coradia order is for €96,500 per meter of train length, the other three orders are for about €70,000. A US-length (that is, 25 meters) car would cost around \$2.5 million at this rate. 800 cars times \$2.5 million equals \$2 billion, not the \$10 billion the MBTA claims.

Railway Gazette also discusses a maintenance contract: “Vy has awarded Stadler a contract worth nearly SFr100m for the maintenance in 2020-24 of more than 100 five-car Flirt EMUs.” These trains are 105 meters long; scaled to US car length, this means the annual maintenance cost of an EMU car is around \$50,000, or \$40 million for the entire fleet necessary for electrified service.

The actual net cost is even lower, since the MBTA needs to replace its rolling stock very soon anyway. If the choice is between 800 EMUs and a larger diesel fleet, the EMUs are cheaper; in effect, the rolling stock cost of electrification is then negative.

Why are they like this?

I struggle to find a problem with Boston’s transportation network that would not be alleviated if Massachusetts’ secretary of transportation Stephanie Pollack and her coterie of hacks, apparatchiks, and political appointees were all simultaneously fired.

There is a chain of command in the executive branch of the Massachusetts state government. Governor Charlie Baker decides that he does not want to embark on any big project, such as NSRL or rail electrification, perhaps because he is too incompetent to manage it successfully. He then intimates that such a project is unaffordable. Secretary Pollack responds by looking for reasons why the project is indeed unaffordable. Under pressure to deliver the required results, the planners make up outrageously high figures: they include fleet replacement in the electrified alternative but not in the unelectrified one (“incremental cost”), and then they lie about the costs by a factor of five.

Good transit activists can pressure the state, but the state has no interest in building good transit. The do-nothing governor enjoys no-build options and multi-billion dollar tweaks – anything that isn’t transformative is good to him. The do-nothing state legislature enjoys this situation, since it is no more capable of managing such a project, and having a governor who says no to everything enables it to avoid taking responsibility.

# West Station is an Overbuilt Mess

Boston has been on a commuter rail infill binge lately; it has opened four stations on the Fairmount Line this decade, with general success, and is now eying the Worcester Line, where the MBTA has already opened a single in-city station called Boston Landing. The next station to be opened is called West Station, serving Allston, a middle-class urban neighborhood home to Boston University. Unfortunately, the West Station project has suffered from budget and schedule overruns: the current projection is \$90 million, where past stations in the area have opened for about \$15-25 million each, and construction will start next decade and only wrap up by 2040.

The cause of the extreme cost is poor design. The station as currently proposed is an overbuilt mess. It is development-oriented transit, sited next to an area that Harvard wishes to redevelop as a new campus, and the compromises made between good rail service, intermodal bus-rail connections, and encouraging development make the project fail at all of its objectives. The idea of an infill station in Allston is solid and the MBTA should keep working on the project, but it should do it right – that is, maximize passenger utility while also slashing the budget by a factor of about 4.

I encourage readers to look at a presentation about the status of the project from May, and at another presentation from June, which was sent to members of the media and neighborhood.

Intermodal integration done wrong

The West Station site is roughly in the center of the new development. Unfortunately, it is poorly-located relative to the street network. With its hierarchy of major and minor streets, Boston is not forgiving to wrong station siting: buses would have to meander to reach the site.

The busiest bus in the area, and among the busiest in the region, is the 66. See image below:

The Red and Green Lines of the subway are in their respective colors (and the Green Line’s branches are surface light rail), the Worcester Line is in purple with its existing stations marked alongside the proposed West Station site, and the 66 bus is in black. The dashed purple line is the disused Grand Junction Railroad – see below for more explanation.

North of the West Station site, the bus could still reach the platforms relatively easily, as the plan includes mapping new streets over the entire site. But to the south, the streets are narrow and practically unusable. All north-south through-traffic is funneled through Harvard Avenue – anything else would meander at speeds not much higher than that of walking.

What’s more, the zigzag in the image above comes from a detour to the center of Allston, called Union Square. The West Station site would move service farther away from Union Square, forcing it to either abandon its single busiest stop or have a more circuitous route. Serving both West Station and Union Square requires running two separate north-south bus routes sharing much of their southern legs, which is bad for frequency. Already the 66 runs every 10 minutes off-peak in one direction and every 14 in the other; this is worse than the minimum acceptable on such a key route, and any further reduction in frequency through route splitting is unacceptable.

Finally, the station design as shown in the presentations includes ample room for bus bays, so that buses can terminate at the station. Such a layout may be appropriate at the center of a small town with timed bus-rail transfers; in the middle of the city, it is pointless. The 66 crosses the rail tracks and has no use for terminal berths. Nor is there any need for terminating buses running parallel to the tracks – passengers could walk to another train station on the Worcester Line or on the Green Line.

The MBTA has never released any public plan for a bus redesign around West Station. It talks about intermodal transfers but refuses to give any details, and it’s likely these details don’t even exist yet. There are occasional excuses, such as intercity buses (why would they terminate there instead of continuing to South Station?), buses to Kendall Square (they don’t need bus bays either), and buses to Longwood (Longwood is south of the Worcester Line and would be better-served by a commuter rail-to-Green Line transfer near Fenway Park).

Track design for maximum conflict

The latest option for West Station is called the flip option. The diagrams below are from the June presentation, pp. 8-10, going west to east:

There are to be two bypass tracks (“WML Express”), located where the current mainline is. There are also to be three tracks with station access, both on the other side of the railyard. The tracks serving the platforms cross the bypass tracks in a flat junction, forcing dependency between the inbound and outbound schedule. The flat junction is not especially quick, either – it is a long ladder track, requiring inbound local trains to South Station to make two slow diverging moves in succession.

The MBTA is planning to spend tens of millions of dollars on station platforms in Newton turning the line into full double-track all the way from Boston to Worcester, freeing the schedule from such dependency, but at the same time it’s planning to add new conflicts.

While the diagrams label two tracks as freight tracks, there is little to no freight on that portion of the line. A freight rail spur in the area, serving Houghton Chemical, was just removed in preparation for the project. The line can and should be designed exclusively around the needs of regional passenger trains, for which the most important thing is continuous operation of double track, preferably with no flat junctions with oncoming traffic, and not any ancillary frills.

The Grand Junction tangential

The MBTA has grandiose plans to use the Grand Junction Railroad to allow trains from Allston and points west to avoid South Station entirely. The Grand Junction provides a bypass to the west of Downtown Boston, which currently sees no passenger service but is used for non-revenue moves between the South Station and North Station networks. There are periodic plans to reactive service so as to enable trains from the west to serve Cambridge and North Station instead. In the flip option, all local trains are required to go to the Grand Junction or switch back to the mainline using the ladder track.

Consult the following table, sourced to OnTheMap, for the number of jobs accessible within walking distance of the various station sites:

 Station Walkshed boundaries Jobs South Station Essex, Tremont, State, the harbor 119,191 Back Bay Hereford, Belvidere, Columbus, Arlington, Storrow 62,513 Kendall Binney, Third, Wadsworth, Memorial, Mass Ave, Windsor, Bristol 29,248 North Station Blossom, Cambridge, State, Prince, the river 33,232

Jobs accessible on the existing mainline outnumber ones accessible via the Grand Junction by a factor of about three. It is not technically sound to avoid city center on an urban rail line, much less a suburban one. Only if the line is a consistent circumferential line is there a good reason to go around the center.

A far-future subway duplicating the 66 route may succeed. The same may be true of a shuttle using the Grand Junction, but such shuttle may well need extensive new track – West Station is not necessarily the best south-of-Charles footprint (turning east toward BU to form a loop with a future North-South Rail Link is better). In contrast, the current plan for diversion of Newton trains toward a secondary job center and away from Downtown Boston has no chance of getting substantial ridership.

The railyard as an obstacle

For a project so focused on redevelopment, West Station does not do a good job encouraging construction in the area. It plans to keep the railyard in the middle, and even forces local and express trains to go on opposite sides of it. But the railyard is an obstacle not only to sound railway operations but also to redevelopment.

Building anything over rail tracks is complicated. New York supplies a few such examples: the link mentions the difficulties of Atlantic Yards, and to that I will add that the construction of the Hudson Yards towers cost around \$12,000/m^2, compared with \$3,000-6,000 for Manhattan supertall office towers on firma. Hudson Yards has managed to be financially successful, albeit with tax breaks, but it’s located right outside Midtown Manhattan. Allston’s location is not so favored. The cost penalty of building over railyards is likely to make air rights unviable.

There is still an extensive portion of the site that’s on firma. However, if the point is to maximize redevelopment potential, the city and the state must discard any plans for air rights. The railyard should go in order to increase the buildable area.

In lieu of parking at a railyard in a desirable near-center location, trains should circulate back and forth between Boston and Worcester. The MBTA keeps saddling itself with capital costs because it likes running trains one-way to Downtown Boston in the morning and then back to the suburbs in the afternoon, parking them near South Station midday. This is bad practice – trains are not just for suburban salarymen’s commutes. Urban infill stations in particular benefit from high all-day frequency and symmetric service. If the MBTA needs space for train parking, it should sell the railyard in Allston and charge Allston land prices, and instead buy space in Framingham and Worcester for Framingham and Worcester land prices.

West Station, done right

Thanks to delays and cost overruns, West Station is still in preliminary design. There is plenty of time to discard the flip option as well as the original plan in favor of a route that maximizes intermodal connections at minimum cost. A better West Station should have all of the following features:

• A simple four-track design, either with two stopping tracks and two bypass tracks or four stopping tracks and two island platforms, depending on long-term plans for train timetables
• High design speed, as high as the rest of the line for nonstop trains, as the tracks are straight and do not require any speed restriction
• Retention of double-track rail service throughout construction, even at the cost of more disruption to the Massachusetts Turnpike
• No at-grade conflicts in opposing directions: tracks should go slow-fast-fast-slow or fast-slow-slow-fast rather than slow-slow-fast-fast
• No bus bays: crosstown buses (that is, the 66) should stop on the street crossing the station right above the tracks, with vertical circulation directly from the bus stop to the platform in order to minimize transferring time
• Subject to site availability, platforms reaching Cambridge Street for a connection to the present-day 66 and a shorter walk to Union Square
• Elimination of the railyard to make more room for development, and if the line needs more yard space, then the state should find cheaper land for it in Framingham and Worcester

There is no reason for such a project to cost more than past infill stations built in Boston, which have cost around \$15-25 million, about the same range as Berlin. By removing unnecessary scope, the MBTA can make West Station not only cheaper and easier to build but also more useful for passengers. The idea of an infill commuter rail station in Allston is good and I commend the MBTA for it, but the current plan is overbuilt and interferes with good rail and bus operations and needs to be changed immediately, in advance of engineering and construction.

# Assume Nordic Costs: London Edition

A month ago I made maps proposing some subway and regional rail extensions in New York and noting what they would cost if New York could build as cheaply as the Scandinavian capitals. Here is the same concept, but with London rather than New York. Here is everything in a single large map:

A full-size (74 MB) map can be viewed here.

Solid lines are existing or under construction, that is Crossrail and the Battersea extension; proposed lines are dashed. Commuter rail lines, that is Thameslink, the soon-to-open Crossrail, and four additional Crossrail tunnels labeled 2 through 5, are always depicted as having separate stations from the other modes, to avoid confusion where one Crossrail station has connections to two adjacent Tube stations (such as Farringdon-Barbican and Moorgate-Liverpool Street). It has many additional interchanges between lines and branches, including some that were left out on purpose, like a Crossrail 1 connection to Oxford Circus, omitted from the under-construction line to discourage riders from using the oversubscribed Victoria line; with four more cross-city lines, the capacity problems would be lessened substantially.

The overall picture is sparser than my New York map. The total projected cost of all of these projects, including some allocated for redoing stations on commuter branches to be given to Tube lines, is £6.8 billion, compared with \$37 billion for the New York maps. The reason is that unlike New York, London already has excellent coverage thanks to extensive branching – what it needs is core capacity, which consists of city center tunnels that have high cost per kilometer but need not be long.

There is considerable overbuilding planned in London. Crossrail 2 as depicted on my map is a 6.5 km tunnel between the approach to Victoria Station and the approach to Kings Cross. But as planned, Crossrail 2 extends to a long tunnel parallel to the South West Main Line, a four-track line in a right-of-way that could if truly necessary accommodate six, as well as a long tunnel going north to take over the Lea Valley Lines, which on my map go into Crossrail 5. With gratuitous suburban tunnels and extremely high British construction costs, the budget for Crossrail 2 is around £30 billion, about 20 times what Scandinavia might spend on such a project. Even allowing for the possibility that crossing under three lines at once at Bank is more complex than crossing under two at T-Centralen, this is a difference of a full order of magnitude, counting both total required tunnel length and cost per km.

In addition, there is network simplification. On the Tube this consists of segregating the Northern line’s Bank and Charing Cross branches (already in planning pending the Battersea extension and reconstruction of Camden Town) and through breaking the Circle line into separate Metropolitan and District lines. The latter was estimated by a British blogger to cost £5 billion, based on a rubric in which the Met/District transfer at Aldgate (or Tower Hill) should by itself cost £1 billion; Crossrail and Second Avenue Subway stations cost around half that much, and the more complex T-Centralen and Odenplan stations on Citybanan cost less.

On mainline rail, the service plan is supposed to be deinterlined, as is Transport for London’s long-term goal. The slow tracks of the various mainlines feeding into Central London turn into Crossrail branches, or occasionally Underground extensions, such as Hayes and the Hounslow Loop. The fast tracks stay on the surface to avoid interfering with high-frequency regional metro service. For historic reasons Thameslink mostly stays as-is, with a combination of fast and stopping services, but the curve toward London Bridge should not be used – instead, passengers should have access to Crossrail 3 plus interchanges to the City at London Bridge and a new infill station at Southwark.

London owes it to itself to understand why its construction costs are so high that instead of solving its transport capacity problems with multiple cross-city tunnels in a decade, it’s taking multiple generations to build out such a system. There’s a lot of ongoing discussion about the last-minute delays and cost overruns on Crossrail, but the absolute costs even before the overrun were very high, the highest in the world outside New York City – and Crossrail 2 is set to break that record by a margin.

# Assume Nordic Costs

I wrote a post last year proposing some more subway lines for New York, provided the region could bring down construction costs. The year before, I talked about regional rail. Here are touched-up maps, with costs based on Nordic levels. To avoid cluttering the map in Manhattan, I’m showing subway and regional rail lines separately.

A full-size 52 MB version of the subway map can be found here and a 52 MB version of the regional rail map can be found here.

Subways are set at \$110 million per km underground, outside the Manhattan core; in more difficult areas, including underwater they go up to \$200-300 million per km, in line with Stockholm Citybanan. Lacking data for els, I set them at \$50 million per km, in line with normal subway : el cost ratios. The within-right-of-way parts of Triboro are still set at \$20 million per km (errata 5/30: 32 out of 35 km are in a right-of-way and 3 are in a new subway, despite what the map text says, but the costs are still correct).

Overall, the subway map costs \$22 billion, and the regional rail one \$15 billion, about half as high as the figure I usually quote when asked, which is based on global averages. This excludes the \$2 billion for separated intercity rail tracks, which benefit from having no stations save Penn (by the same token, putting the express rather than local lines in the tunnel is a potential cost saving for Crossrail 2). It also excludes small surface projects, such as double-tracking the Northern Branch and West Shore Line, a total of 25 and 30 km respectively, which should be \$300-550 million in total, and some junction fixes. There may also be additional infill stations on commuter rail, e.g. at intersection points with new subway extensions; I do not have Nordic costs for them, but in Madrid they cost €9 million each.

The low cost led me to include some lines I would not include elsewhere, and decide marginal cases in favor of subways rather than els. There is probably no need for the tunnel connecting the local tracks of Eighth Avenue and Fulton Street Lines, but at just \$1.2 billion, it may be worth it. The line on Northern Boulevard and the Erie Main Line should probably be elevated or in a private right of way the entire way between the Palisades and Paterson, but at an incremental cost of \$60 million per km, putting the Secaucus and East Rutherford segments underground can be justified.

In fact, the low cost may justify even further lines into lower-density areas. One or two additional regional rail tunnels may be cost-effective at \$300 million per kilometer, separating out branches like Port Washington and Raritan Valley and heading to the airports via new connections. A subway line taking over lanes from the Long Island Expressway may be useful, as might another north-south Manhattan trunk feeding University Avenue (or possibly Third Avenue) in the Bronx and separating out two of the Brighton Line tracks. Even at average costs these lines are absurd unless cars are banned or zoning is abolished, but at low costs they become more interesting.

The Nordic capitals all have extensive urban rail networks for their sizes. So does Madrid: Madrid and Berlin are similar in size and density, but Berlin has 151 km of U-Bahn whereas Madrid has 293 km of metro, and Madrid opened a second Cercanías tunnel in 2008 for around \$100 million per km and is planning a third tunnel for next decade (source, PDF-pp. 104-108). Things that are completely ridiculous at American costs – say, any future subway expansion – become more reasonable at average costs; things that are completely ridiculous at average costs likewise become more reasonable at Nordic or Spanish costs.

# Amtrak is Blocking MBTA Electrification

Ten years ago, Amtrak began putting out its outrageously expensive proposals for high-speed rail on the Northeast Corridor. Already then, when it asked for \$10 billion to barely speed up trains, there was a glaring problem with coordination: Amtrak wanted hundreds of millions of dollars to three-track the Providence Line so that its trains could overtake the MBTA’s commuter trains between Providence and Boston, even though the same benefit could be obtained for cheaper by building strategic overtakes and electrifying the MBTA so that its trains would run faster. Unfortunately, Amtrak has not only displayed no interest in coordinating better service with the MBTA this way, but has just actively blocked the MBTA.

The issue at hand is MBTA electrification: the MBTA runs an exclusively diesel fleet. These trains are slow, polluting, and unreliable. Lately they have had breakdowns every few thousand kilometers, whereas electric trains routinely last multiple hundreds of thousands of kilometers between breakdowns. The current scheduled trip time between Boston and Providence is about 1:10 on the MBTA with a total of nine stops, whereas Amtrak’s southbound trains do the same trip in 35 minutes with three stops, leading to a large schedule difference between the trains, requiring overtaking. Fortunately, modern electric multiple units, or EMUs, could make the same stops as the MBTA in about 45 minutes, close enough to Amtrak that Amtrak could speed up its trains without conflict.

The MBTA would benefit from electrification without any reference to Amtrak. Connecting Boston and Providence in 45 minutes rather than 70 has large benefits for suburban and regional travelers, and the improved reliability means trains can follow the schedule with fewer unexpected surprises. The line is already wired thanks to Amtrak’s investment in the 1990s, and all that is required is wiring a few siding and yard tracks that Amtrak did not electrify as it does not itself use them. With the diesel locomotives falling apart, the MBTA has begun to seriously consider electrifying.

Unfortunately, the MBTA has made some questionable decisions, chief of which is its attempt to procure electric locomotives rather than self-propelled EMUs. The MBTA’s reasoning is that EMUs require high platforms, which cost about \$10 million per station, which is a small but nonzero amount of money on the Providence Line. As a result, it neglected any solution involving buying new EMUs or even leasing them from other railroads for a pilot project. It’s only looking at electric locomotives, whose travel time benefits are about half as large as those of EMUs.

And yet, Amtrak is blocking even the half-measures. The MBTA sought to lease electric locomotives from Amtrak, which uses them on its own trains; Amtrak quoted an unreasonably high monthly price designed to get the MBTA to lose interest. As of last week, the MBTA put the plan to lease electric locomotives for its electrification pilot on hold. No plans for purchase of rolling stock are currently active, as the MBTA is worried about lead time (read: having to actually write down and execute a contract) and does not know how to buy lightly-modified European products on the open market.

As far as Amtrak is concerned, speeding up the MBTA is not really relevant. Yes, such a speedup would improve Amtrak’s own scheduling, removing a few minutes from the Northeast Corridor’s travel time that would otherwise cost hundreds of millions of dollars. But Amtrak has time and time again displayed little interest in running fast trains. All it wants is money, and if it can ask for money without having to show anything for it, then all the better. Coordinating schedules with other railroads is hard, and only improves the experience of the passengers and not Amtrak’s managers.

The MBTA’s decisionmaking is understandable, in contrast, but still questionable. It was worth asking; the MBTA is no worse for having received an unreasonable offer. However, it is imperative that the MBTA understand that it must be more proactive and less hesitant. It must electrify, and commit a real budget to it rather than a pilot. This means immediately raising the platforms on the stations of the Providence Line that do not yet have level boarding and buying (not leasing) modern EMUs, capable of running fast schedules.

Even with some infill, there are only seven low-platform stations on the mainline and two on the branch to Stoughton, none in a constrained location where construction is difficult. This is at most a \$100 million project, excluding the trains themselves. The MBTA could operate the Providence Line with seven to eight trainsets providing service every 15 minutes and the Stoughton Line with another four providing the same. Procuring trains for such service would cost another \$250 million or so, but the MBTA needs to buy new rolling stock anyway as its diesel locomotives are past the end of their useful lives, and buying EMUs would pay for itself through higher ridership and lower operating expenses coming from much faster trips.

The MBTA is fortunately salvageable. It has a serious problem in that the state leadership is indecisive and noncommittal and prefers a solution that can be aborted cheaply to one that provides the best long-term financial and social return on investment. However, it is seriously looking in the right direction, consisting of better equipment providing higher-quality service to all passengers.

Amtrak is unfortunately not salvageable. An intercity railroad whose reaction to a commuter railroad’s attempt to improve service for both systems is to overcharge it on rolling stock proves that it is ignorant of, indifferent to, and incurious about modern rail operations. A chain of managers from the person who made the decision to offer the MBTA bad lease terms upward must be removed from their positions if there is any hope for improved intercity rail in the Northeastern United States.

# Optimization

This post may be of general interest to people looking at optimization as a concept; it’s something I wish I’d understood when I taught calculus for economics. The transportation context is network optimization – there is a contrast between the sort of continuous optimization of stop spacing and the discrete optimization of integrated timed transfers.

Minimum and maximum problems: short background

One of the most fundamental results students learn in first-semester calculus is that minimum and maximum points for a function occur when the derivative is zero – that is, when the graph of the function is flat. In the graph below, compare the three horizontal tangent lines in red with the two non-horizontal ones:

A nonzero derivative – that is, a tangent line slanting up or down – implies that the point is neither a local minimum nor a local maximum, because on one side of the point the value of the function is higher and on the other it is lower. Only when the derivative is zero and the tangent line is flat can we get a local extreme point.

Of course, a local extreme point does not have to be a global one. In the graph above, there are three local extreme points, two local maxima and one local minimum, but only the local maximum on the left is also a global maximum since it is higher than the local maximum on the right, and the local minimum is not a global minimum because the very left edge of the graph dips lower. In real-world optimization problems, the global optimum is one of the local ones, rather than an edge case like the global minimum of the above graph.

First-semester calculus classes love giving simplified min/max problems. This class of problems is really one of two or three serious calc 1 exercises; the other class is graphing a function, and the potential third is some integrals, at universities that teach the basics of integration in calc 1 (like Columbia and unlike UBC, which does so in calc 2). There’s a wealth of functions that are both interesting from a real-world perspective and doable by a first-semester calc student, for example maximizing the volume of some shape with prescribed surface area.

My formulas for stop spacing come from one of these functions. The overall travel time is a function of walking time, which increases as stops get farther apart, and in-vehicle time, which decreases as stops get farther apart. A certain stop spacing produces the minimum overall trip time; this is precisely the global minimum of the travel time function, which is ultimately of the form $f(x) = ax + b/x$ where a and b are empirical parameters depending on walking speed and other relevant variables.

Continuous optimization

The fundamental fact of continuous optimization, one I wish I’d learned in time to teach it to students, is that at the optimum the derivative is zero, and therefore making a small mistake in the value of the optimum is not a big problem.

What does “mistake” mean in this context? It does not mean literally getting the computation wrong. There is no excuse for that. Rather, it means choosing a value that’s slightly suboptimal for ancillary reasons – perhaps small discontinuities in the shape of the network, perhaps political considerations.

Paul Krugman brings this concept up in the context of wages. The theory of efficiency wages asserts that firms often pay workers above the bare minimum required to get any workers at all, in order to get higher-quality workers and incentivize them to work harder. In this theory, the wage level is set to maximize employer productivity net of wages. At the employer’s optimum the derivative of profit is by definition zero, so a small change in wages has little impact to the employer. However, to the workers, any wage increase is good, as their objective function is literally their wage rather than profits. They may engage in industrial action to raise wages, or push for favorable regulations like a high minimum wage, and these will have a limited effect on profits.

In the context of transit, this has the obvious implication to wages – it’s fine to set them somewhat above market rate since the agency will get better workers this way. But there are additional implications to other continuous variables.

With stop spacing specifically, the street network isn’t perfectly continuous. There are more important and less important streets. Getting transit stops to align with major streets is important, even if it forces the stop spacing to be somewhat different from the optimum. The same is true of ensuring that whenever two transit lines intersect, there is a transfer between them. This is the reason my bus redesign for Brooklyn together with Eric Goldwyn involved drawing the map before optimizing route spacing – the difference between 400 and 600 meters between bus stops is not that important. For the same reason, my prescription for Chicago, and generally other American cities with half-mile grids of arterial roads, is a bus stop every 400 meters, to align with the grid distance while still hewing close to the optimum, which is about 500.

When I talked about stop consolidation with a planner at New York City Transit who worked on the Staten Island express bus redesign, the planner explained the philosophy to me: “get rid of every other stop.” In the context of redesigning a single route, this is an excellent idea as well: the process of adding and removing bus stops in New York is not easy, so minimizing the net change by deleting stops at regular intervals so as to space the remaining stops close to the optimum is a good idea.

The world of public transit is full of these tradeoffs with continuous variables. It’s not just wages and interstations. Fares are another continuous variable, involving particular tensions as different political factions have different objective functions, such as revenue, social rate of return, and social rate of return for the working class alone. Frequency is a continuous variable too in isolation. Top speed for a regional train is in effect a continuous variable. All of these have different optimization processes, and in all cases, it’s fine to slightly deviate from the strict optimum to fulfill a different goal.

Discrete optimization

Whereas continuous optimization deals with flat tangent lines, discrete optimization may deal with delicate situations in which small changes have catastrophic consequences. These include connections between different lines, clockface scheduling, and issues of integration between different services in general.

An example that I discussed in the early days of this blog, and again in a position paper I just wrote to some New Hampshire politicians, is the Lowell Line, connecting Boston with Lowell, a distance of 41 km. The line is quite straight, and were it electrified and maintained better, trains could run at 160 km/h between stops with few slowdowns. The current stop spacing is such that the one-way trip time would be just less than half an hour. The issue is that it matters a great deal whether the trip time is 25 or 27 minutes. A 25-minute trip allows a 5-minute turnaround, so that half-hourly service requires just two trainsets. A 27-minute trip with half-hourly service requires three trainsets, each spending 27 minutes carrying passengers and 18 minutes depreciating at the terminal.

A small deterioration in trip time can literally raise costs by 50%. It gets to the point that extending the line another 50 kilometers north to Manchester, New Hampshire improves operations, because the Lowell-Manchester trip time is around 27-28 minutes, so the extension can turn a low-efficiency 27-minute trip into a high-efficiency 55-minute trip, providing half-hourly service with four trainsets.

In theory, frequency is a continuous variable. However, in the range relevant to regional rail, it is discrete, in fractions of an hour. Passengers can memorize a half-hourly schedule: “the inbound train leaves my stop at :10 and :40.” They cannot and will not memorize a schedule with 32-minute frequency, and needing to constantly consult a trip planner will degrade their travel experience significantly. Not even smartphone apps can square this circle. It’s telling that the smartphone revolution of the last decade has not been accompanied with rapid increase in ridership on transit lines without clockface schedules, such as those of the United States – if anything, ridership has grown faster in the clockface world, such as Germany and Switzerland.

Transit networks involving timed connections are another case of discrete optimization in which all parts of the network must work together, and small changes can make the network fall apart. If a train is late by a few minutes and its passengers miss their connection, the short delay turns into a long one for them. As a result, conscientious schedule planners make sure to write timetables with some contingency time to recover from delays; in Switzerland this is 7%, so in practice, out of every 15 minutes, one minute is contingency, typically spent waiting at a major station.

But this gets even more delicate, because different aspects of the transit network impact how reliable the schedule is. If it’s a bus, it matters how much traffic there is on the line. Buses in traffic not reliable enough for tight connections, so optimizing the network means giving buses dedicated lanes wherever there may be traffic congestion. Even though it’s a form of optimization, and even though there’s a measure of difficulty coming from political opposition by drivers, it is necessary to overrule the opposition, unlike in continuous cases such as wages and fares.

Infrastructure planning for rail has the same issues of discrete optimization. It is necessary to design complex junctions to minimize the ability of one late train to delay other trains. This can take the form of flying junctions or reducing interlining; in Switzerland there are also examples of pocket tracks at flat junctions where trains can wait without delaying other trains behind them. Then, the decision of how much to upgrade track speed, and even how many intermediate stations to allow on a line, has to come from the schedule, in similar vein to the Lowell Line’s borderline trip time.

Continuous and discrete optimization

Many variables relevant to transit are in theory continuous, such as trip time, frequency, stop spacing, wages, and fares. However, some of these have discontinuities in practice. Stop spacing on a real-world city street network must respect the hierarchy of more and less important destinations. Frequency and trip times are discrete variables except at the highest intensity of service, perhaps every 7.5 minutes or better; 11-minute frequency is worse to the passenger who has to memorize a difficult schedule than either 10- or 12-minute frequency.

New York supplies a great example showcasing how bad it can be to slavishly hew to some optimal interstation and not consider the street network. The Lexington Avenue Line has a stop every 9 blocks from 33rd Street to 96th, offset with just 8 blocks between 51st and 59th and 10 between 86th and 96th. In particular, on the Upper East Side it skips the 72nd and 79th Street arterials and serves the less important 68th and 77th Streets instead. As a result, east-west buses on the two arterials cross Lexington without a transfer.

Just east of Lex, there is also a great example of optimization on Second Avenue Subway. The stops on Second Avenue are at 72nd, 86th, and 96th, skipping 79th. It turns out that skipping 79th is correct – the optimum for the subway is to the meter the planned stop spacing for the line between 125th and Houston Streets, so it’s okay to have slightly non-uniform stop spacing to make sure to hit the important east-west streets.

Frequency and trip times are subject to the Swiss maxim, run trains as fast as necessary, not as fast as possible. Hitting trip times equal to an integer or half-integer number of hours minus a turnaround time has great value, but small further speedups do not. Passengers still benefit from the speedup, but the other benefits of higher speed to the network, such as better connections and lower crew costs, are no longer present.

The most general rule here is really that continuous optimization tolerates small errors, whereas discrete optimization does not. Therefore, it’s useful to do both kinds of optimization in isolation, and then modify the continuous variable somewhat based on the needs of the discrete one. If you calculate and find that the optimal frequency for your bus or train is once every 16 minutes, you should round it to 15, based on the discrete optimization rule that the frequency should be a divisor of the hour to allow for clockface timetable. If you calculate and find that the optimal bus stop spacing is 45% of the distance between two successive arterial streets, you should round it to 50% so that every arterial gets a bus stop.

Getting continuous optimization right remains important. If the optimal stop spacing is 500 meters and the current one is 200 meters, the network is so far from the local maximum of passenger utility that the derivative is large and stop consolidation has strong enough positive effects to justify overruling any political opposition. However, it is subsequently fine to veer from the optimum based on discrete considerations, including political ones if removing every 1.7th bus stop is harder than removing every other stop. Close to the local maximum or minimum, small changes really are not that important.

# Circles

Rail services can be lines or circles. The vast majority are lines, but circles exist, and in cities that have them they play an important niche. Owing to an overreaction, they are simultaneously overused and underused in different parts of the world. However, that some places overuse circles does not mean that circles are bad, nor does it mean that specific operational problems in certain cities are universal.

In particular, what I think of as the ideal urban rapid transit network should feature circles once the network reaches a certain scale, as in the following diagram that I use as my Patreon avatar:

Circles and circumferentials

Circles are transit lines that run in a loop without having a definitive start or end. Circumferentials are lines that go around city center, connecting different branches without passing through the most congested part of the city. In the ideal diagram above, the purple line is both a circle and a circumferential. However, lines can be one without being the other, and in fact examples of lines that are only one of the two outnumber examples of lines that are both.

For example, here is the Paris Metro:

Paris has a circle consisting of Metro Lines 2 and 6, which are operationally lines; people wishing to travel on the arcs through the meeting points at Nation and Etoile must transfer. Farther out, there is an incomplete circle consisting of Tramway Line 3, where the forced transfer between 3a and 3b is Porte de Vincennes. Even farther out there is an under-construction line not depicted on the map, Line 15 of Grand Paris Express, which has a pinch point at its southeast end rather than continuous circular service. All three systems are great example of circumferential lines with very high ridership that are not operationally circles.

Another rich source of circumferential lines that are not circles is cities near bodies of water. In those cities, a circumferential line is likely to be a semicircle rather than a circle. This is responsible for the current state of the Singapore Circle Line, although in the future it will be closed to form a full circle. The G train in New York is a single-sided circumferential line to the east of Manhattan, not linking with anything to the west of Manhattan because of the combination of wide rivers and the political boundaries between New York and New Jersey.

In the opposite direction – circles that are not circumferentials – there are circular lines that don’t neatly orbit city center. The Yamanote Line in Tokyo is one such example: its eastern end is at city center, so it combines the functions of a north-south radial line with those of a north-south circumferential line connecting secondary centers west of Central Tokyo. London’s Circle Line is no longer operationally a circle but was one for generations, and yet it was never a circumferential – it combined the central legs of two east-west radial mainlines, the Metropolitan and District lines.

We can collect this distinction into a table:

 Circle, not circumferential Circumferential, not a circle Circumferential circle Yamanote Line Osaka Loop Line Seoul Metro Line 2 London Circle line (until 2009) Madrid Metro Line 12 Paris M2/6, T1, T2, T3, future M15 Copenhagen F train New York G train, proposed Triboro London Overground services Chicago proposed Circle Line Singapore Circle line (today) Moscow Circle Line, Central Circle Berlin S41/S42 Beijing Subway Line 2, Line 10 Shanghai Metro Line 4 Madrid Metro Line 6

Operational concerns: the steam era

In the 19th century, it was very common to build circular lines in London. In the steam era, reversing a train’s direction was difficult, so railways preferred to build circles. This was the impetus for joining the Metropolitan and District lines to form the Circle line. Mainline regional rail services often ran in loops as well: these were as a rule never or almost never complete circles, but instead involved trains leaving one London terminus and then looping around to another terminus.

Another city with a legacy inherited from steam-era train operations is Chicago. The Loop was built to easily reverse the direction of trains heading into city center. At the outer ends they would need to reverse direction the traditional way, but there was no shortage of land for yards there, unlike in the Chicago CBD since named after the Loop.

As soon as multiple-unit control was invented in the 1890s, this advantage of circles evaporated. Subsequently rapid transit lines mostly stopped running as circles unless they were circumferential. London’s Central line, originally pitched as two long east-west lines forming a circle, became a single east-west line, on which trains would reverse direction.

Operational concerns: the modern era

Today, it is routine to reverse the direction of a rapid transit train. The vast majority of rapid transit routes run as lines rather than circles.

If anything, there have been complaints that circles are harder to run service on than lines. However, I believe these concerns are all specific to London, which changed its Circle line from a continuous loop to a spiral in 2009. I have heard concerns about the operations of the Ringbahn here, but as far as I can tell the people who express them are doing so in analogy with what happened in London, and are not basing them on the situation on the ground here. Moreover, there are no plans to make the Yamanote Line run as anything other than the continuous loop it is today.

The situation in London is that the Circle line has always shared tracks with both the Metropolitan and District lines. There has always been extensive branching, in which a delay on one train propagates to the entire network formed by these two mainlines. To this day, Transport for London does not expect the lines in the subsurface network to have the same capacity as the isolated deep tube lines: with moving block signaling it expects 32 trains per hour, compared with 36 on isolated lines.

What’s more, the junctions in London are generally flat. Trains running in opposite directions can conflict at such junctions, which makes the schedules more fragile. Until 2009, London ran the Circle line trains every 7 minutes, which was bound to create conflicts with other lines.

The importance of this London-specific background is that the argument against circles is that they make schedules more fragile. If there is no point on the line where trains are regularly taken out of service, then it is hard to recover from timetable slips, and delays compound throughout the day. However, this is relevant mainly in the context of an extensively-branching system like London’s. Berlin has some of that branching as well, but much less so; one of the sources of reverse-branching on the S-Bahn is a line that should get its own cross-city route anyway, and another is a Cold War relic swerving around West Berlin (S8/85).

The benefits of complete circles

The complete circle of the Yamanote Line or the Ringbahn can be compared with incomplete circles, such as the Oedo Line or the various circumferentials in Paris. From passengers’ perspective, it’s better to have a complete circle, because then they can undertake more trips.

Circumferential lines broadly have two purposes:

1. They offer service on strong corridors that are orthogonal to the direction of city center, such as the various boulevards hosting the M2/6 ring as well as the Boulevards des Maréchaux hosting T3.
2. They offer connections between two radial lines that may not connect in city center, or may connect so far from the route of the circumferential that transferring via the circumferential is faster.

Both purposes are enhanced when the route is continuous. In the case of Paris, a north-south trip east of Nation is difficult to undertake, as it requires a transfer at Porte de Vincennes. Passengers connecting from just south, on M8 or even on M7, may not save as much time traveling to lines just north, such as M9 or M3, and might end up transferring at the more central stations of Republique or Opera, adding to congestion there.

In contrast, in Berlin the continuous nature of the Ring makes trips across the main transfer points more feasible. Just today I traveled from my new apartment to a gaming event on the Ringbahn across Ostkreuz. At Ostkreuz the trains dwelled longer than the usual, perhaps 2 minutes rather than the usual 30 seconds, which I imagine is a way to keep the schedule. That delay was, all things considered, minor. Had I had to transfer to a new train, I would have almost certainly taken a different combination of trains altogether; the extra waiting time adds up.

Why are circles so uncommon?

The operational concerns of London aside, it’s still uncommon to see complete circles on rapid transit networks. They are the ideal for cities that grow beyond the scale of three or four radial trunks, but there are only a handful of examples. Why is that?

The answer is always some sort of special local concern. If city center is offset to one side of the built-up area, such as in a coastal city, then circumferential lines will be semicircles and not full circles. If there is some dominant transfer point that requires a pinch, then cities prefer to build a pinch into the system, as is the case for Porte de Vincennes on T3 or for some of the lines cobbled together to form the London Overground.

This is similar to the question of missed connections. Public transportation networks must work hard to ensure that whenever two lines meet, they will have a transfer. Nonetheless, missed connections exist in virtually all large rapid transit networks. Some of those are a matter of pure incompetence, but in many, rail networks that developed over generations may end up having one subway line that happens to intersect another far from any station on the older line, and there is little that can be done.

Likewise, it is useful to ensure that circumferential lines be complete circles whenever the city is symmetric enough to warrant circles. Paris, like other big cities with strong transit networks, is good but not perfect, and it is important to call it on the mistakes it makes, in this case building M15 to have a jughandle rather than running as a complete circle.