# 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.

# What Berlin is Building is Not What It Needs to Build

Berlin has a deceptively simple S-Bahn network. There’s the Ringbahn circling city center. There’s the elevated east-west Stadtbahn, which has two tracks dedicated to S-Bahn service and two for everything else, including longer-range regional trains and intercity trains. And there’s the two-track North-South Tunnel, which only carries S-Bahn traffic; longer-range traffic uses the four-track north-south mainline through Berlin Hauptbahnhof, whereas the North-South Tunnel intersects the Stadtbahn one station east of Hauptbahnhof, at Friedrichstrasse.

The main S-Bahn capacity needs in Berlin are east-west; meanwhile, the North-South mainline is underfull, with Wikipedia listing around 7 trains per hour. And yet, Berlin’s big S-Bahn capital project is a new tunnel, dubbed S21, adding yet another north-south track pair through Hauptbahnhof. Fortunately, the project is salvageable, but only if the city and the federal government act quickly, within a few years, to change yet-unbuilt phases to run in the right direction.

Berlin urban rail traffic map

Here is a map of traffic demand on every interstation on the combined Berlin U- and S-Bahn network (source, p. 6):

The numbers are in thousands of passengers per weekday in both directions combined.

The U-Bahn is in blue. It’s a weird-looking network because two lines (U7, running northwest-southeast in the west, and U9, running north-south also in the west) were built in the Cold War to serve West Berlin’s center around Kurfürstendamm, whereas the S-Bahn and the older U-Bahn lines serve the historic center. Since reunification, Germany has made an effort to move the Berlin central business district back to the historic center, and S21 is to reinforce that, serving the western end of Mitte.

Unfortunately, as we see in the green lines, that’s not where the pressing S-Bahn capacity needs are. First, the Stadtbahn is busier than the North-South Tunnel. Second, the busiest branches heading into the city come from the east, with substantially more traffic than from the north and south.

And then there’s the Görlitz Railway. It is the line heading to the southeast, without its own trunk line through the city – it reverse-branches to the two directions of the Ringbahn. Moreover, going north there’s additional reverse-branching, to the Stadtbahn (S9) and around the Ring to the northern branches (S8, S85), with each service running only every 20 minutes. Total traffic across these services is quite high, 107,000 weekday passengers, compared with 144,000 on the Prussian Eastern Railway (S5, S7, S75; S5 is the mainline), 128,000 between the two branches feeding the North-South Tunnel from the south, and 133,000 between the two branches feeding the North-South Tunnel from the north. The brief segment where S9 runs alongside the Ring has 184,000 weekday passengers, the city’s busiest.

S21: what Berlin is actually building

Berlin Hauptbahnhof is a new station. It only opened in 2006, when the North-South Intercity Line opened. The new four-track line has ample capacity for additional S-Bahn traffic, but nonetheless it hosts no S-Bahn trains in regular service. Instead, there are plans for two additional S-Bahn tracks, mostly in tunnel, parallel to the line, with service to Hauptbahnhof:

The map does not show the phasing. The segment from the Ringbahn in the north down to Hauptbahnhof is just about complete, with opening expected soon. The segment from Hauptbahnhof to Potsdamer Platz, which contrary to the map is to be nonstop, is in early stages of construction, and Wikipedia says it is expected to open in 2023.

Farther south of Potsdamer Platz is still not under construction, and frankly should not be built as is. The only real addition this would give to the network is the stop at Gleisdreieck, where the line intersects the east-west U1; the North-South Tunnel intersects U1 without a connection, the only place in the city where there is a missed U-Bahn/S-Bahn connection unless one counts the marginal U9/Stadtbahn miss in which the next station, Zoologischer Garten, is a transfer.

However, the North-South Main Line’s tunnel portal lies just south of Gleisdreieck, and thus it should be feasible if nontrivial to add platforms there for two of the tracks. Farther south, at Yorckstrasse, it is well outside the portal and adding platforms should be fairly easy.

Görlitz Railway S-Bahn: what Berlin should be building

A radial rail network with three lines should aim to have them meet at a triangle in city center. Berlin has two S-Bahn radial lines, and S21 is to add a third. Instead of running parallel to the North-South Tunnel, it should provide a third trunk line. North of Potsdamer Platz the route is already baked in, but farther south, the Görlitz Railway route is a perfect legacy line to link to. It is quite busy, and the likely locations of the intermediate stops between existing infrastructure and Potsdamer Platz are busy U-Bahn stations in their own right.

I was delighted to see this already discussed on the technical transit blog Zukunft Mobilität. It has a long list of potential Berlin rail extensions, some in accordance with current long-term plans, some not. It specifically criticizes S21 for duplicating existing infrastructure, and proposes an extension to the southeast, mentioning that there were plans to that effect in the 1930s. There are two variants, one through Hermannplatz and one through the old route of the Görlitz Railway.

A higher-zoom 11 MB image is available here.

The dashed lines denote under-construction lines, including S21 to Potsdamer Platz, the 4.5-kilometer Siemens Railway to the northwest, and the U5-U55 connection. Dotted lines denote lines I am proposing: either variant connecting S21 toward the southeast, paired with the Siemens Railway as well as two new-build lines through the area of Tegel Airport, which is slated for redevelopment after the Berlin-Brandenburg Airport finally opens. Two branches are depicted toward Tegel, one toward airport grounds to be redeveloped, and one going farther north taking over S25; there are already discussions of a rapid transit line to Tegel, branching off of U6, but this option does not force the outer parts of U6 to contend with reduced frequency.

The two branches should of course not both be built. The main advantage of the southern option is that it hits Hermannplatz, one of the busiest stations in the system: the above diagram of rail ridership shows a large change in U8 demand north and south of the station, and a factsheet from 2010 asserts that it is the second busiest U-Bahn station, closely behind Alexanderplatz. In effect, it functions as an express link from Neukölln to city center. U8 isn’t especially crowded – nothing in Berlin is – but it’s busiest than the North-South Tunnel; this link is at least as justified as the S21 tunnel to the south. This would require about 7 km of tunnel. While S-Bahn tunnels cost more than U-Bahn tunnels, this is deliberately an express line, so keeping costs down to the per-km level of the U5-U55 connection (525 million for 2.2 km) is reasonable, making it a 1.8 billion project or thereabout.

The northern option works differently. It doesn’t hit anything as interesting as Hermannplatz on the way, but it does serve Alt-Treptow, one of the bigger rapid transit deserts inside the Ring. The infill station would also break what is the second or third longest interstation on the Ring. Closer in, it has better coverage in the center – Checkpoint Charlie offers another CBD station in addition to Potsdamer Platz. The cost is more of an open question here. From Görlitzer Bahnhof to Potsdamer Platz it’s about 4 km; east of Görlitzer Bahnhof it’s plausible that the line could reuse the Görlitz Railway’s right-of-way and run elevated, or at worst underground with cut-and-cover. However, the per km cost of the tunnel would be higher, since proportionately more of it is in city center, and it has the same number of stations over shorter length; my vague guess is somewhat less than 1.5 billion.

The Berlin S-Bahn would become a system with three radial lines, meeting at Hauptbahnhof, Friedrichstrasse, and Potsdamer Platz. All reverse-branching would cease: the various branches on the Görlitz Railway, including the existing ones as well as an under-construction one to the airport-to-be, would feed into the S-Bahn trunk, rather than to the Ring or the Stadtbahn. The removal of S25 from the North-South Tunnel would create space for the S8 and S85 services in Pankow to use the North-South Tunnel instead of diverting to the Ring and Görlitz Railway. Potentially, the North-South Tunnel could also be realigned to serve Gleisdreieck, as depicted on the map. Finally, with S9 removed from the Stadtbahn, there would be room to beef up service on S3 and/or end the current practice in which S75 trains from the east stop at Ostbahnhof rather than running through.

Germany isn’t perfect

Writing about North America, I talk a lot about how it can Germanize its regional rail network. But it’s important to understand that while far better than North America, Germany is not perfect. It makes mistakes of many kinds: some involving high construction costs, some involving schedule slips, some involving unnecessary prestige projects. These can mostly be prefaced by “by Continental standards,” though the Berlin-Brandenburg Airport disaster is bad even by the standards of the Anglosphere and its billion-dollars-per-kilometer subways.

The Berlin S-Bahn is a case in point. It has a pretty hefty peak-to-base ratio by German standards – the Ring lines (S41 and S42) run every 5 minutes peak and every 10 off-peak, and a number of other lines have a peak-to-base ratio of 2 as well. It also has a peculiarity in that S75 trains only run east of Ostbahnhof; I can’t tell if there’s a problem with track capacity or demand mismatch, but if it’s the former then it’s strange since peak S-Bahn traffic on the Stadtbahn is only 18 trains per hour (Munich achieves 30 through its central tunnel, with much higher crowding levels), and if it’s the latter then it’s again strange – why not run through to Westkreuz like S5?

S21 is another of these little mistakes. It’s a prestige project on the heels of the construction of Hauptbahnhof, rather than a solution to a transportation need. There are six north-south tracks through Berlin between the S-Bahn and the mainline and they’re not anywhere near capacity; the mind boggles at why anyone would add seventh and eighth tracks before adding fifth and sixth east-west tracks.

Fortunately, the mistake is fixable. Germany’s dragging infrastructure timeline means that there’s often room for modifications to make things more useful. The airport is a lost cause, but S21 is not. From Potsdamer Platz south there’s a good option that adds S-Bahn service exactly where it is needed and simplifies citywide schedules by making it feasible to eliminate reverse-branching. In lieu of building more autobahns, Berlin should commit to building the southeastern extension via Alt-Treptow or Neukölln.

My post about the boundary zone between the transit-oriented city and its auto-oriented suburbs led to a lot of interesting discussions in comments, including my favorite thing to hear: “what you said describes my city too.” The city in question is Philadelphia, and the commenter, Charles Krueger, asked specifically about park-and-ride commuter rail stations. My post had mentioned Southeast on the Harlem Line as an interface between commuter rail and the Westchester motorway network, and the natural followup question is whether this is true in general.

The answer is that it’s complicated, because like the general concept of the cars/transit boundary zone, park-and-rides have to be rare enough. If they’re too common, the entire rail system is oriented around them and is not really a boundary but just an extension of the road network. This is the situation on every American commuter rail system today – even lines that mostly serve traditional town centers, like the New Haven Line, focus more on having a lot of parking at the station and less on transit-oriented development. Even some suburban rapid transit lines, such as the Washington Metro, BART, and the recent Boston subway extensions, overuse park-and-rides.

However, that American suburban rail systems overuse such stations does not mean that such stations must never be built. There are appropriate locations for them, provided they are used in moderation. Those locations should be near major highways, in suburbs where there is a wide swath of low-density housing located too far from the rail line for biking, and ideally close to a major urban station for maximum efficiency. The point is to use suburban rail to extend the transit city outward rather than the auto-oriented suburban zone inward, so the bulk of the system should not be car-oriented, but at specific points park-and-rides are acceptable, to catch drivers in suburbs that can’t otherwise be served or redeveloped.

Peakiness and park-and-rides

I’ve harped on the importance of off-peak service. The expensive part of rail service is fixed costs, including the infrastructure and rolling stock; even crew labor has higher marginal costs at the peak than off-peak, since a high peak-to-base ratio requires split shifts. This means that it’s best to design rail services that can get ridership at all times of day and in both directions.

The need for design that stimulates off-peak service involves supportive service, development, and infrastructure. Of these, service is the easiest: there should be bidirectional clockface schedule, ideally with as little variation between peak and off-peak as is practical. Development is politically harder, but thankfully in the main example case, the Northeastern United States, commuter rail agencies already have zoning preemption powers and can therefore redevelop parking lots as high-intensity residential and commercial buildings with walkable retail.

Infrastructure is the most subtle aspect of design for all-day service. Park-and-ride infrastructure tends to be peaky. Whereas the (peakier, more suburban) SNCF-run RER and Transilien lines have about 46% of their suburban boardings at rush hour, the LIRR has 67%, Metro-North 69%, and the MBTA 79%. My linked post explains this difference as coming from a combination of better off-peak service on the RER and more walkable development, but we can compare these two situations with the Washington Metro, where development is mostly low-density suburban but off-peak frequency is not terrible for regional rail. Per data from October 2014, this proportion is 56%, about midway between Transilien and the LIRR.

This goes beyond parking. For one, railyards should be sited at suburban ends of lines, where land is cheap, rather than in city center, where land is expensive and there is no need to park trains midday if they keep circulating. But this is mostly about what to put next to the train stations: walkable development generating a habit of riding transit all day, and not parking lots.

Where parking is nonetheless useful

In response to Charles’ comment, I named a few cases of park-and-rides that I think work well around New York, focusing on North White Plains and Jersey Avenue. There, the parking-oriented layout is defensible, on the following grounds:

1. They are located in suburban sections where the reach of the highway network is considerable, as there is a large blob of low density, without much of the structure created by a single commuter line.
2. They are near freeways, rather than arterials where timed connecting buses are plausible.
3. They are immediately behind major stations in town centers with bidirectional service, namely White Plains and New Brunswick, respectively.

The importance of proximity is partly about TOD potential and partly about train operating efficiency. If the park-and-rides are well beyond the outer end of bidirectional demand, then the trains serving them will be inefficient, as they will get relatively few off-peak riders. A situation like that of Ronkonkoma, which is located just beyond low-ridership, low-intensity suburbs and tens of kilometers beyond Hicksville, encourages inefficient development. Thus, they should ideally be just beyond the outer end, or anywhere between the city and the outer end.

However, if they are far from the outer end, then they become attractive TOD locations. For example, every station between New York and White Plains is a potential TOD site. It’s only near White Plains that the desirability of TOD diminishes, as White Plains itself makes for a better site.

On rapid transit in American suburbia, one example of this principle is the Quincy Adams garage on the Red Line just outside Boston. While the station itself can and should be made pedestrian-friendlier, for one by reopening a gate from the station to a nearby residential neighborhood, there’s no denying the main access to the station will remain by car. Any TOD efforts in the area are better spent on Quincy Center and Braintree, which also have commuter rail service.

Where parking should urgently be replaced by TOD

American suburban rail lines overuse park-and-rides, but there are specific sites where this type of development is especially bad. Often these are very large park-and-ride structures built in the postwar era for the explicit purpose of encouraging suburban drivers to use mainline rail for commuter and intercity trips. With our modern knowledge of the importance of all-day demand, we can see that this thinking is wrong for regional trips – it encourages people to take rail where it is the most expensive to provide and discourages ridership where it is free revenue.

The most important mistake is Metropark. The station looks well-developed from the train, but this is parking structures, not TOD. Worse, the area is located in the biggest edge city in the Northeast, possibly in the United States, possibly in the world. Middlesex County has 393,000 jobs and 367,000 employed residents, and moreover these jobs are often high-end, so that what the Bureau of Economic Analysis calls adjustment for residence, that is total money earned by county residents minus total money earned in the county, is negative (Manhattan has by far the largest negative adjustment in the US, while the outer boroughs have the largest positive one). The immediate area around Metropark and Woodbridge has 46,000 jobs, including some frustratingly close to the station and yet not oriented toward it; it’s a huge missed opportunity for commercial TOD.

In general, edge cities and edgeless cities should be prime locations for sprawl repair and TOD whenever a suburban rail line passes nearby. Tysons, Virginia is currently undertaking this process, using the Silver Line extension of the Metro. However, preexisting lines do not do so: Newton is not making an effort at TOD on the existing Green Line infrastructure, it’s only considering doing so in a part of town to be served by a potential branch toward Needham; and the less said about commuter rail, the better. Mineola and Garden City on Long Island, Tarrytown in Westchester, and every MBTA station intersecting Route 128 are prime locations for redevelopment.

Commuter rail for whomst?

I believe it’s Ant6n who first came up with the distinction between commuter rail extending the transit city into the suburbs and commuter rail extending the suburbs into the city. If the trains are frequent and the stations well-developed, then people from the city can use them for trips into suburbia without a car, and their world becomes larger. If they are not, then they merely exist to ferry suburban drivers into city center at rush hour, the one use case that cars are absolutely infeasible for, and they hem car-less city residents while extending the world of motorists.

Park-and-rides do have a role to play, in moderation. Small parking lots at many stations are acceptable, provided the station itself faces retail, housing, and offices. Larger parking structures are acceptable in a handful of specific circumstances where there is genuinely no alternative to driving, even if the rest of the rail service interfaces with walkable town centers. What is not acceptable is having little development except parking at the majority of suburban train stations.

In 2011, Chuck Marohn of Strong Towns coined the word stroad for a street that functions as a road. Chuck argues that there should be a separation between streets, which are destinations in and of themselves and are to be lined with walkable retail, and roads, which exist to move people between destinations. In contrast, auto-oriented arterials function as both: they are designed for high speed for through-traffic but also have extensive streetside destinations built at automobile scale, hence the portmanteau stroad.

In the last seven years this mentality has become quite popular within online urbanist circles. Unfortunately, it misses why major streets arise in the first place. Moreover, this is not just an issue for cars and car traffic – other modes of transportation want to funnel local and interregional traffic through the same corridors, creating a number of arteries that are in essence strails, like the Berlin S-Bahn. Good planning has to recognize that where people to go through and where people want to go to are often the same, and provide road and rail infrastructure of sufficient size to accommodate.

What is a street, anyway?

The main purpose of a city street is to connect destinations within the city. Major streets routinely form out of trails, post roads, and turnpikes connecting the city with villages that it swallows as it industrializes and grows. Broadway in New York started out as an Indian trail, the Strand grew as a road connecting London with Westminster and had previously been part of an intercity Roman road, Champs Elysees was built as a promenade into the periphery of Paris and gradually filled in with palaces, the Sveavägen/Götgatan axis goes back to the Early Modern era with connections from Stockholm to Roslag to the north and Götland in the south.

Not every street has this intercity or suburban history, but the important ones frequently do. The Manhattan grid was mapped as an entirely urban street network, but the wide north-south avenues were designed for easy access to the Lower Manhattan core from future residential areas. In ungridded cities, usually you can tell which streets are the oldest because they are longer, more continuous, and more commercially developed, and the exceptions come from heavyhanded state planning, like the shift from Rue Saint-Jacques to Boulevard Saint-Michel in Haussmannian Paris.

The importance of through-streets within cities continues even today, and even when cars are not too relevant. People who walk or take transit are likelier to do so on the main streets, and as a result, businesses prefer locating there. In Manhattan there’s even an expression for this: avenue rents versus street rents. In Vancouver, I could walk on any street, but crossing wasn’t any harder on the main streets than on the side streets, and there was more interesting stuff to look at on the main streets; even ignoring zoning, retail would prefer to locate on the main streets because that’s where all the other retail is. There’s a wealth of good restaurants I discovered just by walking next to them, to say nothing of the gaming store on 4th Avenue near MacDonald, which I saw from the bus to UBC.

All of this is magnified in cities that do not have consistent grids, like Paris, Berlin, and even Stockholm. In those cities, zoning does not micromanage use as much as in North America, and yet businesses locate on major streets where possible. Here is a map of the area I live in: the green dot is where I live, and the red dot is a government office I went to last week to register.

Walking east or west, I exclusively use Bernauer Strasse, the street the M10 tramway runs on; walking north or south, I use Brunnen Strasse, which hosts U8. Other streets can function as shortcuts, but with parks and small changes interrupting the grid, they’re less reliable for through-walking. And indeed, they are much quieter and largely residential, with retail mostly at street corners.

The early American roads connected distinct cities, or linked cities with rural hinterlands. Within the cities, they fed preexisting arterial streets. For the most part these arterial streets were fairly wide – they were mapped in the 19th century based on 19th-century design standards, often 30 meters of width, rather than the narrow medieval streets London is famous for – but they still filled with cars fast. Two parking lanes and four moving lanes in a dense city with busy crossings aren’t much. American cities had traffic jams in the 1920s already.

My two go-to references about the history of American roadbuilding – Owen Gutfreund’s 20th-Century Sprawl, and Earl Swift’s The Big Roads – both explain what happened beginning in the 1920s: cities built bypasses. The idea was that the bypasses would segregate through-traffic from urban traffic, separating roads from streets properly.

This never happened. For the same reason preindustrial roads turned into busy streets, bypasses turned into busy auto-oriented streets. Retailers found that the best place to locate was where all the cars were. These bypasses became congested roads themselves, partly due to the induced auto-oriented development and partly due to general growth in car traffic volumes. This trend intensified after WW2, with the freeways leading another cycle of bypasses around congested urban roads becoming congested with urban traffic themselves. Wal-Mart and Carrefour invented the hypermarket in 1962-3, and in the 1960s office space began suburbanizing as well, since traffic conditions were better than in congested city centers.

This is not an obscure history, and Chuck is fully aware of it: among his complaints about stroads is that they reduce the tax base of the city by encouraging retail to decamp for the suburbs. He just fails to follow this through to the logical conclusion: the most intense demand for real estate is near the busiest through-routes. There is no real separation between the street and the road; the best you can do for walkability is run better public transit to the urban core and make sure the roads have street-facing retail rather than front parking lots.

Strails

The principle that the best place for local traffic is where long-distance traffic is is equally true of trains. An intermediate station on an intercity railway sited a convenient commute away from the city will soon fill with suburban travelers. The term commuter itself derives from the discounted commutation tickets American intercity railroads offered regular riders, starting in New York and Boston in the middle of the 19th century.

19th-century railways were not a complex system of branched lines dedicated to regional traffic. Such lines existed, for example the Ligne de Saint-Germain-en-Laye, now part of the RER A, but most of the lines continued onward to long-distance destinations, or had been built with the intention of continuing so. Look at this map of extant London-area railways by year of construction: there aren’t that many branches predating the Late Victorian era, and the branches that do exist tend to be reverse-branches in South London offering service to either a City station like Cannon Street or Blackfriars or a West End station like Victoria. The remainder are loop lines, built to offer four tracks’ worth of capacity on lines that had originally been built with only two, but then both routes filled with local traffic, making it harder to schedule express trains; for an example easily visible on the map, see the Lea Valley lines connecting to Cheshunt.

In contrast with the London loop lines, Prussian State Railways made sure to rebuild the Ringbahn and Stadtbahn to have adequate capacity, that is four tracks, two for local service and two for longer-distance service; the Ringbahn had initially been built with two tracks, but would be expanded to four in the 1880s and 90s. But even here, there are seams. German Wikipedia explains that the Stadtbahn had to take a less desirable route to avoid expensive takings on Leipziger Strasse, and has a winding route with S-curves between Alexanderplatz and Jannowitz Brücke. Moreover, some individual branches only have two tracks even if they are the best intercity routes: the S2 route is the most direct route to Dresden, but with two tracks, heavy local traffic, and only DC electrification, it cannot host intercity trains, and thus intercity trains to Dresden spend 20 minutes out of a 2-hour trip getting around this line.

Berlin at least has the good fortune that four tracks here are enough. Tokyo is so big and strongly-centered that it has ten tracks going south of Tokyo on the Tokaido Line and eight going north on the Tohoku Line, including four for local service, two for Shinkansen service, and two or four for medium-distance express regional trains. Widening railways to serve city centers is expensive, and only done when absolutely necessary, and yet JR East spent considerable money on widening the innermost Tohoku trunk from six to eight tracks.

Even high-speed rail can induce the same development effect as a freeway. It doesn’t have closely-spaced stations, but people might demand stations as a mitigation of construction impact and train noise. The Tohoku Shinkansen diverges from the Tohoku Main Line a few kilometers north of Tokyo, but the local communities demanded local service as well as a mitigation, and as a result Japan National Railways built a four-track line, with two Shinkansen tracks and two local tracks for the Saikyo Line.

Main streets want to be everything

Major streets are the best location for every destination and every mode of transportation. This extends beyond walking. Buses prefer wide streets optimized for higher traffic speed – and the few main streets that are not so optimized, such as the Manhattan crosstown streets (since traffic is optimized for north-south avenue throughput), have buses that win awards for how slow they are. Bicyclists prefer riding on major streets as well, which is why Copenhagen prioritizes bike infrastructure on major streets rather than on side streets – on side streets car traffic is so light and slow that mixed traffic is not so bad, but the desirable through-routes remain the major streets.

The problem is that every mode of transportation requires some piece of the street, whereas street width is finite. Brunnen Strasse is 40 meters wide, and hosts very wide sidewalks including a dedicated path for on-sidewalk cycling, a combination of parallel and angled parking, two moving lanes in each direction, and a generous road median. Even that width does not include dedicated public transit infrastructure: U8 runs underneath the street, leaving the street’s width for sidewalks and roadways.

The same situation occurs on railroads: all uses want the same piece of infrastructure, leading to the usual problems of mixing trains of different speed classes on the same tracks. Freight bypasses are possible, but passenger bypasses are rare – train passengers tend to want to go to the city rather than to some suburb, and unlike cars, trains have prescribed stop patterns. By rail as by road, bigger infrastructure is needed: four tracks for a mixed local and interregional railway, or about 36-40 meters or even more on a main street.

Wide enough streets don’t exist everywhere. New England streets are narrow. Midwestern streets are wider, but at least the one I’m most familiar with, Ann Arbor’s Washtenaw Avenue, is only around 25 meters wide – it only gets up to 40 if one includes setbacks. Road widening would be needed, which is exactly the opposite of what the Strong Towns approach prescribes. Cities this small could mix decent local and intercity rail service on two tracks with timed overtakes, but that would require them to run any passenger rail service to begin with, and to make sure to have enough development near the stations, both residential and commercial, that people would ride the trains.

But on a 30-meter wide street, something has to give. There simply is not enough room for everything. Give pedestrians their 4 or 5 meters of sidewalk in each direction, cyclists their 2 meters of bike lane, and cars their parking lane and two moving lanes, and you’re already at 30-32 meters. You can go with complete streets and reduce the extent of car infrastructure, for example by turning a moving lane per direction into a bus or tram lane, or by getting rid of street parking, but unless you’re in a city with high transit mode share, you’re driving away eyeballs from retailers. Paris can definitely do it, New York and Berlin can do it, even Boston can do it. Can a small American city where planners aspire to run a handful of buses every 15 minutes do it? Probably not.

# Corey Johnson’s Report on City Control of the Subway

Yesterday, New York City Council speaker and frontrunner in the 2021 mayoral race Corey Johnson released a document outlining his plan to seek city control of the subway and buses. In addition to the governance questions involved in splitting the state-run MTA between a city-owned urban transit agency and state- or suburb-owned commuter rail, it talks about what Johnson intends to do to improve public transit, befitting a mayor in full control of subway and bus operations. There are a lot of excellent ideas there, but also some not so good ones and some that require further work or further analysis to be made good.

Governance

Johnson proposes to spin the urban parts of the MTA into a new agency, called BAT, or Big Apple Transit. The rump-MTA will remain in control of suburban operations and keep MTA Capital Construction (p. 35), and there will be a shared headquarters. Some cooperation will remain, such as contributions toward cheaper in-city commuter rail fares, but there is no call for fully integrated fares and schedules: the recommendation “all trains and buses in the city will cost the same and transfers will be free” does not appear anywhere in the document.

Johnson also proposes that the BAT board will be required to live in the city and use transit regularly. There is a serious problem today with senior managers and board members driving everywhere, and the requirement is intended to end this practice. Cynically, I might suggest that this requirement sounds reasonable in 2019 but would have been unthinkable until the 2000s and remains so in other American cities, even though it would be far more useful there and then; the off-peak frequency-ridership spiral is nowhere nearly as bad in New York as it is in Washington or Boston.

One strong suggestion in this section involves appointing a mobility czar (p. 36), in charge of the NYC Department of Transportation as well as BAT. Given the importance of the subway, this czar would be in effect the new minister of transportation for the city, appointed by the mayor.

Ultimately, this section tends toward the weaker side, because of a problem visible elsewhere in the report: all of the recommendations are based on internal analysis, with little to no knowledge of global best practices. Berlin has city-controlled transit in full fare union with Deutsche Bahn-run mainline rail, but there has been no attempt to learn how this could be implemented in New York. The only person in New York who I’ve seen display any interest in this example is Streetsblog’s David Meyer, who asked me how DB and Berlin’s BVG share revenue under the common umbrella of the Berlin Transport Association (or VBB); I did not know and although I’ve reached out to a local source with questions, I could not get the answer by his filing deadline.

Finance and costs

This is by far the weakest section in the proposal. The MTA funds itself in large part by debt; Johnson highlights the problem of mounting debt service, but his recommendations are weak. He does not tell New Yorkers the hard truth that if they can’t afford service today then they can’t afford it at debt maturity either. He talks about the need to “address debt” but refrains from offering anything that might inconvenience a taxpayer, a rider, or an employee (pp. 42-43), and offers a melange of narrow funding sources that are designed for maximum economic distortion and minimum visible inconvenience.

In fact, he calls transit fares regressive (pp. 59, 61) and complains about century-long fare increases: real fares have risen by a factor of 2.1 since 1913 – but American GDP per capita has risen by a factor of 7.7, and operating costs have mostly risen in line with incomes.

He brings up ways to reduce costs. In operations these involve negotiations with the unions; even though the report mentions that drivers get paid half-time for hours they’re not working between the morning and afternoon peaks (“swing shift,” p. 48), it does not recommend increasing off-peak service in order to provide more mobility at low marginal cost. There is no mention of two-person crews on the subway or of the low train operator efficiency compared with peer cities – New York City Transit train operators average 556 revenue hours per year, Berlin U-Bahn operators average 829.

In capital construction the recommendations are a mixed bag of good and bad, taken from a not-great RPA report from a year ago. Like the RPA, Johnson recommends using more design-build, in flagrant violation of one of the rules set by global cost reduction leader Madrid. However, to his credit, Johnson zooms in on real problems with procurement and conflict resolution, including change orders (pp. 50-51), and mentions the problem of red tape as discussed in Brian Rosenthal’s article from the end of 2017. He suggests requiring that contractors qualify to bid, which is a pretty way of saying that contractors with a history of shoddy work should be blacklisted; I have heard the qualify-to-bid suggestion from some sporadic inside sources for years, alongside complaints that New York’s current bid-to-qualify system encourages either poor work or red tape discouraging good contractors. Unfortunately, there is no talk of awarding bids based on a combination of technical score and cost, rather than just cost.

Overall the talk of cost is better than what I’ve seen from other politicians, who either say nothing or use high costs as an excuse to do nothing. But it has a long way to go before it can become a blueprint for reducing subway construction costs, especially given the other things Johnson proposes elsewhere in the document.

Accessibility

Another mixed part of the document is the chapter about accessibility for people with disabilities. Johnson recounts the lack of elevators at most subway stations and the poor state of the bus network, featuring drivers who are often hostile to people in wheelchairs. However, while his analysis is solid, his recommendations aren’t.

First of all, he says nothing of the cost of installing elevators on the subway. An MTA press release from last year states the cost of making five stations accessible as $200 million, of$40 million per station. This figure contrasts with that of Madrid, where a non-transfer station costs about 5 million to equip with elevators, and a transfer station costs about 5 million per line served (source, PDF-pp. 11-12). In Berlin, which is not a cheap city for subway construction, the figure is even lower: about 2 million per line served, with a single elevator costing just 800,000.

And second, his proposal for finding money for station accessibility involves using the zoning code, forcing developers to pay for such upgrades. While this works in neighborhoods with ample redevelopment, not all city neighborhoods are desirable for developers right now, and there, money will have to come from elsewhere. For a document that stresses the importance of equality in planning, its proposals for how to scrounge funds can be remarkably inequitable.

That said, in a later section, Johnson does call for installing bus shelters (p. 74). A paper referenced in a TransitCenter report he references, by Yingling Fan, Andrew Guthrie, and David Levinson, finds that the presence of shelter, a bench, and real-time arrival information has a large effect on passengers’ perceived wait times: in the absence of all three amenities, passengers perceive wait time as 2-2.5 times as long as it actually is, rising to a factor of almost 3 for 10-minute waits among women in unsafe areas, but in the presence of all three, the factor drops to around 1.3, and only 1.6 for long waits for women in unsafe areas. Unfortunately, as this aspect is discussed in the bus improvement section, there is no discussion of the positive effect shelter has on people with disabilities that do not require the use of a wheelchair, such as chronic pain conditions.

I do appreciate that the speaker highlights the importance of accessibility and driver training – drivers often don’t even know how to operate a wheelchair lift (p. 63). But the solutions need to involve more than trying to find developers with enough of a profit margin to extract for elevators. Bus stops need shelter, benches, and ideally raised curbs, like the median Berlin tramway stations. And subway stations need elevators, and they need them at acceptable cost.

Bus improvements

By far this is the strongest part of the report. Johnson notes that bus ridership is falling, and recommends SBS as a low-cost solution. He does not stop at just making a skeletal light rail-like map of bus routes to be upgraded, unlike the Bloomberg and de Blasio administrations: he proposes sweeping citywide improvements. The call for bus shelter appears in this section as well.

But the speaker goes beyond calling for bus shelters. He wants to accelerate the installation of bus lanes to at least 48 km (i.e. 30 miles) every year, with camera enforcement and physically-separated median lanes. The effect of such a program would be substantial. As far as I can tell, with large error bars caused by large ranges of elasticity estimates in the literature, the benefits in Eric Goldwyn’s and my bus redesign break down as 30% stop consolidation (less than its 60% share of bus speedup since it does involve making people walk longer), 30% bus lanes, 30% network redesign, 10% off-board fare collection.

There is no mention of stop consolidation in the paper, but there is mention of route redesign, which Johnson wishes to implement in full by 2025. The MTA is in support of the redesign process, and allowing for integrated planning between NYCDOT and the MTA would improve the mutual support between bus schedules and the physical shape of the city’s major streets.

Moreover, the report calls for transit signal priority, installed at the rate of at least 1,000 intersections per year. This is very aggressive: even at the average block spacing along avenues, about 80 meters, this is 80 kilometers per year, and at that of streets, it rises to 200+ km. Within a few years, every intersection in the city would get TSP. The effects would be substantial, and the only reason Eric’s and my proposal does not list them is that they are hard to quantify. In fact, this may be the first time an entire grid would be equipped with TSP; some research may be required to decide how to prioritize bus/bus conflicts at major junctions, based on transportation research as well as control theory, since conditional TSP is the only way to truly eliminate bus bunching.

Reinforcing the point about dedicated lanes, the study calls for clawing back the space given to private parking and delivery. It explicitly calls for setting up truck routes and delivery zones in a later section (pp. 86-87); right now, the biggest complaint about bus lanes comes from loss of parking and the establishment of delivery zones in lieu of letting trucks stop anywhere on a block, and it is reassuring to see Johnson commit to prioritizing public transit users.

Livable streets

This is another strong section, proposing pedestrian plazas all over the city, an expansion of bike lanes to the tune of 80 km (50 miles) a year with an eye toward creating a connected citywide bike lane network, and more bike share.

If I have any criticism here, it’s that it isn’t really about city control of the MTA. The bus improvements section has the obvious tie-in to the fact that the buses are run by the MTA, and getting the MTA and NYCDOT on the same page would be useful. With bikes, I don’t quite understand the connection, beyond the fact that both are transportation.

That said, the actual targets seem solid. Disconnected bike lane networks are not really useful. I would never bike on the current network in New York; I do not have a death wish. I wasn’t even willing to bike in Paris. Berlin is looking more enticing, and if I moved to Amsterdam I might well get a bike.

Conclusion

The sections regarding costs require a lot of work. Overall, I get the impression that Johnson based his recommendations on what he’s seen in the local press, so the suggestions are internal to the city or occasionally domestic; the only international comparisons come from the RPA report or from Eric’s and my invocation of Barcelona’s bus redesign. This works for such questions as how to apportion the MTA’s debt service or how to redesign the bus network, but not so much for questions involving subway capital construction.

New York has a large number of fluent Spanish speakers. It should have no problem learning what Spanish engineers know about construction costs, and the same is true for other communities that are well-represented in the cities, such as Korean-, Russian-, Chinese-, Brazilian-, and Polish-New Yorkers. Moreover, in most big cities that don’t send large communities to New York, such as those of Northern Europe, planners speak English. Johnson should not shy from using the expertise of people outside New York, ideally outside the United States, to get subway construction costs under control.

The speaker’s plan is still a very good first step. The proposed surface improvements to buses, bikes, and street allocation are all solid, and should be the city’s consensus for how to move forward. What’s needed is something to tie all of this together with a plan to move forward for what remains the city’s most important transportation network: the subway.

# 30-30-30 is Feasible

This piece first appeared as a study attached to an article in the Connecticut Mirror by SE Coast’s Gregory Stroud.

Fresh off the election, Connecticut Governor Ned Lamont has proposed an ambitious infrastructure plan, dubbed 30-30-30, in which train travel between New York and Stamford, Stamford and New Haven, and New Haven and Hartford would be cut to 30 minutes. With an average speed of about 110 km/h, this is only about half the average speed typical of high-speed rail, but still slightly higher than that of the Northeast Regional between New York and Washington, which is competitive with cars and buses provided there is enough capacity.

For 30-30-30 to truly be cost-effective, the plan needs to speed up trains with relatively little infrastructure investment, at a cost measured in hundreds of millions of dollars. Is that feasible? The topline answer is yes. All three segments can be done in the specified amount of time. North of New Haven, there are generous margins, but 30-minute travel times will rely on electrifying the Shuttle and running high-quality electric trains. South of New Haven, each segment has just seconds to spare to achieve the governor’s goal, and no big-ticket capital investment would be needed, but the plan will require a complete overhaul in Metro-North operations.

Some additional repairs are needed on tracks straight enough to allow trains to run at 160 km/h, which are today only maintained to allow 75 mph, or 120 km/h. The state may also need to procure lighter trains, able to accelerate faster than the current equipment. On a fast schedule, with few intermediate stops, the difference with the current M8 trains is small, but in practice north of Stamford, where trains are likely to make many stops, the difference would be noticeable.

Most of all, reliability must improve enough that is possible to remove the extensive schedule padding in the timetable today. Metro-North is in a perpetual maintenance cycle. At any time there is a slow zone somewhere on the tracks, with generous schedule padding on top of it. Maintenance must be switched to the nighttime, as is practiced on high-speed lines in Japan and France and on subways everywhere in the world outside New York, in order to improve daytime reliability.

The simulation of train performance

In order to figure out the best possible trip times, I made a table of speed zones on the New Haven Line, from Grand Central to New Haven. But instead of using current speed zones, which are very conservative, I looked for the maximum speed that is feasible within the current right-of-way.

The most important rule I followed is no curve modifications, even modifications that are likely to happen under any high-speed rail scenario. While some capital investment may still be required, it is entirely within existing rights-of-way.

In the simulation, I used code outputting slow penalties for trains based on prescribed performance characteristics. For this, I used two sets of characteristics. The first, is for the M8 trains used by Metro-North today. The second is an average of modern European regional trains, such as the Stadler FLIRT, the Alstom Coradia, the Bombardier Talent 2, the CAF Civity, and the Siemens Mireo. Because they are much lighter-weight, all have about 50% better acceleration than the M8 at any speed. Both sets of trains can reach the same top speed, 160 km/h, but when the M8 slows down from top speed to make a station stop, the extra acceleration and deceleration time add another 69 seconds to the trip, compared with only 46 seconds on the European regional trains.

That said, the proposed schedule has few intermediate stops, and even with frequent slowdowns due to curves, the total difference in time between the two sets of trains is about two minutes. So, while I would urge Connecticut to buy modern trains at its next procurement, based on the latest revision in FRA regulations permitting lightly-modified European trains, the present-day rolling stock is good enough, it’s just much heavier than it needs to be.

While I did not assume any curve modifications, I did assume that trains could run faster on curves than they do today. The New Haven Line has conservative values for the permitted centrifugal force acting on trains. I explain more about this in a previous post about trains in Connecticut, but the relevant figures are about 8” of total equivalent cant on the New Haven Line today, or about 200 mm, whereas light trackwork increasing total cant and already-existing regulatory changes above the rails could raise this to 12” on existing trains, about 300 mm, and even more on tilting trains like the Acela. The difference between 200 and 300 mm of total equivalent cant corresponds to a 22% increase in speed; the formula is $\sqrt{1.5} = 1.22$.

Moreover, in some areas the maximum speeds are even lower than one might assume based on curve radius and current permitted curve speeds. These include the movable bridges over the waterways, which have very low speed limits even when the tracks are mostly straight; if the bridges physically cannot accommodate faster trains then they should be replaced, a capital investment already on the state and the region’s official wishlist.

In addition to speed limits imposed by curves and bridges, there is a uniform speed limit of 90 mph (145 km/h) on the New York segment of the line and 75 mph on the Connecticut segment. This is entirely a matter of poor maintenance: the right-of-way geometry could support higher speed today in some places, even without curve modifications.

Finally, trains today go at excruciatingly slow speed in the throat heading into the bumper tracks at Grand Central, 10 miles per hour. This is bad practice: even with bumper tracks, German train throats with complex switches are capable of 70 km/h. This change alone would save about 4 minutes. Overall, trains today are scheduled to take about 11-12 minutes between Grand Central and Harlem, and the proposed schedule cuts this down to 5-6.

The proposed schedule

I am attaching a spreadsheet with exact speed zones, rounded down in 5 km/h increments. People who wish to see what’s behind the timetable I’m proposing can go look there for intermediate times. These may be especially useful to people who want to see what happens if more stops on the Lower New Haven Line are included. For example, one might notice that all technical travel times are padded 7%, as is standard practice in Switzerland, and that trains dwell exactly 30 seconds at each station, which is observed on busy commuter lines in Zurich as well as Paris.

I am including two stopping patterns: regional and intercity. Regional trains make the same stops as the Upper New Haven Line trains do today, plus New Rochelle. Intercity trains only make a few stops beyond Stamford, with a stopping pattern close to that of Amtrak. In addition, I am including two different sets of rolling stock: the current M8, and lighter, faster-accelerating European trainsets. The difference in the regional train pattern is noticeable, while that in the intercity one is less so.

Finally, at stations, it’s possible to state the scheduled the time the train arrives at the station or the one it departs. At all intermediate stations, the timetable below states the arrival time, unlike the attached spreadsheet, which uses departure times to permit calculating exact average speeds.

 Stop Regional, M8 Regional, euro Intercity, M8 Intercity, euro Grand Central 0:00 0:00 0:00 0:00 Harlem-125th 0:05 0:05 0:05 0:05 New Rochelle 0:17 0:16 0:17 0:16 Stamford 0:30 0:29 0:30 0:29 Noroton Heights 0:34 0:33 Darien 0:37 0:35 Rowayton 0:39 0:37 South Norwalk 0:42 0:40 0:37 0:36 East Norwalk 0:45 0:42 Westport 0:48 0:45 Greens Farms 0:52 0:48 Southport 0:55 0:51 Fairfield 0:57 0:53 Fairfield Metro 1:00 0:56 Bridgeport 1:04 0:59 0:49 0:47 Stratford 1:09 1:03 Milford 1:13 1:07 West Haven 1:19 1:13 New Haven 1:23 1:17 1:03 1:01

New Haven-Hartford-Springfield

In theory, achieving the governor’s proposed timetable is easier north of New Haven. The Hartford Line is a straight route. Most of it has a top speed of 80 mph, and outside the approaches to New Haven and Hartford, the speed restrictions are caused by arbitrarily slowdowns for grade crossings rather than by constrained geometry.

However, in practice, the line is in poor state of repair. Grade crossings are unprotected. The entire line is not electrified, and there are no plans to electrify it, for reasons that can only be explained as an allergy that North American railroaders have to electrification. The stations have low platforms, which are not accessible to people in wheelchairs without labor-intensive, time-consuming lift operations—and even if there are no riders with disabilities, it just takes longer for passengers to board from low platforms.

The above schedule assumes 7% padding and 30-second dwell times at stations, but such assumptions only work when the equipment is reliable, and when there are wide doors letting passengers on the train with level boarding or at worst short steps. Traditional commuter lines pulled by diesel locomotives, serving low-platform stations with narrow doors, have to be much slower. Clem Tillier‘s example timetable for Caltrain requires 15% padding and 45-second dwell times with today’s diesel operations—and at rush hour some station dwells stretch over minutes due to the railroad’s uniquely high number of passengers with bicycles.

The good news is that electrification and high platforms are, in the grand scheme of things, cheap. Amtrak electrified the Northeast Corridor between New Haven and Boston at $3.5 million per kilometer in the 1990s, adjusted for inflation; at that cost, wiring the entire New Haven-Springfield shuttle would run up to$350 million. Moreover, Boston has been equipping a number of commuter rail stations with high platforms in order to provide wheelchair accessibility, and in ordinary circumstances, the costs have been on the order of $6-10 million per station. This entire package on the Hartford Line would be cheaper than replacing any of the movable bridges on the New Haven Line. Moreover, upgrading grade crossings with four-quadrant gates, which make it impossible for cars to drive around the gates while they are closed, is affordable as well—and would permit the towns along the route to institute quiet zones, eliminating the loud train horns. In Boulder, the same installation costs about$500,000 per grade crossing for quad gates and another $300,000 for an alternative to horns; in federal regulations, quad gates are good up to 110 mph. There are 23 level crossings between New Haven and Hartford and another 11 between Hartford and Springfield;$30 million would upgrade them all.

The importance of a good maintenance regime

In Switzerland, schedules are padded by 7% over the technical travel time, to permit trains to recover from delays. By American standards, this is a low figure: the LIRR’s schedules are padded by 20-30%, and I have personally seen an express New Haven Line train do Stamford-Grand Central in about 15% less than the scheduled trip time.

Switzerland achieves high punctuality with relatively tight scheduling by making sure delays do not propagate. Railroad junctions are grade-separated when possible, and if not then they are equipped with pocket tracks to allow trains to wait without delaying crossing traffic. To achieve comparable reliability, Metro-North should grade-separate its most important junctions: Shell, where the line joins with the Northeast Corridor tracks carrying Amtrak (and soon Penn Station Access); and Stam, where the New Canaan Branch joins. It could potentially also grade-separate Berk, where the Danbury Branch joins, and Devon, where the Waterbury Branch joins, but the traffic at these junctions is lighter and delayed branch trains can wait without disturbing mainline trains.

Moreover, like the rest of Europe as well as Japan, Switzerland conducts maintenance at night. The daytime maintenance with work zones that are a common sight on American passenger railroads are unknown on most European railroads. Only mixed lines running high-speed passenger trains in the day and freight at night have to schedule trains next to active work zones, and those are indeed much harder to maintain.

The laws of physics are the same on both sides of the Atlantic. If it’s possible to maintain tracks adequately during four-hour nighttime windows in Europe, it’s possible to do the same in the United States. Freight traffic on the Northeast Corridor is lighter than on many Swiss mainlines, and while passenger traffic at rush hour is very heavy, in the off-peak it is considerably lighter than on the urban commuter rail line trunks of Zurich. While four Metro-North trains run between New York and Stamford every off-peak hour, as does a single Amtrak train, ten Zurich S-Bahn trains run per hour between Zurich and Winterthur, as do six interregional and intercity trains.

The importance of maintenance was underscored in a recent article describing an independent plan to drastically cut travel times through better track standards, spearheaded by Joe McGee of the Business Council of Fairfield County and authored by San Francisco consultant Ty Lin and former Metro-North president Joseph Giulietti. In response to their plan, CDOT said it was not possible—and to emphasize this fact, the article notes that an upcoming schedule revision will slow down the trains by 6 to 10 minutes due to trackwork delays.

The one thing that the state must avoid is funneling any money into State of Good Repair (SOGR) programs. SOGR is a black hole permitting incompetent officials to spend capital money without anything to show for it: agencies around the country have SOGR programs decade after decade and somehow their stated maintenance backlogs never shrink.

Instead, 30-30-30 is the closest thing to a true program for what SOGR is supposed to be. Were the tracks in good shape, and were speeds on curves in line with modern railroading practices in other developed countries, express trains would take exactly half an hour to travel between Grand Central and Stamford and between Stamford and New Haven. So 30-30-30 is really setting a standard for a program that, up until now, has only served as an excuse for CDOT to do nothing.

It’s not yet clear what CDOT and Metro-North’s reaction to 30-30-30 will be. Is the governor’s goal achievable? Absolutely, give or take a few minutes. Is it achievable on a reasonable budget? Definitely. Are the managers who have let train schedules slip over the years, as their counterparts in New York have, capable of running the trains punctually enough in order to meet the timetable? That is the big question mark.

# Fix the Slowest Speed Zones

I am wrapping up a project to look at speedup possibilities for trains between New York and New Haven; I’ll post a full account soon, but the headline result is that express trains can get between Grand Central and New Haven in a little more than an hour on legacy track. In this calculation I looked at speed zones imposed by the curves on the line. The biggest possible speedups involve speed limits that are not geometric – and those in turn come from some very sharp slow zones. The worst is the Grand Central station throat, and I want to discuss that in particular since fixing the slowest zones usually yields the most benefits for train travel times.

Best practice for terminal approaches

Following Richard Mlynarik’s attempt to rescue the Downtown Extension in San Francisco, I’ve assumed that trains can approach terminals at 70 km/h, based on German standards. At this speed, an EMU on level track can stop in about 150 meters. In Paris, the excellent Carto Metro site details speed limits, and at most terminals with bumper tracks the speed limit is 60 km/h, with a few going up to 100 km/h.

Even with bumper tracks, 70 km/h can be supported, provided the train is not intended to stop right at the bumpers. At a fixed speed, the deceleration distance is the inverse of the deceleration rate. There is some variation in braking performance, but it’s in a fairly narrow range; on subway trains in New York, everything is supposed to brake at the same nominal rate of 3 mph/s, or 1.3 m/s^2, and when trains brake more slowly it’s because of a deliberate decision to avoid wearing the brakes out. As long as the train stops 1-2 car lengths away from the bumpers, as is routine on Metro-North, the variation will be much smaller than the margin of safety.

Fast movement through the station throat is critical for several reasons. First, as I’ll explain below, sharp speed limits have an outsize effect on trip times, and can be fixed without expensive curve easements or top-rate rolling stock. And second, at train stations with a limited number of tracks, the station throat is the real limiting factor to capacity, since trains would be moving in and out frequently, and if they move too slowly, they’ll conflict. With its 60 km/h throat, Saint-Lazare on the RER E turns 16 trains per hour at the peak on only four tracks.

American practice

I had a conversation with other members of TransitMatters in Boston yesterday, in which we discussed work to be done for our regional rail project. One of the other members, I forget who, asked me, do European train protection systems shut down in station throats too?

The answer to the question is so obviously yes that I wanted to understand why anyone would ask it. Apparently, the American mandate for automatic train protection on all passenger rail lines, under the name positive train control, or PTC, is only at speeds higher than 10 miles per hour. At 10 mph or less train operators can drive the train by sight, and no signaling is required, which is why occasionally trains overrun the bumpers even on PTC-equipped lines if the driver has sleep apnea.

Without video, nobody could see the facial expressions I was making. I believe my exact words were “…What? No! What? What the hell?”.

The conversation was about South Station, but the same situation occurs at Grand Central. Right-of-way geometry is good for decent station approach speed – there is practically no limit at Grand Central except tunnel clearances, which should be good for 100 km/h, and at South Station the sharp curve into the station from the west is still good for around 70 km/h given enough superelevation.

The impact of slow zones near stations

Last year, I published code for figuring out acceleration penalties based on prescribed train characteristics. The relevant parameters for Metro-North’s M8 is initial acceleration = 0.9 m/s^2, power/weight = 12 kW/t. Both of these figures are about two-thirds as high as what modern European EMUs are capable of, but it turns out that at low speed it does not matter too much.

Right now the Grand Central throat has a 10 mph speed limit starting just north of 59th Street, just south of milepoint 1. The total travel time over this stretch is 6 minutes, a familiar slog to every regular Metro-North rider; overall, the schedule between Grand Central and Harlem-125th Street is 10 minutes northbound and 12-13 minutes southbound, the difference coming from schedule padding. The remaining 65 or so blocks are taken at 60 mph, nearly 100 km/h, and take around 4 minutes.

Now, let’s eliminate the slow zone. Let trains keep cruising at 100 km/h until they hit the closer-in parts of the throat, say the last kilometer, where the interlocking grows in complexity and upgrading the switches may be difficult; in the last kilometer, let trains run at 70 km/h. The total travel time in the last mile now shrinks to a minute, and the total travel time between Grand Central and Harlem shrinks to 5 minutes and change. Passengers have gained 5 minutes based on literally the last mile.

For the same reason, the Baltimore and Potomac Tunnel imposes a serious speed limit – currently 30 mph through the tunnel, lasting about 2 miles; removing this limit would cut 2-2.5 minutes from the trip time, less than Grand Central’s 5 because the speed limit isn’t as wretched.

The total travel time between New York and New Haven on Metro-North today is about 1:50 off-peak, on trains making all stops north of Stamford. My proposed schedule has trains making the same stops plus New Rochelle doing the trip in 1:23. Out of the 27-28 minutes saved, 5 come from the Grand Central throat, the others coming from higher speed limits on the rest of the route as well as reduced schedule padding; lifting the blanket 75 mph speed limit in Connecticut is only worth about 3 minutes on a train making all stops north of Stamford, and even on an express train it’s only worth about 6 minutes over a 73 kilometer stretch.

What matters for high-speed travel

High-speed rail programs like to boast about their top speeds. But in reality, the difference between a vanilla 300 km/h train and a top of the line 360 km/h only adds up to a minute every 30 kilometers, exclusive of acceleration time. Increasing top speed is still worth it on lines with long stretches of full-speed travel, such as the Tohoku Shinkansen, where there are plans to run trains at 360 over hundreds of kilometers once the connection to Hokkaido reaches Sapporo. However, ultimately, all this extra spending on electricity and noise abatement only yields a second-order improvement to trip times.

In contrast, the slow segments offer tremendous opportunity if they are fixed. The 10 mph limit in the immediate Penn Station throat slows trains down by around 2 minutes, and those of Grand Central and South Station slow trains by more. A 130 km/h slog through suburbia where 200 km/h is possible costs a minute for every 6.2 km, which easily adds up to 5 minutes in a large city region like Tokyo. An individual switch that imposes an undue speed limit can meaningfully slow the schedule, which is why the HSR networks of the world invented high-speed turnouts.

Richard Mlynarik notes that in Germany, the fastest single end-to-end intercity rail line used to be Berlin-Hamburg, a legacy line limited to 230 km/h, where trains averaged about 190 km/h when Berlin Hauptbahnhof opened (they’ve since been slowed and now average 160). Trains go at full speed for the entire way between Berlin and Hamburg, whereas slow urban approaches reduce the average speed of nominally 300 km/h Frankfurt-Cologne to about 180, and numerous compromises reduce that of the nominally 300 km/h Berlin-Munich line to 160; even today, trains from Berlin to Hamburg are a hair faster than trains to Munich because the Berlin-Hamburg line’s speed is more consistent.

The same logic applies to all travel, and not just high-speed rail. The most important part of a regional railway to speed up is the slowest station throats, followed by slow urban approaches if they prove to be a problem. The most important part of a subway to speed up is individual slow zones at stations or sharp curves that are not properly superelevated. The most important part of a bus trip to speed up is the most congested city center segment.

# The Rhine-Neckar Region

The weekend before last, I visited Kaiserslautern and Mainz; I have photos from Mainz and will blog about it separately later this week. Due to a train cancellation, my 2.5-hour direct train to Kaiserslautern was replaced with a three-leg itinerary via Karlsruhe and Neustadt that took 5.5 hours. Even though neither Kaiserslautern nor Karlsruhe is contained within the region, they are both served by the Rhine-Neckar regional rail network. After riding the trains I looked up the network, and want to explain how things work in a metro area that is not very well-known for how big it is.

How polycentric is the system?

The Rhine-Neckar is polycentric, but only to a limited extent. It does have a single central city in Mannheim, with 300,000 people, plus another 170,000 in Ludwigshafen, a suburb across the Rhine. With Heidelberg (which has 160,000 people) and many surrounding suburbs, the total population of this region is 2.5 million, about comparable to Stockholm, Copenhagen, and Hamburg.

The liminal polycentricity comes from the fact that Mannheim has a distinguished position that no single central city has in the Ruhr or Randstad. However, Heidelberg, Neustadt, Worms, and Speyer are all independent cities, all of which have long histories. It’s not like Paris, where the suburbs were all founded explicitly as new towns – Versailles in the Early Modern era, and the rest (Cergy, La Defense, Evry, Marne-la-Vallee, etc.) in the postwar era.

The rail network has the same liminal characteristic, which is what makes it so interesting. There is an S-Bahn, centered on Mannheim. There are two main trunk lines, S1/2 and S3/4: every numbered line runs on an hourly clockface schedule, and S2 and S4 provide short-turn overlays on the S1 and S3 lines respectively, giving half-hourly service on the combined lines. Some additional lines are not Mannheim-centered: the S33 is circumferential, and the S5/51 are two branches terminating at Heidelberg. Additional lines fanning out of Mannheim are under construction, to be transferred from the RegionalBahn system; already S6 to Mainz is running every half hour, and there are plans for lines going up to S9.

However, it is wrong to view the Rhine-Neckar regional rail network as a Mannheim-centric system the way the RER is Paris-centric and the Berlin S-Bahn is Berlin-centric. The Mannheim-centered S-Bahn lines run alongside a large slew of legacy RegionalBahn lines, which run on hourly clockface schedules. The S3 serves Karlsruhe and the S1 and S2 serve Kaiserslautern, but this is not how I got from Karlsruhe to Kaiserslautern: I took a regional train via Neustadt, running on a more direct route with fewer stops via Wörth and Landau, and transferred to the S1 at Neustadt.

Integrated timed transfers

Kaiserslautern is not really part of the Rhine-Neckar region. It is too far west. However, it is amply connected to the core of the region: it has S1 and S2 rail service (in fact it is the western terminus of the S2), and it has regional trains to Mannheim as well as to other cities within the region. The regional train from Mannheim to Kaiserslautern and points west is timed to leave Neustadt a few minutes ahead of the S1, as it runs on the same line but makes fewer stops.

In addition, all these trains to cities of varying levels of importance have a system of timed transfers. I took this photo while waiting for my delayed train back to Paris:

Other than the S-Bahn east, the trains all leave a few minutes after 8:30, and I saw them all arrive at the station just before 8:30, allowing passengers to interchange across as well as between platforms. Judging by static arrival boards posted at stations, this integrated timed transfer repeats hourly.

Some of the lines depicted on the map serve cities of reasonable size, including Mannheim and Heidelberg, but also Homburg, the western terminus of the S1. Others don’t; Pirmasens is a town of 40,000, and the intermediate towns on the line as it winds through the Palatinate valleys have a few thousand people each. Nonetheless, there is evidently enough demand to run service and participate in the integrated timed transfer plan.

Population density and the scope of the network

As I’ve mentioned above, neither Kaiserslautern nor Karlsruhe is properly part of the Rhine-Neckar. Neither is Mainz, which is within the Frankfurt region. Nonetheless, all are on the Rhine-Neckar S-Bahn, and Kaiserslautern isn’t even an outer terminus – it’s on the way to Homburg.

This is for two reasons. The first is that this is a new S-Bahn network, cobbled together from regional lines that were formally transferred to the S-Bahn for planning purposes. It lacks the features that bigger S-Bahn networks have, like strong urban service. The Rhine-Neckar is about the same size as Hamburg, where the S-Bahn provides 10-minute frequencies to a variety of urban neighborhoods; in contrast, the S1/2 and S3/4 trunk lines in Mannheim aren’t even set up to overlay to exact 15-minute frequencies on the shared segment to Heidelberg.

I’ve talked about the distinction between regional and intercity service in the context of Boston. In Boston I recommend that some lines be run primarily as intercities, with long-range service and fewer stops, such as the Providence and Lowell Lines, both serving independent urban centers with weak inner suburbs on the way, while others be run primarily as locals, with more urban stops, such as the Fairmount-Franklin Line, which has no strong outer anchor but does pass through dense neighborhoods and inner suburbs.

The same distinction can be seen in Germany, all falling under the S-Bahn rubric. Wikipedia has a map of all S-Bahn systems in Germany at once: it can be readily seen that Hamburg, Berlin, Munich, Stuttgart, and Frankfurt have predominantly local systems, while Hannover, Nuremberg, the Rhine-Neckar, and Middle Germany (where the largest city is Leipzig) have predominantly intercity systems that are run as if they were S-Bahns.

The second reason owes to the urban geography of the Rhineland. Paris, Berlin, and Hamburg are all clearly-defined city centers surrounded by rings of suburbs. The Rhineland instead has a variety of smaller urban centers, in which suburb formation often takes the form of people hopping to a nearby independent city and commuting from there. All of these cities have very small contiguous built-up areas relative to the size of their metropolitan regions, and contiguous suburbs like Ludwigshafen are the exception rather than the rule.

Moreover, the background population density in the Rhineland is very high, so the cities are spaced very close together. This enabled the Rhine-Ruhr to form as a polycentric metro area comparable in size to London and Paris without having any core even approaching the importance of Central London or central Paris. The Upper Rhine is not as industrialized as the Ruhr, but has the same interconnected network of cities, stretching from Frankfurt and Wiesbaden up to Karlsruhe. In such a region, it’s unavoidable that commuter lines serving different urban cores will touch, forcing an everywhere-to-everywhere network.

To reinforce the importance of high density, we can look at other areas of high population density. The Netherlands is one obvious example, underlying Randstad and an extremely dense national rail network in which it’s not really possible to separate different regions for planning purposes. England overall is dense as well, but the south is entirely London-centric; however, the same interconnected network of cities typical of the Middle and Upper Rhine exists in Northern England, which not only invented the railway but also maintains a fairly dense rail network and has a variety of connecting services like TransPennine. Finally, the Northeastern United States has commuter rail line on nearly the entire length of the Northeast Corridor, touching in Trenton between New York and Philadelphia, with perennial plans to extend services in Maryland, Connecticut, and Rhode Island to close the remaining gaps.

Swiss lessons

Switzerland has long had a national integrated transfer timetable, overlaying more local S-Bahn trains in the biggest cities. As long as there is more than one node in such a network, it is necessary to ensure travel times between nodes permit trains to make multiple transfers.

This leads to the Swiss slogan, run trains as fast as necessary, not as fast as possible. This means that, in a system based on hourly clockface schedules, the trip times between nodes should be about an hour minus a few minutes to allow for transfer time and schedule recovery. Potentially it’s possible to set up some intermediate nodes to have transfers at half-integer hours rather than integer hours, allowing half-integer hour timed transfers. Switzerland’s main intercity lines run on a half-hourly takt, with timed transfers on the hour every half hour in Zurich, Bern, and Basel, which are connected in a triangle with express trains taking about 53 minutes per leg; additionally, some smaller cities have timed transfers 15 and 45 minutes after the hour.

Germany’s rail network is less modern than Switzerland’s, and the Rhine-Neckar schedule shows it. S-Bahn trains run between Kaiserslautern and Mannheim in a few minutes more than an hour, which is why the S-Bahn train depicted in the photo above does not participate in the hourly pulse. In contrast, the regional express trains take 45 minutes, which allows them to participate in the pulse with a little bit of wasted time at Mannheim. Potentially, the region may want to level these two service patterns into one local pattern with a one-way trip time of about 50 minutes, through speeding up the trains if possible. A speedup would not be easy – the rolling stock is already very powerful, and the line is 64 km and has 16 stations and a curvy western half. Discontinuing service on the S2 to two neighborhood stations in Ludwigshafen, which the S1 already skips, is most likely required for such a hybrid S-Bahn/RegionalExpress service.

However, it’s critical to stress that, while Germany is lagging Switzerland, Austria, the Netherlands, and Sweden, it is not to be treated as some American basket case. The Rhine-Neckar rail network is imperfect and it’s useful to understand how it can improve by learning from comparable examples, but it’s good enough so as to be a model for other systems in polycentric regions, such as New England, the Lehigh Valley, Northern England, and Nord-Pas-de-Calais.

# Where Line 2 Should Go Depends on Where Line 1 Goes

A city that is building a rapid transit network piecemeal has to decide on priorities. There are tools for deciding where to build the first line, such as looking at the surface transit network and seeing what the busiest corridor is. These are relatively well-understood. In this post I’d like to focus on where to build the second line, because that question depends not only on the usual factors for where to build transit, but also on how the first line is expected to change the network. This is relevant not only to cities that are building a new rapid transit system, but also to cities that have such a network and are adding new lines one at a time: the usual tools can straightforwardly suggest where to build one line, but figuring out where to build a second line requires some additional work.

A toy model

Consider the following city, with its five busiest buses, labeled A-E from busiest to fifth busiest:

Let’s stipulate that there’s a wealth of arterial roads radiating in the right directions, and no motorways entering city center, so the exceptions to the rule that trains should go where the busiest buses are don’t apply. Let’s also stipulate that the other buses in the city don’t affect the internal ranking of the first five much – so if there are a bunch of north-south buses close to route C not depicted on the map, they’re not busy enough to make it busier than route A.

Clearly, based on the A > B > C > D > E ranking, the top priority for a first rapid transit line is A. Not only is it the busiest bus but also it is parallel to the second busiest.

But the second priority is not B, but C. The reason is that a rapid transit line on A captures east-west traffic, and then from the eastern and western neighborhoods people on route B are likely to walk south or ride a circumferential bus to get to the train. In the presence of a subway underneath the arterial carrying route A, the strongest bus corridor will almost certainly become C, and thus planners should aim to build a subway there as their second line, and begin design even before the first subway opens.

Fourth Avenue in Vancouver

Vancouver already has a rapid transit system, with three SkyTrain lines. However, the issue of the second line crops up when looking at remaining bus corridors and future subway plans. The strongest bus route is by far Broadway, which had higher ridership than the buses that became the Millennium and Canada Lines even when those lines were planned. The Millennium Line was only built first because it was easier, as it is elevated through the suburbs, and the Canada Line because Richmond demanded a SkyTrain connection.

Fortunately, Broadway is finally getting a subway, running from the Millennium Line’s current terminus at VCC-Clark to Arbutus, halfway toward the corridor’s natural end at UBC. The question is, what next? The second busiest bus corridor in Vancouver is Fourth Avenue, where the combined ridership of the 4, 44, and 84 buses and the part of the 7 that is on Fourth exceeds that of any corridor except Broadway; only Hastings, hosting the 95 and 160, comes close.

And yet, it is obviously wrong to plan any subway on Fourth Avenue. Fourth is half a kilometer away from Broadway; the 44 and 84 are relief for the 99 on Broadway. TransLink understands it and therefore there are no plans to do anything on Fourth – the next priority is extending the Expo Line farther out into Surrey or Langley, with the exact route to be determined based on political considerations.

Regional rail and subways in New York

In New York, two commonly-proposed subway extensions, down Nostrand and Utica, are closely parallel. The fact that they are so close to each other means that if one is built, the case for the other weakens. But these two corridors are so strong it is likely that if one is built, the second remains a very high priority. The only subway priority that is plausibly lower than the first of the two and higher than the second, regardless of which of Utica and Nostrand is built first, is a 125th Street crosstown extension of Second Avenue Subway.

But a more serious example of one future line weakening another occurs for regional rail. The top priority for regional rail in New York is four-tracking the tunnels to Penn Station under the Hudson; based on this priority, organizations that look beyond the next gubernatorial or congressional election have come up with farther-reaching proposals. Here, for example, is the map from the RPA’s Fourth Regional Plan:

In addition to four-tracking the North River Tunnels under the aegis of the Gateway project, the RPA calls for two additional two-track tunnels under the Hudson, in phases 2 and 3 of its proposal. Both are to feed Midtown: the phase 2 tunnel is to connect regional rail lines to be reactivated with Columbus Circle, Grand Central, and other destinations in the city, and the phase 3 tunnel is to then carry the same line out of the city and back into New Jersey via Hoboken and the existing commuter lines serving southern and southwestern suburbs.

The logic, as I understand it, is that Midtown is the core of the New York region, and so it is the most important to connect there. I don’t know if this is what the RPA was thinking, but I asked at an IRUM meeting in 2010 why all plans involve connections to Midtown rather than Lower Manhattan and was told Lower Manhattan was not as important a business district.

The toy model has one fixed city center and varying outlying areas, the opposite of the situation here. Here, my criticism is of plans that serve the dominant city center while ignoring the second most important center. The total number of jobs in Midtown is 800,000 whereas Lower Manhattan has 250,000 – but Lower Manhattan is more compact, so a single station at Fulton with several exits can plausibly serve the entire area, whereas Midtown has areas that are too far from both Penn Station and Grand Central. The next pair of tracks should serve Midtown, but the pair after them should serve Lower Manhattan, to ensure good coverage to both business districts.