Category: Good Transit

New York Has Too Few Subway Countdown Clocks

When I was visiting New York in June-July, I was stricken by how hard it was to figure out when the next train would come. Every subway station is equipped with countdown clocks, the A Division (numbered lines) and L trains having older installations than the rest of the B Division (lettered lines). However, the B Division stations that I used did not have many countdown clocks, and I found myself having to walk long distances along hot platforms to figure out which train to take. I counted the number of clocks at a few stations, and asked ETA members to do the same; now back in Berlin, I’ve done some counts here as well, confirming that it’s not just me – New York’s B Division platforms have fewer and harder to find countdown clocks than the standard on the Berlin U- and S-Bahn platforms, even though New York’s more complex subway network requires if anything more clocks as passengers have multiple options. Based on what I’ve seen in Berlin, I recommend that New York install a minimum of four overhead clocks per B Division platform, with the screen going in both directions.

The situation in Berlin

The U-Bahn platforms seem standardized to me. The traditional norm was that stations were built cut-and-cover, right underneath a major street, with an entrance at each end of the central island platform. Nowadays almost all stations have elevators and there are plans for retrofitting the rest, which BVG estimates will be completed in 2028, the date having been pushed later over the years I’ve lived in the city. The elevators always connect two levels, with opposite side doors for the two levels, so that wheelchair users don’t have to turn.

There are, at the stations I use, two overhead countdown clocks for each platform face. Nearly all platforms are islands, and each direction has separate countdown clocks. The clocks display the times on both sides, and are typically located at the quarter points of the station, so that passengers are never more than a quarter of the platform length from a clock, with good sight lines; the platforms are 100-110 meters long.

The S-Bahn is less standardized. A full-length eight-car train is 150 meters is long. The countdown clocks are double-sided and overhead as on the U-Bahn, and each platform face has a separate clock even when the tracks are in the same direction (as at Ostbahnhof), but the number is inconsistent; there are stations with just one, but Friedrichstraße on the North-South Tunnel has three.

The situation in New York

The A Division has overhead countdown clocks, connected to the train control system (automated train supervision, or ATS), installed in the early 2010s; the L has countdown clocks of the same provenance. The number of clocks per station is not fixed, but ranges between two and four per track. The B Division’s train control system let the control center know where trains were but not which train was which – that is, which train on the same track is an A, which is a D, and so on – and therefore the same system was not installed at the time. Years later, a different system was installed, with nicer graphics and a different connection to the control center, which is sometimes less accurate.

This newer system on the B Division has a combination of overhead clocks, often single- rather than double-sided, and floor-mounted clocks facing sideways, toward the tracks rather than toward the front and back of the platforms. The floor-mounted clocks are difficult to read unless I’m standing right there. The platforms are obstructed so it’s hard to tell from a distance where the clock is. Worse, many floor-mounted installations look identical from a distance to the clocks, but instead display advertisements or service changes but no information about the next train.

What’s more, there just aren’t a lot of these clocks. At 2nd Avenue on the F, heading downtown toward Marron, I counted a single clock, but six boards displaying system maps or ads. ETA’s Alex Sramek checked several stations in Lower Manhattan, including Chambers on the A/C/E and on the J/Z, Fulton Street, Cortlandt Street on the R/W, and Broad Street, and found one to three clocks, always a mix of overhead and floor-mounted – and the floor-mounted clocks sometimes would only show the next train and not the subsequent ones, even for platforms serving multiple routes.

There should be more clocks in New York than in Berlin. The platforms are much longer – the A Division platforms are 155 meters, the L and J/Z platforms are 145 meters, the other B Division platforms are 185 meters. The extensive branching means that even while waiting on the platform, regardless of what information is displayed outside the station, it is important to know when each service using the station will come, to plan out which line to take. I made mistakes on trips from Brooklyn to Queens just because I wasn’t sure what to do when transferring at West 4th, where, having just missed the E, I needed to make a decision on whether to wait for a delayed F or try to make the B/D and transfer to the E at 53rd, opted for the latter, and missed the E at 53rd.

If a Berlin U-Bahn station has two double-sided clocks, and a major S-Bahn station has three, then New York should have four per B Division platform. These should be overhead and double-sided – the floor-mounted screens are difficult to see from a distance along the direction relevant to most passengers, and easily confused with ads, ensuring that their utility is marginal.

The Meaning of Construction Costs Per Rider

I’ve written a lot about urban rail construction costs per kilometer, but from time to time, my colleagues and I have been asked about what happens if we compare costs, not per kilometer, but per rider. There’s an intuition among people in transportation advocacy (including anti-transit activists who prefer cars) that the construction costs of urban rail lines per rider are a meaningful measure of cost-effectiveness. This intuition is true, and yet, it must be interpreted delicately.

First, modes of transit with different operating cost structures should tolerate different levels of capital costs; in particular, the current practice in which subways are built at higher cost per rider than light rail, which in turn is built at higher cost than bus lanes, reflects real differences in operating costs and does not mean there is overinvestment in subways and underinvestment in buses. And second, costs per rider can be too low, in a sense – if a city’s construction costs per rider are very low, indicating a very high benefit-cost ratio, then it shouldn’t be lauded for its fiscal prudence but scolded for not having built these lines long ago and for not building more today. In truth, places with healthy decisionmaking about infrastructure expand their networks to the limit of cost-effectiveness, which means that costs per rider averaged over an entire region vary less than costs per kilometer, and this just reflects that cities build what they can, so low-cost cities can afford to build lines to lower-ridership areas, which higher-cost cities would reject as too expensive for the benefit. This way, costs per rider are not too different in New York and in cities that build for an order of magnitude lower cost per km than New York.

The meaning of cost per rider

In the remainder of this post, the meaning of “cost per rider” is “cost divided by the ridership on a working day.” In Europe, workers get around six weeks of paid vacation, and tend to take them in the summer, leading to depressed ridership around July or August, depending on the city; daily counts usually avoid this period, so for example Stockholm specifies that daily ridership figures are taken in winter. This, as I will explain shortly, does not unduly make European lines look more cost-effective than they actually are.

The cost per rider is best understood as a cost-benefit measurement. All benefits of public transportation scale with ridership, generally linearly: higher ridership indicates tighter economic and social ties if it comes from more travel, and better environmental outcomes if it is at the expense of car travel. What’s more, raw ridership measured in trips is better at capturing these benefits than passenger-km. The issue is that focusing on p-km overrates the success of extremely suburban systems, which have low environmental benefits for their p-km (the users are typically park-and-riders and therefore drive extensively, just not to their city center jobs) and usually also high net operating costs since they are peaky and tend to charge low per-p-km fares. Conversely, the short-hop trip is a net profit to the system – even subways with distance-based fares charge degressive rather than linear fares – and comes from dense networks that cut out car-based travel entirely. These effects roughly cancel out to the point that ridership is a good proxy for actual benefits.

That said, all outcomes need to be scaled to regional or even national incomes. Economic benefits are usually measured relative to worker wages anyway; in some business case analyses, such as that of the United Kingdom, the economic benefit is even scaled to rider income rather than regional or national income, which favors lines built to rich neighborhoods over lines built to poor ones, and isn’t really how cities need to think about their public transit networks. Social benefits are usually taken on a willingness-to-pay basis, and the same is true of health benefits including reduced air and noise pollution from cars and reduced car accidents.

The next step is then to compare the cost per rider with GDP per capita, which is not perfect but is good enough as a proxy for incomes. This also takes care of the issue of Europe’s synchronized summer troughs in local travel: those six weeks of paid vacation are visible in reduced GDP per capita, so the apparent bonus to the European system of using cost per daily trip where “day” means “workday outside the summer vacation season” rather than cost per annual trip cancels out with reduced annual GDP per capita.

The rough rule of thumb I use is that the absolute limit of cost-effectiveness for a subway or commuter rail line is when the cost per rider is equal to GDP per capita. This is a coincidence: a one-time cost has no reason to be equal to an annual income – this just follows from Börjesson-Jonsson-Lundberg’s estimate of the Stockholm Metro’s benefit-cost ratio compared with its cost per rider relative to the GDP per capita of 1960s’ Sweden. In practice, infrastructure is never built down to a benefit-cost ratio of 1, due to construction risks; in countries that make decisions based on benefit-cost analyses, the minimum is usually 1.2 or 1.3. In this schema, the United States can afford to build up to an envelope of $85,373/1.3 to $85,373, which is $65,000-70,000/rider in 2024 prices. The frontier lines, like the Interborough Express, are fairly close to this limit already; in practice, there’s a range, with some lines in the same city built well over the limit for political reasons (often airport connectors) and others built far below it.

Cost per rider by mode

The above analysis works for subways and commuter rail. It does not work for trams or buses. The reason is that surface transit never achieves the same low operating costs as metros, so in practice, the total cost to be truly comparable needs to be incremented by the additional operating costs.

To be clear, this is just a rule of thumb. There are different metro lines, even with the exact same technology in the same city, with different projected operating cost profiles; for example, in Vancouver, the Broadway extension of SkyTrain toward UBC was projected in the 2010s to reduce net operating costs as many buses would be replaced by fewer, larger trains, but the outward extension of the same system deeper into Surrey and Langley is projected to increase net operating costs. There are different ways to interpret this – for example, the Surrey extension is in a more auto-oriented area, with more likely car-to-train switchers (this is still much denser than an American park-and-ride); on net, though, I think the differences are not huge and could to an extent even be folded into the notion of cost per rider, which is substantially better on Broadway than in Surrey and Langley.

That said, metros consistently have much lower operating costs than light rail and buses in the same city; here are American cost profiles. As far as I can tell from CoMET data, most European and Asian metros cluster toward the bottom end of the American cost profile (such as the Chicago L; the New York City Subway is the top end among the big systems); bus operating costs are more or less proportional to driver wages times operating hours throughout the developed world. Here we need to briefly switch to cost per p-km, since mature urban rail networks use buses as short-hop feeders – the counterfactual to a bus-based network for New York isn’t people riding the same bus routes as today but at higher intensity, but people riding longer bus routes, so the cost would roughly scale to cost per p-km, not per passenger.

In rich Asia, metros are profitable. In Europe, it depends – the London Underground operationally broke even in the early 2010s, and the Berlin U-Bahn was said to do the same in the late 2010s. In healthy European systems, it’s never reported directly, since there’s fare integration across the region, so financial data are reported at metropolitan scale without much breakdown between the modes, but the farebox operating ratios in at least Germany and Scandinavia, and probably also Paris (which has much higher ridership density than London or Berlin, comparable costs per car-km, and higher fares than pre-2022 Berlin), suggest that metros and the inner sections of commuter rail systems can break even, and then the subsidies go to the buses and to suburban extensions.

Individual bus systems can be profitable, but never at metropolitan scale, not in the first-world cities I’m aware of. In New York, the buses between New Jersey and Manhattan are profitable and run by private companies, but that’s one specific section of the system, and on net the bus system in New Jersey, including not just these cross-tunnel buses but also internal buses within the state, loses money, covered by New Jersey Transit subsidies, and the financial performance of buses within New York is, frankly, terrible.

One potential complication is that BRT infrastructure is usually installed on the highest-performing individual routes, and those can have rather low operating costs. But then, the operating costs of the buses on Broadway in Vancouver are extraordinarily low, and still the projections are for the SkyTrain extension that would replace them to, on net, reduce systemwide operating subsidies. If your city has a bus corridor so strong that ordinary BRT would be profitable, the corridor has high enough ridership for a subway.

Light rail is essentially a via media between metros and buses: higher operating costs than metros, in theory lower ones than buses. I say in theory, because in the United States, light rail as a mode comprises different things, some behaving like lower-efficiency subways with shorter cars like the Boston Green Lines, and others running as mostly grade-separated urban rail in cities like the Los Angeles and Portland cities with extremely low ridership and high resulting operating costs. But a light rail system with serious ridership should comfortably obtain better operating outcomes than buses, if worse ones than metros.

Costs per rider can be too low

In New York, as mentioned above, the current urban rail extensions under construction (Second Avenue Subway Phase 2) or discussion (Interborough Express) have costs not far from the frontier relative to American incomes. In Berlin, the extensions instead are far cheaper; U8 to Märkisches Viertel was projected to cost 13,160€ per daily rider in 2021, which is a fraction of Germany’s GDP per capita.

This does not mean Berlin builds cost-effectively. It means Berlin builds too little. A line that costs less than one third the country’s GDP per capita should have been built when the GDP per capita was one third what it is now. If there are a lot of such possibilities in the city, it means there was a crisis it’s only now recovering from or there has been too much austerity, or both, in the case of Berlin.

Healthy construction environments – that is, not Germany, which has normal costs per kilometer and chooses to barely build intercity or urban rail – will instead build to the frontier of what’s cost-effective. In New York, it’s Second Avenue Subway; in Madrid, it’s extensions into deep suburbia making the system almost as long as that of New York, on one third the metro area population. Rational yes/no decisions on whether to build at all can coexist with good construction practices or with deeply irrational ones.

Northeast Corridor Realignment Webtool

Here is an interactive webtool for the Northeast Corridor alignment options we’re timetabling. All credit for the data visualization goes to Devin Wilkins; my contribution is to draw the options in a more static format.

There are still some tweaks to the system, but the physical location of the tracks should be considered secure, and the same is true of the curve database. The units are mixed; curves use the formula 1° = 1,746 meter radius, and speeds are in metric units, with lateral acceleration in the horizontal plane of 2.2 m/s^2 (330 mm total equivalent cant) at low and medium speed and 2.07 at high speed (310), both of which are limit values but do exist in this part of the world and are a rounding error away from American limit values. If there is any discrepancy between the listed speed and the curve radius, the curve radius is correct, and corresponds to the correct speed in our timetable spreadsheets.

Deviations from the current alignment are marked with yellow triangles. The bigger ones are presented as alternatives: it’s possible to build the deviation or stay on the present course. This is especially notable in Connecticut, with many build-or-no-build choices for New Haven Line bypasses as well as for the longer New Haven-Kingston bypass; at one place, Milford, there are two build options, a bypass along I-95 and a straightening of the route close to its current alignment.

I believe but am not completely certain the choice alignment we’ll present will include the bypasses east of New Haven but few to none west of it, of which the likeliest is the one in Greenwich and Cos Cob, where the bypass would provide a six-track section where there are three speed classes (commuter local, commuter express, intercity). South of New York, the curve easement in Metuchen is not currently part of our timetables – it’s too much property acquisition for too little speed gain – but the deviations in Frankford Junction and northeast Maryland are, and the Douglass Tunnel in Baltimore is already funded and in the design phase before physical construction.

Reports on High-Speed Rail and the Northeast Corridor

Two reports that I’ve collaborated on are out now, one about high-speed rail planning for Marron and one about Northeast Corridor maintenance for ETA. A third piece is out, not by me but by Nolan Hicks, about constant-tension catenary and its impact on speed and reliability. The context for the latter two pieces is that the Northeast Corridor has been in a recurrent state of failure in the last three weeks, featuring wire failures, circuit breaker failures, track fires, and transformer fires. The high-speed rail planning piece is of different origin – Eric interviewed officials involved in California High-Speed Rail and other American projects that may or may not happen and this led to synthesizing five planning recommendations, which aren’t really about the Northeast Corridor but should be kept in mind for any plan there as well.

The broader context is that we’re going to release another report specific to the Northeast Corridor, one that’s much more synthetic in the sense of proposing an integrated infrastructure and service planning program to cut trip times to about 1:53 New York-Washington and 2:00 New York-Boston, informed by all of these insights. Nolan’s piece already includes one key piece of information that’s come out of this work, about the benefits of constant-tension catenary upgrades: 1:53 requires constant-tension catenary, and if it is not installed, the trip time is 2:04 instead, making this the single biggest piece of physical infrastructure installation the Northeast Corridor needs.

The catenary issue

Trying to go to Philadelphia, I was treated to a train stuck at Penn Station without air conditioning, until finally, after maybe 45 minutes of announcements by the conductor that it would be a while and they’d make announcements if the train was about to move, I and the other passengers got out to the station, waiting for anything to change, eventually giving up as the train and several subsequent ones were canceled. My post from three days ago about Germany has to be read with this context – while publishing I was waiting for all three pieces above to appear.

I encourage people to read the ETA report for more detail about the catenary. In brief, overhead wires can be tensioned by connecting them to fixed places at intervals along the tracks, which leads to variable tension as the wires expand in the heat and contract in the cold; alternatively, they can be tensioned with spring wires or counterweights, which automatically provide constant tension. The ETA report explains more, with diagrams, some taken from Garry Keenor’s book on rail electrification, some made by Kara Fischer (the one who made the New Mexico public transit maps and others I’ll credit upon request, not the USDOT deputy chief of staff). The catenary on the Northeast Corridor has constant tension north of New York, and for a short stretch in New Jersey, but not on the vast majority of the New York-Washington half of the line.

Variable-tension catenary is generally unreliable in the heat, and is replaced with constant-tension catenary on main lines even in Europe, where the annual temperature range is narrower than in the United States. But it also sets a blanket speed limit; on the Northeast Corridor, it is 135 mph, or 217 km/h – the precision in metric units is because 217 km/h is the limiting speed of a non-tilting train on a curve of radius 1,746 meters, a common radius in the United States as it is a round number in American units (it’s 1°, the degree being the inverse of curve radius). This blanket speed limit slows trains by 11 minutes between New York and Washington, subject to the following assumptions:

  • The tracks otherwise permit the maximum possible speed based on curvature, up to 320 km/h; in practice, there are few opportunities to go faster than 300 south of New York. There is an FRA rule with little justification limiting trains to 160 mph, or a little less than 260 km/h, on any shared track; the rule is assumed removed, and if it isn’t, the cost is about one minute.
  • Trains have the performance of the Velaro Novo, which trainset is being introduced to the United States with Brightline West. Other trainsets may have slightly better or worse performance; the defective Avelia Liberty sets are capable of tilt and therefore the impact of maximum speed is larger.
  • Intercity trains make one stop per state, counting the District of Columbia as a state.
  • Intercity and regional trains are timetabled together, on a clockface schedule with few variations. If a train cannot meet these requirements, it stays off the corridor, with a forced transfer at Philadelphia or Washington. All train schedules are uniformly padded by 7%, regardless of the type of catenary. If variable-tension catenary requires more padding, then the impact of constant-tension catenary is increased.

The bulk of the difference between 1:53 and the current trip time of about 2:50 is about timetabling, not infrastructure – when the trains are running smoothly, there is extensive schedule padding, in one case rising to 35 minutes south of New York on a fast Regional. Rolling stock quality provides a boost as well, to both reliability and acceleration rates. Faster speeds on curves even without tilt matter too – American standards on this are too conservative, and on a built-out line like the Northeast Corridor, being able to run with 180 mm of cant and 130 mm of cant deficiency (see explanation here) is valuable. But once the regulatory and organizational issues are fixed, the biggest single piece of infrastructure investment required is constant-tension catenary, simultaneously reducing trip times and improving reliability.

Nolan’s piece goes more into costs for catenary repair, and those are brutal. The Northeast Corridor Project Inventory includes $611 million to just replace the catenary between Newark and New Brunswick, without constant-tension upgrades. This is 36.5 route-km, some four- and some six-track; the $16.7 million/cost electrifies a new line from scratch around six times over in non-English-speaking countries, and while the comparison is mostly to double-track lines, around half the cost of electrification is the substations and transformers, and those aren’t part of the project in New Jersey.

State of Good Repair projects always end up as black holes of money, because if half the money is spent and there’s no visible improvement, it’s easy for Amtrak to demand even more money, without having to show anything for it. An improvement project would be visible in higher speeds, better ride quality, higher reliability, and so on, but this is free money in which the cost is treated as a positive (jobs, the appearance of work, etc.) and not something to be minimized in pursuit of another goal. One conclusion of this is that no money should be given to catenary renewal. Money can be spent on upgrades with visible results, in this case constant-tension catenary. On all else, Amtrak cannot be trusted.

High-speed rail planning

The report we wrote on high-speed rail planning at Marron is longer than the ETA report, but I encourage people to read it as well, especially anyone who wishes to comment here. In brief, we give five broad recommendations, based on a combination of reviewing the literature on high-speed rail, cost overruns, and public infrastructure management, and interviewing American sources in the field.

  1. The federal government needs to nurture local experimentation and support it with in-house federal expertise, dependable funding, and long-term commitment.
  2. The FRA or another federal entity should have consistent technical standards to ensure scale and a clear operating environment for contractors.
  3. The federal government should work with universities to develop the technology further, which in this case means importing standards that work elsewhere – high-speed rail in 2024 is a mature technology, not requiring the inventions of new systems that underlay the Japanese, French, and German networks.
  4. Agencies building high-speed rail should have good project delivery, following the recommendations we gave in the subway construction costs report. Using consultants is unavoidable, but there needs to be in-house expertise, and agencies should avoid being too reliant on consultants or using consultants to manage other consultants.
  5. Agencies and states should engage in project planning before environmental reviews and before making the decision whether to build; the use of environmental reviews as a substitute for planning leads to rushed designs, which lead to mistakes that often prove fatal to the project.

Currently, all American high-speed rail plans should be treated as case studies of what to avoid. However, this does not mean that all of them fail on all five criteria. For one, California High-Speed Rail largely used pan-European technical standards in its planning; Caltrain did not in related planning including the electrification project and the associated resignaling (originally intended to be the bespoke CBOSS). The criterion on technical standards becomes more important as different projects interact – for example, Brightline West is inconsistent about what it’s using. Then there’s Texas Central, which uses turnkey Shinkansen standards, but as it’s turned over to Amtrak is bound to get modifications that conflict with what Japan Railways considers essential to the Shinkansen, such as total lack of any infrastructure mixing with legacy trains.

Notably, none of this is about the Northeast Corridor directly. My own interpretation of the report’s recommendations points out to other problems. For example, the Northeast Corridor’s technical standards are consistent but also bad, coming from an unbroken legacy of American railroader traditions whose succors can barely find Germany on a map, let alone bother to learn from it or any other foreign country. This way, the New Haven Line, which with modern trainsets and associated standards has few curves limiting trains to less than 150 km/h, is on a blanket speed limit of 75 mph, or 121 km/h, in Connecticut, with several further slowdowns for curves. There’s long-term planning for the corridor, and it’s bipartisan, but this long-term planning involves agencies that fight turf wars and mostly want to get the others out of what they perceive as their own turfs. There is lush funding, but it goes to the wrong things – Moynihan Train Hall but no improvements at the track level of Penn Station, extensive track renewal at 1.5 orders of magnitude higher cost than in Germany, in-place bridge replacements on curvy track instead of nearby bypasses.

The current planning does use too many consultants – in fact, Penn Reconstruction’s interagency agreement stipulates that they use consultant-centric project delivery methods, with one possibility, progressive design-build (what most of the world calls design-build; what New York calls design-build is different and better), not even legal in New York state law, but the local power brokers are trying to legalize it and break their own construction cost records. But it’s not quite the same as not bothering to develop in-house talent – there is some, and sometimes it isn’t bad, but poor project management and lack of interagency coordination has caused the budgets for the big-ticket items that Amtrak wants to explode beyond anyone’s ability to manage. The five recommendations, applied to the Northeast, mostly speak to the low quality of the existing agencies, rather than to a hodgepodge of standards as is happening at the interface between California High-Speed Rail and Caltrain or Brightline West.

The ultimate problem on the Northeast Corridor is that it is held together with duct tape, by people who do not know how to use more advanced tools than duct tape. They constantly fight fires, sometimes literally, and never ask why fires always erupt when they’re around; it’s not the heat, because the Northeast isn’t any warmer than Japan or South Korea or Italy, and it’s not underinvestment 30+ years ago, because Germany has that history too. Nolan points out the electric traction backlog on the Northeast Corridor grew from less than $100 million in 2018 to $829 million today; the people in charge are substantially the same ones who deferred this much maintenance over the six-year period that included the Bipartisan Infrastructure Law. I didn’t get into this project in order to study other people’s failures again, as we did with the construction costs report. But everything I’m seeing on the Northeast Corridor, even more than in California or Texas, points to what may be the worst intercity rail planning of any even vaguely modern country.

Red Hook-Manhattan Buses

In 2018, Eric’s and my Brooklyn bus redesign proposal included a new route to run between Red Hook and Lower Manhattan using the Brooklyn-Battery Tunnel. This was not our idea; a junior planner we talked to suggested this. Our plan was not adopted, but in the formal process New York City Transit and consultancy Sam Schwartz engaged in, at community meetings riders proposed the same idea, and junior staff seemed to like it but it was still not adopted. Now, a coalition of neighborhood groups and city-wide transit advocacy groups is directly calling for such a bus to be included in the Brooklyn bus redesign, including ETA. My goal in this post is to look at some alignment possibilities, more carefully than we did in the 2018 proposal. On the Manhattan side, it is not too hard to hit Lower Manhattan jobs and subway transfers on a short bus loop, but on the Brooklyn side, the Red Hook street network and its connection to the tunnel force serious compromises.

Current conditions

There are express buses in the tunnel from points much farther out to Lower Manhattan, but they don’t make stops along the way. Red Hook is instead served exclusively within Brooklyn, in three directions: one north along Van Brunt to Downtown Brooklyn, one east along Lorraine to the Smith/9th Street subway station and Park Slope, and one also along Lorraine to Smith/9th but then going north to Downtown Brooklyn. The first two are together the B61 route, in an awkward C-shaped through-route; the third is the B57, which through-runs past Downtown Brooklyn to points northeast along Flushing Avenue.

The neighborhood has roughly three major destinations to serve. Visible in the center-bottom of the map are the Red Hook Houses, with a total of 6,000 residents. At the very bottom of the map is Ikea, the main destination for people coming into the neighborhood from elsewhere. Then on the left there is Van Brunt, the local commercial drag.

Per OnTheMap, the entire neighborhood has 6,700 jobs and 5,000 employed residents as of 2019; it is not at all a bedroom community. Ikea is not even one of the main job centers – the biggest are elsewhere, such as the nearby Amazon warehouse. The neighborhood’s residents work about 40% in Manhattan, 40% in Brooklyn, and 20% elsewhere, while the workers are half from Brooklyn with no other origin having much concentration (the second biggest county origin, Queens, is 14%). Only 300 people both live and work in Red Hook, so a transit system connecting the neighborhood to the rest of the city, for both origins and destinations, is vital.

Why the tunnel?

Red Hook’s current bus connections are only with the rest of Brooklyn. This materially slows down travel for the 40% of residents who work in Manhattan and roughly 10% who work in places one accesses via Manhattan, such as the Bronx or Long Island City. The on-street bus connections are slow, and the neighborhood is not well-located relative to the Brooklyn subway network. The B57 only kind of hits Smith/9th southbound, since Smith is one-way northbound and the southbound trip is one block west on Court. Smith/9th itself is not accessible, and is the highest subway station in the system above the local street level as it was built with high clearance below for shipping through the Gowanus Canal.

Let’s look at how fast it is to get to 42nd Street. Via the B57 or B61, it’s about 10 minutes by bus from Ikea to Smith/9th; the B61 runs every 12 minutes and the B57 every 15 or 20, for maximum inconvenience. Then from Smith/9th to Bryant Park, it’s 27 minutes on the F. A bus in the tunnel would get to Fulton Street in 25 minutes and then it’s 12 minutes on the A. In theory, it’s the same trip time from Ikea, and around three minutes faster in relative terms from the Red Hook Houses depending on the route. In practice, being able to connect in Manhattan means having a much wider variety of destinations than just what’s on the F, which doesn’t even get to Lower Manhattan. The benefits for Red Hook-to-rest-of-city commuters would be noticeable.

The Manhattan street section would have variable traffic. On the other hand, the tunnel is less congested than its approaches, and congestion pricing stands to reduce traffic exactly there, as on other roads into the Manhattan core. With no bus stops in the tunnel, the average speed would be reasonable even with a short loop through Lower Manhattan. Diverting ridership from slower buses to Downtown Brooklyn would save revenue-hours, which could then be spent on higher frequency on all remaining routes.

Compromises on the route

The routing within the neighborhood for any bus route using the tunnel cannot be perfect; the neighborhood is not laid out for it. This is seen in how awkward the buses through Red Hook are today, as mentioned above; none of them even goes through the Red Hook Houses, which are the dominant origin. All of the following constraints require creating a single compromise bus route:

  • The ridership potential is not there for more than one route. Whatever option is chosen, whether it’s a shuttle as I’m implying in this post or an extension of an existing route that goes deeper into Manhattan (or Brooklyn), that’s the only thing that can run. Even with one route, there may need to be compromises on frequency (by which I mean a bus every 8-10 minutes instead of 6, not 12).
  • Van Brunt, Ikea plus the other waterfront jobs, and the Red Hook Houses are not at all collinear.
  • The only place to get to the tunnel from Red Hook is the ramp from West 9th or Huntington, and West 9th is one-way west and may need to be converted to two-way. In particular, Van Brunt is too far, and the interface with the tunnel needs to be to and from the Red Hook Houses directly.

In effect, what all of the above implies is that a bus to Manhattan on Van Brunt is not likely to work. Here is one version of what could:

The circles along the path denote control points on Google Maps, and not stops. The western waterfront may have to just not be served; people could walk from Van Brunt across Coffey Park and it would be faster than taking the bus the long way around, down Van Brunt and then along Beard and up Columbia.

At the Manhattan end, the route would either loop just far enough north to hit the Fulton Street subway complex, or through-run. Fulton is necessary because the Wall Street stations are inaccessible, and is generally useful for the connection to World Trade Center. Beyond that, one option is to through-run to the M9, which hits more Manhattan destinations. That said, Manhattan bus speeds are so low that nearly all riders would switch to the subway; M9 frequencies are also low, every 15 minutes off-peak, and when there’s not much traffic this is almost unusably low for Red Hook Houses-Wall Street trips.

Scheduling Trains in New Jersey with the Gateway Project

Devin and I have draft timetables for intercity and commuter trains on every segment of the Northeast Corridor; what is left is to merge the segments together and see how they interact, tweak based on further constraints, and look at some alternatives. The good news is that in New Jersey, the last area we looked at, sharing tracks turns out to be easy. It’s a happy accident of how the Northeast Corridor has been designed that, with 21st-century train specs, the places where fast trains need to overtake slow ones already have long sections with additional tracks. Work is still required on grade-separating some junctions (chiefly Hunter Interlocking) and fixing some curves largely within the right-of-way, but it’s rather minor. The upshot is that local commuter trains can do New York-New Brunswick in 38 minutes and would do New York-Trenton in an hour, the express commuter trains can do New York-Trenton in 51 minutes, and the intercity trains can do New York-Philadelphia in 45 minutes, all with new rolling stock but few expensive investments in infrastructure beyond what’s already funded as part of the Hudson Tunnel Project for Gateway.

Three speed classes

The Northeast Corridor near New York presents two planning difficulties. First, there is a very large volume of peak commuter traffic into Manhattan, which forces agencies to build infrastructure at the limit of track capacity. And second, there is a long stretch of suburbia from Manhattan, which means that some express commuter rail service is unavoidable. This means that both the New Haven Line and the NJ Transit Northeast Corridor Line have to be planned around three speed classes: local commuter, express commuter, and intercity; moreover, the total volume of trains across these classes must be large, to accommodate peak demand, reaching 24 peak trains per hour. This is why the Hudson Tunnel Project is being built: the existing tunnels run 24 trains per hour already split across many different commuter rail branches, and all of the trains are crowded.

The difficulties in New Jersey and in Metro-North territory are different; for a taste of what is needed for Metro-North, see here. In New Jersey, the quality of the right-of-way is high, and the outer stretches are already cleared for a maximum speed of 160 mph, and with if the Federal Railroad Administration (FRA) had more faith in the quality of rolling stock windows they could run much faster than this. The inner stretches are slower but still straight enough for fairly high speed – there are long stretches straight enough for 250 km/h and one section where trains could even briefly reach 300 km/h. Thus, the express commuter trains are noticeably slower than the intercity trains on these segments despite running nonstop from Newark to Metropark.

All trains are significantly faster than today. Little of the speedup comes from any curve modification; rather, it comes from reduced timetable padding (down to Swiss-standard 7%), plus about 1.5 minutes of speedup in the Penn Station throat from better switch geometry.

Six-track overtakes

The Northeast Corridor is largely quad-track, but two sections have six tracks, both in New Jersey: around Newark Airport, and from just south of Elizabeth to just south of Rahway, where the North Jersey Coast Line branches off. The four-track section through Elizabeth is annoying, and I was hoping that it would not be necessary to delicately schedule around it. It is fortunate that my hopes have proved correct.

Below is a rough line chart. For one, it does not have any schedule padding. For two, there are still some additional slowdowns not coming from right-of-way geometry not incorporated into it, and in particular there’s a minute of Penn Station and tunnel delay not yet depicted for the intercity train and another 30 seconds of same for the commuter trains. For three, all station dwell times are set at 30 seconds, whereas the intercity needs a minute. In total, the last two factors delay the intercity by a minute relative to all commuter trains by when they depart Newark. All of these factors figure into the trip times above, but not the line chart below.

The blue lines are intercity trains, the red lines are express commuter trains, the green lines are local commuter trains to New Brunswick or Jersey Avenue, the purple lines are local commuter trains branching to the North Jersey Coast Line, and the gold lines are SEPTA trains.

Of note, the intercity trains do not share tracks with the local commuter trains except in the tunnel to Penn Station; the current plan after the Hudson Tunnel Project is finished is for the above-depicted trains to use the old tunnel and for other lines (Morris and Essex, Montclair-Boonton, Raritan Valley) to use the new tunnel. This provides just enough separation that there isn’t much interlining to worry about. The express commuter trains are the only ones with any surface track-sharing with trains of different speed classes.

As the line chart shows, the red/green overtake occurs at Elizabeth, where the express commuter trains then need to be on the inner express tracks. Just south of Elizabeth, the line widens to six tracks, and the express commuter trains can be kept separate from both local trains and intercity trains; all that’s required is installing switches to allow this, for a very small number of millions of dollars for high-speed switches or hundreds of thousands for slower switches. By the time the intercity and express commuter trains are within the signal system’s two-minute limit of each other, the express commuter trains don’t need to return to the inner tracks again. Past Rahway, the express and local commuter trains need to use the same tracks, but are adequately separated from each other.

Robustness check

We are still looking at options for how to match this segment with other segments, in particular how this could through-run east of Penn Station. Most likely, the local trains would run through to the Port Washington Branch of the LIRR and the express commuter trains would become local commuter trains to Stamford via Penn Station Access.

The upshot is that the train most likely to be delayed from the north is the express commuter train. It can afford to be about two minutes behind schedule before it messes up the order of trains using the tunnel; the schedule padding up to Elizabeth can recover one of these two minutes, and then, with the extra minute of slowdown of intercities not depicted in the line chart, the express commuter trains are still well clear of the intercities where they share tracks at Elizabeth.

Stop Spacing on Crosstown Routes

Two different issues in New York – the bus redesign process and the Interborough Express – are making me think about optimal stop spacing again. I blogged about it in general about buses a few days ago, but crosstown routes present their own special issues, and this is noticeable on rail more than on buses. Circumferential rail routes, in particular, can justify wider stop spacing than radial routes in certain circumstances. This can explain why, over the iterations of Triboro RX leading to the current IBX proposal, the stop spacing has widened: the Third Regional Plan-era effort in the 2000s had a stop every half mile in Brooklyn and Queens, but more recent efforts proposed fewer stops, and the current one if anything has too few and misses a transfer.

Density and isotropy

The tradeoff in stop spacing on both buses and trains is that more stops reduce the amount of walking to the station but increase the in-vehicle trip time for people going through the stop without getting on or off.

Density by itself does not affect this tradeoff. A uniform increase in density along a line equally increases the costs and benefits of changing the stop spacing. However, relative density matters: stop spacing should be tighter in areas with higher density and wider in areas with lower density, both relative to other areas along the same line. This is because higher relative density means passengers are disproportionately likely to have their origin or destination in this area, and disproportionately less likely to be traveling through it, both of which argue in favor of tighter stop spacing, and lower relative density means the opposite.

This then leads to the issue of isotropy. On an isotropic network, relative density is by definition always the same; spikes in relative density make travel less isotropic. As my previous post explains with bus stop spacing formulas, also valid on rail with different parameters, less isotropic density should mean not just that there should be more stops in some places and fewer in others, but also that there should be fewer stops overall. In the simplest case of non-isotropy, assume everyone is traveling to the same distinguished node, which on a rail line can be thought of as city center (let’s say there’s just one central transfer point) and on a bus can be thought of as the connection to the subway. Then, all passengers can be guaranteed to be going to a place with a station, and therefore the cost of widening the stop spacing is halved, since only the origin walk time is increased, not the destination walk time.

Isotropy and circumferential routes

Successful circumferential routes live off of their ability to connect to the rest of the network. Over time, those connection points may grow to become large destinations in their own right – this is the story of how Ikebukuro, Shinjuku, and Shibuya, all at the intersection of the Yamanote Line with radial rail links (JR, private, or subway), became large business districts. But the connections have to come first. If passengers can’t conveniently transfer, then the route has to live off of origin-and-destination traffic just on the line, and then, because it is circumferential and by definition doesn’t go to city center, traffic will be low. This principle is why the G train in New York is so weak: it may connect the two largest non-Manhattan job centers in the region, but that’s still neither Manhattan nor service to the entire city, and with poor transfers, it has to live off of the small number of people living in Williamsburg and Bedford-Stuyvesant working in Long Island City or Downtown Brooklyn.

But the same principle also means that non-transfer stops lose value. This doesn’t mean there shouldn’t be any of them, but it does mean that agencies can afford to be pickier about where to place them. They’re unlikely to be destinations, only origins, and even as origins their value is discounted since some passengers use the circumferential line as the second leg of a three-legged trip, between two radial lines.

The impact on IBX

I used to criticize the decision to build fewer stops on IBX. For example, here, when it was still an RPA proposal in what would later become the Fourth Regional Plan, I outlined several criticisms of the then-Triboro route. I think some of them stand, especially the section on the plan to have the route go into the Bronx and provide local commuter rail service to Coop City. However, on the matter of stop spacing, I must withdraw the criticism.

That said, a station at every connection with a radial rail line remains nonnegotiable. IBX errs in only stopping in East New York at Atlantic Avenue, connecting to the L and the LIRR, with no direct connection to Broadway Junction for the A/C and J. The distance between these two locations is only 350 meters, and it may be awkward to have two stops in short succession, but the meaning of high relative density is exactly that it’s okay to have more closely spaced stops. Alternatively, there could be one stop at a compromise location, with in-system connections at both ends, but then the walk times would be higher, which is less desirable.

Bus Stop Consolidation and Blocks

There are arguments over bus stop spacing in my Discord channel. As the Queens bus redesign process is being finalized, there’s a last round of community input, and as one may expect, community board members amplify the complaints of people who reject any stop consolidation on “they’re taking my stop, I’ll have to walk longer” grounds. I wrote about this in 2018, as Eric and I were releasing our proposed Brooklyn bus redesign, which included fairly aggressive consolidation, to an average interstation of almost 500 meters, up from the current value of about 260. I’d like to revisit this issue in this post, first because of its renewed relevance, and second because there’s a complication that I did not incorporate into my formula before, coming from the fact that the city comprises discrete blocks rather than perfectly isotropic distribution of residents along an avenue.

The formula for bus stop spacing

The tradeoff is that stop consolidation means people have to walk longer to the bus stop but then the bus is faster. In practice, this means the bus is also more frequent by a proportionate amount – the resources required to operate a bus depend on time rather than distance, chiefly the driver’s wage, but also maintenance and fuel, since stops incur acceleration and idling cycles that stress the engines and consume more fuel.

The time penalty of each stop can be modeled as the total of the amount of time the bus needs to pull into the stop, the minimum amount of time it takes to open and close the doors, and the time it takes to pull out. Passenger boardings are not included, because those are assumed to be redistributed to other stops if a stop is deleted. In New York and Vancouver, the difference in schedules between local and limited stop buses in the 2010s was consistent with a penalty of about 25 seconds per stop.

The optimum stop spacing can be expressed with the following formula:

\sqrt{d\cdot\frac{\mbox{walk speed}}{\mbox{walk penalty}}\cdot\mbox{stop penalty}\cdot(\mbox{average trip length} + \mbox{average bus spacing})}

To explain in more detail:

  • d is a dimensionless factor indicating how far one must walk, based on the stop spacing; the more isotropic passenger travel is, the lower d is, to a minimum of 2. The specific meaning of d is that if the stop spacing is n, then the average walk is n/d. For example, if there is perfect isotropy, then passengers’ distance from the nearest bus stop is uniformly distributed between 0 and n/2, so the average is n/4, and this needs to be repeated at the destination end, summing to n/2.
  • Walk speed and walk penalty take into account that passengers prefer spending time on a moving bus to walking to the bus. In the literature that I’ve seen, the penalty is 2. Usually the literature assumes the walk speed is around 5 km/h, or 1.4 m/s; able-bodied adults without luggage walk faster, especially in New York, but the speed for disabled people is lower, around 1 m/s for the most common cases.
  • Stop penalty, as mentioned above, can be taken to be 25 s.
  • Average trip length is unlinked; for New York City Transit in 2019, counting NYCT local buses including SBS but not express buses, the average was 3,421 meters.
  • Average bus spacing is the headway between buses on the route measured in units of distance, not speed; it’s expressed this way since the resources available can be expressed in how many buses can circulate at a given time, and then the frequency is the product of this figure with speed. In Brooklyn in the 2010s, this average was 1,830 m; our proposed network, pruning weaker routes, cut it to 1,180. The Queens figure as of 2017 appears similar to the Brooklyn figure, maybe 1,860 m. Summing the average trip length and average bus spacing indicates that passengers treat wait time as a worst-case scenario, or, equivalently, that they treat it as an average case but with a wait penalty of 2, which is consistent with estimates in the papers I’ve read.

In the most isotropic case, with d = 2, plugging in the numbers gives,

\sqrt{2\cdot\frac{1.4}{2}\cdot 25\cdot(3420+1860)} = 430 \mbox{meters}

However, isotropy is more complex than this. For one, if we’re guaranteed that all passengers are connecting to one distinguished stop, say a subway connection point, then consolidating stops will still make them walk longer at the other end, but it will not make them walk any longer at the guaranteed end, since that stop is retained. In that case, we need to set d = 4 (because the average distance to a bus stop if the interstation is n is n/4 and at the other end we’re guaranteed there’s no walk), and the same formula gives,

\sqrt{4\cdot\frac{1.4}{2}\cdot 25\cdot(3420+1860)} = 608 \mbox{meters}

The Queens bus redesign recognizes this to an extent by setting up what it calls rush routes, designed to get passengers from outlying areas in Eastern Queens to the subway connection points of Flushing and Jamaica; those are supposed to have longer interstations, but in practice this difference has shrunk in more recent revisions.

That said, even then, there’s a complication.

City blocks and isotropy

The models above assume that passengers’ origins are equally distributed along a line. For example, here is Main Street through Kew Gardens Hills, the stretch I am most likely to use a New York bus on:

I always take the bus to connect to Flushing or Jamaica, but within Kew Gardens Hills, the assumption of isotropy means that passengers are equally likely to be getting on the bus at any point along Main Street.

And this assumption does not really work in any city with blocks. In practice, neighborhood residents travel to Main Street via the side streets, which are called avenues, roads, or drives, and numbered awkwardly as seen in the picture above (72nd Avenue, then 72nd Road, then 72nd Drive, then 73rd Avenue, then 75th Avenue…). The density along each of those side streets is fairly consistent, so passengers are equally likely to be originating from any of these streets, for the most part. But they are always going to originate from a side street, and not from a point between them.

The local bus along Main, the Q20, stops every three blocks for the most part, with some interstations of only two blocks. Let’s analyze what happens if the system consolidates from a stop every three blocks, which is 240 meters, to a stop every six, which is 480. Here, we assume isotropy among the side streets, but not continuous isotropy – in other words, we assume passengers all come from a street but are equally likely to be coming from any street.

With that in mind, take a six-block stretch, starting and ending with a stop that isn’t deleted. Let’s call this stretch 0th Street through 6th Street, to avoid having to deal with the weird block numbering in Kew Gardens Hills; we need to investigate the impact of deleting a stop on 3rd Street. With that in mind: passengers originating on 0th and 1st keep going to 0th Street and suffer no additional walk, passengers originating on 5th keep going to 6th and also suffer no additional walk, passengers originating on 2nd and 4th have to walk two blocks instead of one, and passengers originating on 3rd have to walk three blocks instead of zero. The average extra walk is 5/6 of a block. This is actually more than one quarter of the increase in the stop spacing; if there is a distinguished destination at the other end (and there is), then instead of d = 4, we need to use d = 3/(5/6) = 3.6. This shrinks the optimum a bit, but still to 576 m, which is about seven blocks.

The trick here is that if the stop spacing is an even number of blocks, then we can assume continuous isotropy – passengers are equally likely to be in the best circumstance (living on a street with a stop) and in the worst (living on a street midway between stops). If it’s an odd number of blocks, we get a very small bonus from the fact that passengers are not going to live on a street midway between stops, because there isn’t one. The average walk distance, in blocks, with stops every 1, 2, 3, … blocks, is 0, 0.5, 2/3, 1, 1.2, 1.5, 12/7, 2, … Thus, ever so slightly, planners should perhaps favor a stop every five or seven blocks and not every six, in marginal cases. To be clear, the stop spacing on each stretch should be uniform, so if there are 12 blocks between two distinguished destinations, there should be one intermediate stop at the exact midpoint, but, perhaps, if there are 30 blocks with no real internal structure of more or less important streets, a stop should be placed every five and not six blocks, especially if destinations are not too concentrated.

Subway Expansion and Bus Redesign

The ongoing designs for the Interborough Express are making me think about bus redesign again. Before the Transit Costs Project, Eric and I worked on a proposal for a bus redesign in Brooklyn, which sadly was not adopted. The redesign was based on the reality of 2017 – the ridership patterns, the bus speeds, the extent of the system, etc. Since then the subway map has not changed, but IBX stands to change the map, and with it, the buses should change as well.

With our program having produced both the bus redesign proposal and soon a comprehensive proposal for how to change the city’s built-up layout to take advantage of the new line, I should probably say something about how the buses should change. I say I and not we, because so far we don’t have a project under our program for this; for now, this is just a blog post, though one informed by past work on the subject.

Parallel and orthogonal buses

In general, when a new line opens, it reduces demand on parallel bus routes, which it outcompetes, and increases it on orthogonal ones, which feed it. However, what counts as parallel and what counts as orthogonal are not always obvious.

Case in point: when Second Avenue Subway opened at the end of 2016, ridership on the east-west buses between the Upper East and West Sides fell. The new line in theory runs north-south, but it undulates from the Upper East Side to Times Square, where passengers can connect to trains to the Upper West Side and points north; when I lived at 72nd and York and commuted to Columbia by bus and subway in 2009-10, I calculated that if Second Avenue Subway had been open already, a two-seat subway ride with a Times Square connection would have cut my one-way commute from 50 to 37 minutes.

This means that to understand how a new rail line will impact buses, it’s necessary to look beyond just the line itself, and think what it connects to.

For example, note on the above map that the increase in job access at the Flatbush Avenue station, intersecting the Nostrand Avenue Line, is relatively small, and doesn’t have a big north-south footprint along Nostrand. This is because the location already has subway service connecting to Manhattan, a much larger job center than anything IBX would connect to; the buses at the station, the B41 on Flatbush and B44 on Nostrand, already function as connectors to the subway at this point, and are unlikely to acquire more ridership as a result.

In contrast, the stations at Myrtle and Metropolitan are both seen to have a large increase in job access, and in particular a large increase in job access along those two avenues even somewhat away from the stations. On Myrtle, the current buses are the B54 and Q55; the B54 connects to the M train, but it’s one branch, and then the bus continues to Downtown Brooklyn, to which there’s no good subway connection from the future IBX station. The B54 is likely to lose ridership to Downtown Brooklyn but gain it to the new IBX station, and the Q55 is likely to gain in general, as they ferry passengers to a station where they can quickly and with one change go to any number of express lines. Metropolitan has a similar issue – the Q54 already connects to the M, but at least from points west, nobody has any reason to make that connection since it would just double back, whereas with IBX, the Q54 would efficiently connect people to Jackson Heights, and with an additional change to anywhere on the Queens Boulevard and Flushing Lines.

New nodes

Public transit lines serve two functions: to run along a corridor, and to connect nodes. New York usually thinks in terms of corridors, and indeed names nearly all subway lines after the streets they run on (such as a Manhattan avenue) rather than after where they go. But nodes are important as well. Some of that is reflected in the above analysis of the Flatbush-Nostrand Avenue station, currently Brooklyn College on the Nostrand Avenue Line: it really needs to be thought of as a node, and IBX will strengthen it, but not by enough to require running more B41 and B44 buses. In contrast, other nodes will be strengthened enough that bus service increases are warranted.

East New York/Broadway Junction is the biggest standout. East New York’s bus network today is not much of a grid – instead, buses connect outlying areas to the nearest subway station; the bus redesign we did for Brooklyn would make it more of a grid but still follow the logic of feeding the subway wherever it is closest. However, IBX makes Broadway Junction and the Atlantic Avenue station more interesting, which should leads to some changes, turning the new station into more of a node for buses. Buses avoiding this node should instead make sure to stop not just at the subway but also at a new IBX stop, such as Linden.

Jackson Heights is the other. It is a node to some extent today, served by the Q32, Q33, Q47, Q49, Q53, and Q70. But in that general area, the intersection of Woodhaven and Queens Boulevard is an even larger node, and in Queens writ large, the ends of the subway in Jamaica and Flushing are far and away the biggest ones. With IBX, more buses should run to Jackson Heights; for example, all Woodhaven buses, and not just the Q53, should continue along Queens Boulevard and Broadway to reach the station.

Substitutions

In Queens, the street network connecting Jackson Heights with the neighborhoods near the borough line with Brooklyn is not at all conducive for good transit. Buses are usually a good indicator of relative demand along a corridor, but sometimes they aren’t; the situation of IBX is generally one in which they are not, but this is especially bad in Queens. This means that the question of which buses would see demand fall as IBX substitutes for them is even harder than on Second Avenue Subway, the north-south line that efficiently substitutes for east-west buses.

In Brooklyn, I think the answer is relatively straightforward, in that the main crosstown routes, like the B35 on Church, exhibit substitutability. In Queens, it’s harder, and I don’t have concrete answers, only general thoughts that we can turn into a report if there turns out to be demand for it:

  • If a bus has sections along the corridor but also away from it, like the Q18 or Q47, then it should be cut to just connect to the line, in these two case at Jackson Heights.
  • If a bus runs directly between two nodes that could get faster service via a subway-IBX connection, and it doesn’t serve much along the way, then it’s likely to be analogous to the east-west buses across Central Park, and see reduced ridership demand.
  • In general, the routes in Central Queens zigzag so much that IBX is likely to represent a massive improvement in trip times, making such buses less useful.

Frequency in Units of Distance

I have annoying commenters. They nitpick what I say and point out errors in my thinking – or if there are no errors, they take it beyond where I thought it could be taken and find new ways of looking at it. After I wrote about frequency relative to trip length last week, Colin Parker pointed out on the Fediverse that this can be simplified into thinking about frequency not in units of time (trains or buses per hour), but in units of distance (trains or buses per km of route). This post is dedicated to developing this idea on various kinds of transit service, including buses and trains.

The key unit throughout, as Colin points out, is the number of buses available per route, the assumption being that the average trip length is proportional to the average route length. However, this is not a perfect assumption, because then the introduction of network effects changes things – generally in the direction of shorter average trip length, as passengers are likelier to transfer, in turn forcing agencies to run more vehicles on a given route to remain useful. Conversely, timed transfers permit running fewer vehicles, or by the same token more routes with the same resources – but the network had better have a strong node to connect to after a series of vehicle changes, more like the Swiss rail network than like a small American city’s bus network.

Frequency and resources

On a bus network with even frequency across all routes, the following formula governs frequency, as I discussed six years ago:

Daily service hours * average speed per hour = daily trips * network length

When Eric and I proposed our Brooklyn bus redesign, we were working with a service-hour budget of about 10,800 per weekday; status quo as of 2017-8 was 11 km/h, 550 km, and thus 216 daily trips (108 per direction), averaging around a bus per 11 minutes during the daytime, while we were proposing speed up treatments and a redesign to change these figures to 15 km/h, 355 km, and thus 456 daily trips (228 per direction). The six-minute service ideal over 16 hours requires 188 trips per direction; the difference between 188 and 228 is due to higher frequencies on the busiest routes, which need the capacity.

To express this in units of length, we essentially eliminate time from the above dimensional analysis. Daily service hours is a dimensionless quantity: 10,800 hours per weekday means 450 buses circulating at a given time on average, in practice about 570 during the daytime but not many more than 100 buses circulating overnight. If there are 570 buses circulating at a given time, then a 550 km network will average a bus every 1.9 km and a 355 km one will average a bus every 1.25 km. With pre-corona New York bus trips averaging 3.4 km unlinked, a bus every 1.9 km means the maximum headway is a little higher than half the trip time, and a bus every 1.25 km means the maximum headway is a little higher than one third the trip time, independently of speed.

This calculation already illustrates one consequence of looking at frequency in units of distance and not time: your city probably needs to aggressively prune its bus network to limit the wait times relative to overall trip times.

Route length and trip length

On an isolated bus or train route, serving an idealized geography with a destination at its center and isotropic origins along the line, the average trip length is exactly one quarter of the route length. The frequency of service in units of distance should therefore be one eighth of the route length, requiring 16 vehicles to run service plus spares and turnarounds. This is around 18-20 vehicles in isolation, though bear in mind, the 10,800 service hours/day figure for Brooklyn buses above is only for revenue service, and thus already incorporates the margin for turnaround times and deadheads.

Colin points out that where he lives, in Atlanta, bus routes usually have around four vehicles circulating per route at a given time, rather than 16. With the above assumptions, this means that the average wait is twice the average trip time, which goes a long way to explaining why Atlanta’s bus service quality is so poor.

But then, different assumptions of how people travel can reduce the number 16:

  1. If destinations are isotropic, then the average trip length rises from one quarter of the route length to 3/8 of the route length, and then the frequency should be 1.5/8 of the route length, which requires 11 vehicles in revenue service.
  2. If origins are not isotropic, then the average trip length can rise or fall, depending on whether they are likelier to be farther out or closer in. A natural density gradient means origins are disproportionately closer-in, but then in a city with a natural density gradient and only four buses to spare per route, the route is likely to be cut well short of the end of the built-up area. If the end of the route is chosen to be a high-density anchor, then the origins relative to the route itself may be disproportionately farther out. In the limiting case, in which the average trip is half the route length, only eight buses are needed to circulate.

To be clear, this is for a two-tailed route; a one-tailed route, connecting city center at one end to outlying areas at the other, needs half the bus service, but then a city needs twice as many such routes for its network.

The impact of transfers

Transfers can either reduce the required amount of service for it to be worth running or increase it, depending on type. The general rule is that untimed transfers occurring at many points along the line reduce the average unlinked trip and therefore force the city to run more service, while timed transfers occurring at a central node lengthen the effective trip relative to the wait time and therefore permit the city to run less service. In practice, this describes both how existing bus practices work in North America, and even why the Swiss rail network is so enamored with timed connections.

To the point of untimed transfers, their benefit is that there can be very many of them. On an idealized grid – let’s call it Toronto, or maybe Vancouver, or maybe Chicago – every grid corner is a transfer point between an east-west and a north-south route, and passengers can get from anywhere to anywhere. But then they have to wait multiple times; in transit usage statistics, this is seen in low average unlinked trip lengths. New York, as mentioned above, averages 3.4 km bus trips, with a network heavily based on bus-subway transfers; Chicago averages a not much higher 3.9 km. This can sort of work for New York with its okay if not great relative frequency, and I think also for Chicago; Vancouver proper (not so much its suburbs) and Toronto have especially strong all-day frequencies. But weaker transit networks can’t do this – the transfers can still exist but are too onerous. For example, Los Angeles has about the same total bus resources as Chicago but has to spread them across a much larger network, with longer average trip times to boot, and is not meaningfully competitive. The untimed grid, then, is a good feature for transit cities, which have the resources and demand to support the required frequencies.

Not for nothing, rapid transit networks love untimed transfers, and often actively prefer to spread them across multiple stations, to avoid overwhelming the transfer corridors. Subways are only built on routes that are strong enough to have many vehicles circulating, to the point that all but the shortest trips have low ratios of wait to in-vehicle times. They are also usually radial, aiming to get passengers to connect between any pair of stations with just one transfer; Berlin, Paris, and New York are among the main exceptions. These features make untimed transfers tolerable, in ways they aren’t on weaker systems; not for nothing, a city with enough resources for a 100 km bus network and nothing else does not mimic a 100 km subway network.

Timed transfers have the opposite effect as untimed transfers. By definition, a timed transfer means the wait is designed to be very short, ideally zero. At this point, the unlinked trip length ceases to be meaningful – the quantity that should be compared with frequency is the entire trip with all timed transfers included. In particular, lower frequencies may be justifiable, because passengers travel to much more than just the single bus or rail route.

This can be seen in small-city American bus networks, or some night bus networks, albeit not with good quality. It can be seen much more so on transfer-based rail networks like Switzerland’s. The idealized timed transfer network comprises many routes all converging on one node where they are timed to arrive and depart simultaneously, with very short transfers; this is called a knot in German transit planning and a pulse in American transit planning. American networks like this typically run a single bus circulating on each one-tailed route; the average wait works out to be four times longer than the average unlinked trip, and still twice as long as a transfer trip, which helps explain why ridership on such networks is a rounding error, and this system is only used for last-resort transportation in small cities where transit is little more than a soup kitchen or on night bus networks that are hardly more ridden. It would be better to redo such networks, pruning weaker routes to run more service on stronger ones, at least two per one-tailed route and ideally more.

But then the Swiss rail network is very effective, even though it’s based on a similar principle: there’s no way to fill more frequent trains than one every hour to many outlying towns, and even what are midsize cities by Swiss standards can’t support more than a train every half hour, so that many routes have a service offer of two to four vehicles circulating at a given time. However, on this network, the timed transfers are more complex than the idealized pulse – there are many knots with pulses, and they work to connect people to much bigger destinations than could be done with sporadic one-seat rides. A succession of timed connections can get one from a small town in eastern Switzerland to St. Gallen, then Zurich, then Basel, stretching the effective trip to hours, and making the hourly base frequency relatively tolerable. The key feature is that the timed transfers work because while individual links are weak enough to need them, there are some major nodes that they can connect to, often far away from the towns that make the most use of the knot system.