Category: Good Transit

Our Brooklyn Bus Redesign

Eric Goldwyn and I spent about six months working on a Brooklyn bus redesign. I mentioned some aspects of it before here, on social media, and in blog comments, but not the overall shape. Eric and I gave a pair of presentations about our plan, one two days ago at the MTA in front of senior MTA planners and NYC DOT people and one today at TransitCenter in front of activists and mid-level MTA planners. We have a still-unreleased writeup explaining everything we’re doing with references to both public reports from various cities and peer-reviewed literature. Here I’m going to condense the 8,000-word writeup into a blog post length, going over the main points, including of course the proposed map.

The map, in brief

The depicted version is 1.1. You can see a lower-resolution version 1.0 on Streetsblog, albeit with a different color code (the map we made for the presentation, reproduced on Streetsblog, uses red for the highest-frequency routes and blue for the lowest-frequency ones whereas the Google Earth version linked above is the opposite). It has 353 route-km, down from about 550 today, not including Grand and Metropolitan Avenues, which are Queens bus routes, shown on the map for completeness’s sake, without stopping pattern.

Some tails are cut due to low ridership or duplication of rail:

  • The B25 on Fulton goes.
  • The B37 on Third Avenue is consolidated into the B63 on Fifth.
  • The B45 and B65 are merged into one compromise route.
  • The B15 is cut east of the Long-Term Parking JFK AirTrain station (where service is free); ideally it would be cut east of City Line with passengers taking the subway to the AirTrain (as was the case in version 1.0), but I do not expect Port Authority to integrate AirTrain fares with the subway.
  • The B41 is cut north of Parkside Avenue, at the transfer to the B/Q.
  • Instead of two routes in Bed-Stuy between Nostrand (i.e. B44) and Malcolm X (i.e. B46), today’s B15 and B43, there’s just one route.
  • The B57 segment on Court and Smith Streets in South Brooklyn goes, as the subway serves the area in several directions.
  • The B39 over the Williamsburg Bridge goes.
  • The B32 and B62, providing north-south service through Williamsburg up to Long Island City, are merged into one compromise route.
  • The East New York bus network is circuitous (buses go to Gateway Center the long way around) and is straightened here.
  • In version 1.0, the B26 on Halsey was cut west of Franklin with a forced transfer to the subway, but the short distance to Downtown Brooklyn argues in favor of continuing to at least Flatbush.

Overall, this is a cut from 54 routes (including the separately-managed MTA Bus routes B100 and B103) to 37. The smaller network is far more frequent. The minimum frequency is,

  • Every 6 minutes between 6 am and 10 pm every day.
  • Every 10 minutes between 5 and 6 am and between 10 pm and midnight.
  • Every 30 minutes between midnight and 5 am; every 20 minutes with timed transfers to the subway is aspirational, but the subway doesn’t run reliably on a timetable overnight for such a system to be viable. The 30-minute night network could potentially involve mini-pulses in Downtown Brooklyn and smaller hubs (like East New York and Bay Ridge).

Routes depicted in red on the Google Maps link, or in blue on the map in the Streetsblog link, have exactly the minimum frequency. Routes depicted in green have higher frequency at the peak; routes depicted in blue on Google Maps or red on Streetsblog have higher frequency peak and off-peak. Higher frequency than the minimum is depicted as “Utica [2/4]” (buses on Utica run every 2 minutes peak, 4 off-peak) or “Avenue U [5/6]” (buses on Avenue U run every 5 minutes peak, 6 off-peak). Peak means 7-9 am and 5-7 pm on weekdays, in both directions; the morning peak is a little earlier and the afternoon peak a little later than the subway peak, but as buses are still mostly subway feeders, an earlier morning peak and a later afternoon peak are justifiable.

Speedup treatments

Pruning the network is not the only or even most important part of bus reform. Buses have to be sped up to be useful for people except as last-resort transit. In interviews about unrelated topics, people have volunteered to me that they do not take trips they used to take due to the degradation in bus speed and reliability. New York City Transit bus ridership peaked in 2002; the fare hike in 2003 led to a small dip in ridership that the mid-2000s oil crisis didn’t quite erase, and then in the recession and subsequent recovery bus ridership crashed. In Manhattan it’s 30% below the 2007 level; in Brooklyn it’s 20% below the 2007 level, with buses extending the subway or letting people connect to a better line (like the B41 and B35) particularly hit.

The current average speed in Brooklyn is about 11 km/h. Excluding limited-stop buses, it’s 10.8. We’re proposing to increase it to 15, even though the redesign is pruning buses in faster areas more than in slower ones. This is using four speedup treatments.

Prepayment

Today, New York prefers to treat off-board fare collection as a special product available only on select buses (i.e. SBS). This should be changed to citywide prepayment, with all-door boarding. German-speaking cities do it; so does San Francisco. Data from San Francisco and from the TRB (PDF-p. 20) suggests a gain of about 2.5-3 seconds per passenger boarding, counting both boarding and alighting time. At Brooklyn’s bus ridership level, this suggests a saving of around 400-450 revenue-hours, or about 4% of total service-hours. This is not a big change, but it helps stabilize the schedule by slowing down the mechanism by which buses bunch.

How to get passengers to pay if not on-board remains an open question; there are several approaches. The Zurich model involves placing a ticket-vending machine (TVM) at every bus stop. While New York severely pays for TVMs on SBS (the RPA says $75,000 per stop), an ATM costs $3,000, so installing the required infrastructure need not cost a lot. But more commonly, passengers can board freely if they have transfers or unlimited monthlies and pay the driver (potentially after the bus has begun moving) otherwise.

Of note, the bus drivers are particularly interested in prepayment. Eric and I explained the issue in a CityLab article a few months back: the drivers are worried about being assaulted by riders who don’t want to pay.

Stop consolidation

About 60% of the time saving in our plan relative to current practices comes from stop consolidation. I discussed the issue here, and our forthcoming report has references to many studies in the literature optimizing stop spacing for minimum door-to-door travel time. With each deleted stop saving 20-30 seconds (say 25 seconds on average), our proposed stop consolidation, from an average of 220 meters to 490 excluding long tails (i.e. the B15’s long nonstop segment toward JFK) saves around a minute per km, cutting travel time from 5.5 minutes per km to 4.5.

Conceptually, stop spacing should be longer when trips are longer, or when relative density is less uniform. New York City Transit bus trips are short, as many are subway extenders, but relative density is extremely spiky, as a large number of people get off at a few dominant stops at the subway connection points. If the on/off density on a route is uniform, then lengthening the stop spacing means passengers have to walk longer at both ends; but if passengers are guaranteed a connection at one end (because of transfer points with the subway or other buses) then they only have to walk longer at the other end. Based on this principle, Utica and Nostrand get particularly long stop spacing. Conversely, routes with extremely short trips, like the Mermaid route inherited from the B74, have shorter stop spacing.

To improve network legibility, we have tried as far as possible to have buses stop on consistent streets. For example, south of Fulton Street (where it’s awkwardly between Nostrand and Franklin), Bedford Avenue gets a stop on every intersecting bus, including east-west routes but also the diagonal B41.

Every bus stop should have shelter. In Central Florida, North Florida, and London, this costs $10,000 per stop, give or take. Our 707-stop plan (700 in version 1.0) would cost $14 million at this cost. Even at Santa Ana’s higher cost of $35,000, it’s $50 million. NIMBYs who oppose stop consolidation argue that having many stops is necessary for people with disabilities, but people with disabilities would benefit from benches and shelter, without needing to stand for 15 minutes waiting for bunched buses.

Bus lanes

Every bus in an area with congestion should get dedicated lanes. SBS implementations so far, imperfect as they are, have saved around 30 seconds per km in traffic. Physically-separated median lanes should do better; the MTA and NYCDOT have so far avoided them on the theory that local and limited bus routes should coexist on the same route and limiteds should pass locals, but in reality, a single stopping pattern is better, and then there are no drawbacks to physical separation.

On wide streets, this is not a problem. On narrow ones, it is. The real headache is Nostrand, about 25 meters wide building to building, enough for just four lanes. The correct thing to do is a moving lane and a bus lane in each direction, with merchants told to park on side streets. If parking is unavoidable, then a contraflow bus lane, with parking on one side, is also feasible, but less safe for pedestrians (Boulevard Saint-Michel has this configuration and has to remind pedestrians crossing the street to look left).

Two-way buses are essential whenever streets are widely separated, as on avenues, in Brooklyn as well as Manhattan. Nostrand is just more important than Rogers and New York Avenue, where northbound B44s go today; today’s configuration forces east-west buses to make too many stops (the B35 limited makes 4 stops in a kilometer).

Signal priority

Buses should get priority at intersections and not just on the street. The studies we’ve seen find a 4-7% gain, bus only on individual bus routes, not gridded networks. In our proposed trip times we are not assuming any speedup from signal priority, just better timekeeping as more delayed buses get priority to stabilize the schedule. This is a counter-bunching mechanism more than a straight speedup.

A process, not an immutable product

Jarrett Walker’s bus network redesigns tend to come as complete products, changed rapidly from radial low-frequency networks. What we’re proposing is a longer process. Nova Xarxa began implementation in 2012 and is wrapping up now, installing a few routes at a time by cannibalizing parallel routes. The map we’re showing is what we estimate would be a good fit for 2022-3. Beyond that, more subway stops are going to be wheelchair-accessible, making it easier to prune more subway-parallel buses (like the B63).

Gradual implementation means starting from the easier parts of the network. East New York’s current network is so circuitous that straightening it should not be too controversial. Our proposed redesign there is also better at connecting to the 2, 3, 4, and 5 trains and not just the L, which should prove valuable during the L shutdown. In Southern Brooklyn, we are proposing more service, but this could be paired with stop consolidation. Central Brooklyn and Bed-Stuy require the most street redesigns and the most robust frequency network-wide (as they are already transfer-based grids, and nobody transfers at 12-15 minute off-peak frequency) and could be done later; the B25 itself should probably not be eliminated until Broadway Junction is made accessible on the A and C lines.

We are not even wedded to the map as a proposal for 2022. Some variations are always possible, as already seen in the differences between versions 1.0 and 1.1. The biggest addition we can think of is adding a second north-south route through Bed-Stuy: the existing one would be moved from Marcus Garvey to Throop (hitting the subway better), while the B17 could be extended up Troy and Lewis.

Overall, Brooklyn has 10,800 service-hours today. Our redesign uses just 10,000, with a 1% gain in efficiency from location relative to bus depots on top of that. There is room for service increases, or restoration of marginal routes required for political reasons, or slowdowns imposed by political unwillingness to install bus lanes.

Win-lose

In a modern developed country, it’s rare to find win-win situations. The US is blessed with these in transit (i.e. it’s so inefficient at construction it might as well be third-world), but not in urban bus networks. Stop consolidation is a net benefit to the average user of the route, but a few people would still see longer trips, e.g. those living at the exact midpoint between two widely-spaced stops. Route consolidation (as in Ocean Hill) is the same thing.

There are sociopolitical groups that would win out: labor would see higher ridership, reducing the pressure to cut jobs; regular commuters (who generally have low transfer penalties) would see faster trips; people with disabilities that make it difficult for them to stand (as is true of some people with chronic pain) would be able to sit at bus stops and wouldn’t need to sit for long. In contrast, small business owners would sometimes lose the ability to park in front of their stores, and occasional users who usually drive would see longer perceived trips because of stiff transfer penalties.

This is equally true on the level of neighborhoods. Southern Brooklyn generally gains, and Borough Park in general gains an extra north-south route (though this is canceled out by high transfer and access penalty among Haredis: in Israel they just won’t walk longer to better service). East New York sees much more direct routes. Flatbush and East Flatbush don’t see much change in network structure but do gain off-peak frequency. Red Hook gains a direct connection to Manhattan. But then Bed-Stuy loses north-south routes, South Brooklyn’s buses are completely gutted, and Williamsburg loses north-south routes.

A political system based on citywide (or nationwide) ideological groups could find the will to build the network we’re proposing or something like it. Could a system based on local representation, treating retirees and small business owners as a vanguard class, deliver the same? We will see in the next year or two.

Sioux City: Straightening Buses and Getting Route-Length Right

A few days ago, Sandy Johnston linked to a diagram of the single bus route in South Sioux City, Nebraska, a suburb of Sioux City, Iowa. While South Sioux City has a traditional main street in Dakota Avenue, the bus does not follow it; it meanders, hitting destinations on and off Dakota. Many destinations are on US Route 77, an arterial bypass around the built-up area, with recent auto-oriented retail and office uses, including a Wal-Mart (in small-town America often the biggest bus trip generator). The discussion around what to do with this region’s bus network made me realize a crucial concept in planning infrequent transit: getting route-length right. To start with, here is a map of the bus, numbered Route 9 within the Sioux City area:

Here is a PDF map of the entire network. It has 10 routes, using 12 buses running hourly, with a timed meet at the center of Sioux City (just off the above map) at :30 every hour. Most routes run as loops, with highly separated inbound and outbound legs. Route 9 above runs one-way southbound on Dakota Avenue in the northern and southern legs but then meanders to run southbound on Route 77; the Dakota Avenue leg in between the two major east-west runs is one-way northbound.

I asked, why need it be so complicated? The major destinations are all on Dakota or Route 77. It should be easy to run two distinct routes, one on each, right? Without the east-west meanders, there would be the same total service-hours, right?

But no. The route runs hourly. The scale of the map is small: from the bridge over the Missouri in the north to I-129 in the south it’s 4.1 km. There is so little traffic that in the evening rush Google Maps said it would be just 10 minutes by car from Downtown Sioux City to the southern edge of Dakota Avenue near I-129. The roundtrip time would be 25-30 minutes, so the bus would sit idle half the time due to the hourly pulse.

Getting route-length right

When designing regional rail schedules, as well as my take on night buses in Boston (since reduced to a single meandering route), I’ve taken great care to deal with roundtrip route length not always being an integer multiple of the headway. A train that comes every half hour had better have a roundtrip length that’s just less than an integer or half-integer number of hours, counting turnaround times, to minimize the time the train sits at the terminal rather than driving in revenue service. The same is true of buses, except that scheduling is less precise.

In Boston, the plan at the time was for hourly buses, and has since changed to half-hourly, but the principle remains. The roundtrip length of each leg of the night bus network, should it expand beyond one (double-ended) route, should be an integer or half-integer number of hours. In practice this means a one-way trip time of about 25-26 minutes, allowing for a little recovery time and for delays for passengers getting on or off; overnight there is no traffic and little ridership, so 25 minutes of driving time correspond to just less than 30 minutes of actual time.

Thus, on each corridor, the bus should extend about 25 minutes of one-way nighttime driving time from the connection point, and the choice of which routes to serve and where to end each route should be based on this schedule. Of course on some shorter routes 12 minutes (for a half-hour roundtrip) and on some long routes 38 minutes (for a 90-minute roundtrip) are feasible with half-hourly frequencies, but in Boston’s case the strong night bus routes in practice would all be 25.

Length and frequency

In the case of Sioux City, hourly buses meeting at the center should have a one-way trip time of 25 minutes. However, the city is so lightly populated that there is little traffic, and the average traffic speed is so high that 25 minutes puts one well outside the built-up area. The driving time from city center to the edge of the built-up area, around I-129, Lakefront Shopping Center, and the various Wal-Marts ringing the city, is around 10 minutes.

Moreover, a car travel time of 10 minutes corresponds to not much longer on a bus. Frequent commenter Zmapper notes that in small American cities, taking the driving time in traffic and multiplying by 1.2, or 1.3 with recovery time, is enough. A one-way driving time of 11-12 minutes involves a roundtrip bus time of half an hour.

With such a small urban extent, then, the bus frequency should be bumped to a bus every half hour, leveraging the fact that few important destinations lie more than 11-12 minutes outside city center. The question is then how to restructure the network to allow for doubling frequency without doubling operating expenses.

The importance of straight routes

Some of Sioux City’s bus routes go beyond the 12-minute limits, such as route 6 to the airport. But most stay within that limit, they’re just incredibly circuitous. Look at the map of route 9 again. It jumps between two main corridors, has multiple loops, and enters the parking lots of the Wal-Mart and other destinations on US 77.

The reason for the meanders is understandable. US 77 is a divided highway without sidewalks or crosswalks, and none of the destinations thereon fronts the road itself. From the wrong side of the road to Wal-Mart it’s 330 meters, and a few other retail locations are more than 100 meters off. Many agencies wince at making passengers walk this long.

However, understandable does not mean justifiable. Traversing even 330 meters takes only about 4 minutes, and even with a hefty walking penalty it’s much less than the inconvenience caused by hourly headways. The other routes in the Sioux City area have the same problem: not a single one runs straight between city center and its outer destination.

With straighter routes, the savings in service-hours would permit running every half hour. A single bus could run every half hour if the one-way car travel time were at most 11-12 minutes; up to 23 minutes, two buses would provide half-hourly service. With 12 buses, there is room to replace route 9 with two routes, one on Dakota and one on US 77 (possibly entering the Wal-Mart, since the route is so short it may be able to get closer to Wal-Mart while still staying under 12 minutes). The Lakeport Commons and Southern Hills Mall area could get buses at the entrance, as it is the logical end of the line (route 1, to Southern Hills).

Some pruning would still be required. Some low-density areas far from the main corridors would have to be stranded. Some circumferential lines would be pruned as well, such as route 10 (to the Commons) on US 75 and route 2 (on Pierce Jackson) to Wal-Mart. Circumferential lines at such a low frequency are not useful unless the transfers to the spokes are timed, which is impossible without breaking the city center interchange since the lines take different amounts of time to get between city center with the plausible connection point. Ultimately, replacing the hourly routes with half-hourly routes would guarantee better service to everyone who’d still get any service, which is nearly everyone.

It’s not just Sioux City

I focus on Sioux City because it’s a good toy model, at such scale that I could redesign the buses in maybe two weeks of part-time work. But it’s not the only place where I’ve seen needlessly circuitous routes wreck what should be a decent bus network for the city’s size and density. In 2014 Sandy wrote about the bus network in New Haven, which has okay trunks (I only needed to hitchhike because of a bus delay once – the other four or five times I took the bus it was fine) but splits into indescribably complex branches near its outer ends.

More recently, I looked at the network in Ann Arbor, partly out of prurient interest, partly out of having gone to two math conferences there and had to commute from the hotel to the university on the city’s most frequent bus, route 4. Zoomed out, the Ann Arbor map looks almost reasonable (though not quite – look at routes 5 and 6), but the downtown inset shows how route 4 reverse-branches. Ann Arbor is a car-oriented city; at my last math conference, in Basel, a professor complained that despite the city’s leftist politics, people at the math department were puzzled when the professor biked to campus. The buses are designed to hit every destination someone who’s too poor to own a car might go to, with speed, frequency, and reliability not the main concerns.

The underlying structure of bus networks in small American cities – radial buses converging on city center, often with a timed transfer – is solid. The problem is that the buses run every hour when cities should make an effort to run them every half hour, and the routes themselves are circuitous. In very small cities like Sioux City, increasing the base frequency is especially urgent, since their built-up extent is so compact a direct bus would reach the limit of the serviceable area in 10-12 minutes, perfect for a half-hourly schedule, and not the 25 minutes more typical of hourly schedules. Sometimes, scaling down requires maintaining higher frequency than the bare minimum, to avoid wasting drivers’ time with low-value meanders.

Overbuilding for Future Capacity

I ran a Patreon poll with three options for posts about design compromises: overbuilding for future capacity needs, building around compromises with unfixably bad operations, and where to build when it’s impossible to get transit-oriented development right. Overbuilding won with 16 votes to bad operations’ 10 and development’s 13.

It’s generally best to build infrastructure based exactly on expected use. Too little and it gets clogged, too much and the cost of construction is wasted. This means that when it comes to rail construction, especially mainline rail, infrastructure should be sized for the schedule the railroad intends to run in the coming years. The Swiss principle that the schedule comes first was just adopted in Germany; based on this principle, infrastructure construction is geared around making timed transfers and overtakes and shortening schedules to be an integer (or half-integer) multiple of the headway minus turnaround time for maximum equipment utilization.

And yet, things aren’t always this neat. This post’s topic is the issue of diachronic optimization. If I design the perfect rail network for services that come every 30 minutes, I will probably end up with a massive upgrade bill if ridership increases to the point of requiring a train every 20 minutes instead. (I chose these two illustrative numbers specifically because 30 is not a multiple of 20.) In some cases, it’s defensible to just build for higher capacity – full double-tracking even if current ridership only warrants a single track with passing sidings, train stations with more tracks in case more lines are built to connect to them, and so on. It’s a common enough situation that it’s worth discussing when what is technically overbuilding is desirable.

Expected growth rates

A fast-growing area can expect future rail traffic to rise, which implies that building for future capacity today is good. However, there are two important caveats. The first is that higher growth usually also means higher uncertainty: maybe our two-track commuter line designed around a peak of 8 trains per hour in each direction will need 32 trains per hour, or maybe it will stay at 8 for generations on end – we usually can’t guarantee it will rise steadily to 16.

The second caveat, applicable to fast-growing developing countries, is that high growth raises the cost of capital. Early British railroads were built to higher standard than American ones, and the explanation I’ve seen in the rail history literature is that the US had a much higher cost of capital (since growth rates were high and land was free). Thus mainlines in cities (like the Harlem) ran in the middle of the street in the US but on elevated structures in Britain.

But with that in mind, construction costs have a secular increase. Moreover, in constrained urban areas, the dominant cost of above-ground infrastructure cost is finding land for multiple tracks of railroad (or lanes of highway), and those are definitely trending up. The English working class spent 4-5% of its income on rent around 1800 (source, PDF-p. 12); today, spending one third of income on rent is more typical, implying housing costs have grown faster than incomes, let alone the general price index.

The upshot is that cities that can realistically expect large increases in population should overbuild more, and optimize the network around a specific level of traffic less. Switzerland and Germany, both of which are mature, low-population growth economies, can realistically predict traffic many decades hence. India, not so much.

Incremental costs

The expected growth rate helps determine the future benefits of overbuilding now, including reduced overall costs from fronting construction when costs are expected to grow. Against these benefits, we must evaluate the costs of building more than necessary. These are highly idiosyncratic, and depend on precise locations of needed meets and overtakes, potential connection points, and the range of likely train frequencies.

On the Providence Line, the infrastructure today is good for an intercity train at current Amtrak speed every 15 minutes and a regional train making every stop every 15 minutes. There is one overtake segment at Attleboro, around three quarters of the way from Boston to Providence, and the line is otherwise double-track with only one flat junction, with the Stoughton branch. If intercity trains are sped up to the maximum speed permitted by right-of-way geometry, an additional overtake segment is required about a quarter of the way through, around Readville and Route 128. If the trains come every 10 minutes, in theory a mid-line overtake in Sharon is required, but in practice three overtakes would be so fragile that instead most of the line would need to be four-tracked (probably the entire segment from Sharon to Attleboro at least). This raises the incremental costs of providing infrastructure for 10-minute service – and conversely, all of this is in lightly developed areas, so it can be deferred without excessive future increase in costs.

An even starker example of high incremental costs is in London. Crossrail 2 consists of three pieces: the central tunnel between Clapham Junction and Euston-St. Pancras, the northern tunnel meandering east to the Lea Valley Lines and then back west to connect to the East Coast Main Line, and the southern tunnel providing two extra tracks alongside the four-track South West Main Line. The SWML is held to be at capacity, but it’s not actually at the capacity of an RER or S-Bahn system (as I understand it, it runs 32 trains per hour at the peak); the two extra tracks come from an expectation of future growth. However, the extreme cost of an urban tunnel with multiple new stations, even in relatively suburban South London, is such that the tunnel has to be deferred in favor of above-ground treatments until it becomes absolutely necessary.

In contrast, an example of low incremental costs is putting four tracks in a cut-and-cover subway tunnel. In absolute terms it’s more expensive than adding passing tracks in suburban Massachusetts, but the effect on capacity is much bigger (it’s an entire track pair, supporting a train every 2 minutes), and moreover, rebuilding a two-track tunnel to have four tracks in the future is expensive. Philadelphia most likely made the right choice to build the Broad Street Line four-track even though its ridership is far below the capacity of two – in the 1920s it seemed like ridership would keep growing. In developing countries building elevated or cut-and-cover metros, the same logic applies.

Sundry specifics

The two main aspects of every infrastructure decision are costs and benefits. But we can discern some patterns in when overbuilding is useful:

  1. Closing a pinch point in a network, such as a single- or double-track pinch point or a flat junction, is usually worth it.
  2. Cut-and-cover or elevated metro lines in cities that are as large as prewar New York (which had 7 million people plus maybe 2 million in the suburbs) or can expect to grow to that size class should have four tracks.
  3. On a piece of infrastructure that is likely to be profitable, like high-speed rail, deferring capacity increases until after operations start can be prudent, since the need to start up the profitable system quickly increase the cost of capital.
  4. Realistic future projections are imperative. Your mature first-world city is not going to triple its travel demand in the foreseeable future.
  5. Higher uncertainty raises the effective cost of capital, but it also makes precise planning to a specific schedule more difficult, which means that overbuilding to allow for more service options becomes reasonable.
  6. The electronics before concrete principle extends to overbuilding: it’s better to complete a system (such as ETCS signaling or electrification) even if some branches don’t merit it yet just because of the benefits of having a single streamlined class of service, and because of the relatively low cost of electronics.

Usually cities and countries should not try to build infrastructure ahead of demand – there are other public and private priorities competing for the same pool of money. But there are some exceptions, and I believe these principles can help agencies decide. As a matter of practice, I don’t think there are a lot of places in the developed world where I’d prescribe overbuilding, but in the developing world it’s more common due to higher future growth rates.

Bus Stop Spacing and Network Legibility

I had an interesting interview of the annoying kind, that is, one where my source says something that ends up challenging me to the point of requiring me to rethink how I conceive of transportation networks. On the surface, the interview reaffirmed my priors: my source, a mobility-limited New Yorker, prefers public transit to cars and is fine with walking 500 meters to a bus stop. But one thing my source said made me have to think a lot more carefully about transit network legibility. At hand was the question of where buses should stop. Ages ago, Jarrett suggested that all other things equal (which they never are), the best stop spacing pattern is as follows:

The bus stops on the north-side arterials are offset in order to slightly improve coverage. The reason Jarrett cites this doesn’t occur much in practice is that there would also be east-west arterials. But maybe there aren’t a lot of east-west arterials, or maybe the route spacing is such that there are big gaps between major intersections in which there’s choice about which streets to serve. What to do then? My source complained specifically about unintuitive decisions about which streets get a bus stop, forcing longer walks.

In the case of the most important streets, it’s easy enough to declare that they should get stops. In Brooklyn, this means subway stations (whenever possible), intersecting bus routes, and important throughfares like Eastern Parkway or Flatbush. Right now the B44 Select Bus Service on Nostrand misses Eastern Parkway (and thus the connection to the 3 train) and the M15 SBS on First and Second Avenues misses 72nd Street (and thus the southernmost connection to Second Avenue Subway). However, there is a bigger question at hand, regarding network legibility.

Bus networks are large. Brooklyn’s current bus network is 550 km, and even my and Eric Goldwyn’s plan only shrinks it to about 340, still hefty enough that nobody can be expected to memorize it. Passengers will need to know where they can get on a stop. For the sake of network legibility, it’s useful to serve consistent locations whenever possible.

This is equally true of sufficiently large subway networks. Manhattan subway riders know that the north-south subway lines all have stops in the vicinity of 50th Street, even though the street itself isn’t especially important, unlike 42nd or 34th. In retrospect, it would have been better to have every line actually stop at 50th, and not at 49th or 51st, but the similarity is still better than if some line (say) stopped at 47th and 54th on its way between 42nd and 59th. A bad Manhattan example would be the stop spacing on the 6 on the Upper East Side, serving 68th and 77th Streets but not the better-known (and more important) 72nd and 79th.

There are similar examples of parallel subway lines, some stopping on consistent streets, and some not. There are some smaller North American examples, i.e. Toronto and Chicago, but by far the largest subway network in the world in a gridded city is that of Beijing. There, subway stops near city center are forced by transfer locations (Beijing currently has only one missed connection, though several more are planned), but in between transfers, they tend to stop on consistent streets when those streets are continuous on the grid.

But outside huge cities (or cities with especially strong grids like Chicago, Philadelphia, and Toronto), consistent streets are mostly a desirable feature for buses, not subways. Bus networks are larger and less radial, so legibility is more important there than on subways. Buses also have shorter stop spacing than subways, so people can’t just memorize the locations of some neighborhood centers with subway stops (“Nation,” “Porte de Vincennes,” etc.).

In the other direction, in cities without strong grids, streets are usually not very long, and the few streets that are long (e.g. Massachusetts Avenue in Boston) tend to be so important that every transit route intersecting them should have a stop. However, streets that are of moderate length, enough to intersect several bus lines, are common even in interrupted grids like Brooklyn’s or ungridded cities like Paris (but in London they’re rarer). Here is the Paris bus map: look at the one-way pair in the center on Rue Reaumur and Boulevard Saint-Denis (and look at how the northbound bus on Boulevard de Strasbourg doesn’t stop at Saint-Denis, missing a Metro transfer). There are a number of streets that could form consistent stops, helping make the Parisian bus network more legible than it currently is.

As with all other aspects of legibility, the main benefits accrue to occasional users and to regular riders who unfamiliar with one particular line or region. For these riders, knowing how to look for a bus stop (or subway station, in a handful of large cities) is paramount; it enables more spontaneous trips, without requiring constantly consulting maps. These occasional spontaneous trips, in turn, are likelier to happen outside the usual hours, making them especially profitable for the transit agency, since they reduce rather than raise the peak-to-base ratio. (Bus operating costs mostly scale with service-hours, but very peaky buses tend to require a lot of deadheading because they almost never begin or end their trip at a bus depot.)

The main takeaway from this is that bus network redesigns should aim to stop buses on parallel routes at consistent streets whenever possible, subject to other constraints including regular stop spacing, serving commercial nodes, and providing connections to the rail network. To the extent cities build multiple parallel subway lines, it’s useful to ensure they serve stations on consistent streets as well when there’s a coherent grid; this may prove useful if New York ever builds a subway under Utica and extends the Nostrand Avenue Line, both of which extensions were on the drawing board as recently as the 1970s.

Radial Metro Networks for Portions of Cities

I’ve harped about the necessity of radial metro networks, looking much like the following schematic:

However, in practice such pure radial networks are rare. Some networks have parallel lines (such as Paris and Beijing), nearly all have lines intersecting without a transfer at least once (the largest that doesn’t is Mexico City), some have chordal lines and not just radial or circular lines, and nearly all have lines that meet twice. Often these variations from pure radii are the result of poor planning or a street network that makes a pure radial system infeasible, but there are specific situations in which it’s reasonable for lines to meet multiple times (or sometimes even be parallel). These come from the need to built an optimal network not just for the whole city but also notable portions of it.

The unsegmented city

The diagram depicted above is a city with a single center and no obvious sub-areas with large internal travel demand. If the city is on a river, it’s not obvious from the subway map where the river passes, and it’s unlikely its non-CBD bank has a strong identity like that of the Left Bank of Paris, South London, or Brooklyn and Queens.

Among the largest metro networks in the world, the one most akin to the diagram above is Moscow. It has seven radial lines through city center (numbered 1-10, omitting the one-sided 4, the circular 5, and the yet-incomplete 8). They have some missed connections between them (3/6, 3/7, 6/9), and one pair of near-parallel lines (2/10, meeting only at Line 10’s southern terminus), but no parallel lines, and no case in which two lines cross twice. And Moscow’s development is indeed oriented toward connecting outlying areas with city center. Connections between areas outside the center are supposed to use the circular lines (5 and 14, with 11 under construction).

In a relatively monocentric city, this is fine. Even if this city is on the river, which Moscow is, it doesn’t matter too much if two neighborhoods are on the same side of the river when planning the network. Even in polycentric cities, this is fine if the sub-centers get connections via circular lines or the odd chordal line (as will eventually happen when Los Angeles builds a real subway network with such chords as Vermont and Sepulveda).

The segmented city

London and Paris are both segmented by their rivers, and their wrong sides (South London, Left Bank) both have strong regional identities, as does to some extent East London. New York, partitioned into boroughs by much wider waterways than the Thames and Seine, has even stronger sub-identities, especially in Brooklyn. I do not know of a single New Yorker whose commute to work or school involves crossing a bridge over a river on foot, nor of any case of anyone crossing a bridge in New York on foot (or bike) except for recreational purposes; in Paris I do so habitually when visiting the Latin Quarter, and at a conference in 2010 another attendee biked from Porte de Vincennes to Jussieu every day.

With a difficult water boundary, the wrong-side part of the city became a center in its own right. Downtown Brooklyn and the Latin Quarter should both be viewed as sub-centers that failed to become CBDs. The Latin Quarter, the oldest part of Paris outside the Ile de la Cite, declined in favor of the more commercial Right Bank as the city grew in the High and Late Middle Ages; Downtown Brooklyn declined in favor of more concentration in Manhattan and more dispersion to other centers (often in Queens) over the course of the 20th century.

Early 20th century New York and Paris were not polycentric cities. There was no everywhere-to-everywhere demand. There was demand specifically for travel within Brooklyn and within the Left Bank. To this day, the connections to the Latin Quarter from Right Bank neighborhoods not on Line 4 are not great, and from Nation specifically the alternatives are a three-seat ride and a long interchange at Chatelet. Ultimately, this situation occurs when you have a region with a strong identity and strong demand for internal travel larger than a neighborhood (which can be served by a few subway stops on a single line) but smaller than an entire city.

In this case, a radial subway network (which neither the New York City Subway nor the Paris Metro is) could justifiably have multiple crossings between two lines, ensuring that lines provide a coherent network for internal travel. South London is a partial example of this principle: not counting the Wimbledon branch of the District line, the South London Underground network is internally connected, and the best route between any two South London stations stays within South London. In particular, the Victoria and Northern lines cross twice, once at Stockwell and once at Euston, in a city that has a generally radial metro system.

Don’t go overboard

The need to serve internal travel within portions of a city is real, and it’s worthwhile to plan metro networks accordingly. But at the same time, it’s easy to go overboard and plan lines that serve only travel within such portions. Most of the examples I give of weak chordal lines – the G train in New York, Line 10 and the RER C in Paris, Line 6 in Shanghai – serve internal demand to the wrong side of a city divided by a river; only Shanghai’s Line 3 is an exception to this pattern, as a weak chordal line that doesn’t come from city segmentation.

In the cases of the G and M10, the problem is partly that the lines have compromises weakening them as radials. The G has too many missed connections to radial lines, including the J/Z and the entire Atlantic-Pacific complex; M10 terminates at Austerlitz instead of extending east to the library, which is the second busiest Left Bank Metro stop (after Montparnasse) and which has a particularly strong connection to the universities in the Latin Quarter.

But Line 6 is constrained because it doesn’t serve Lujiazui, just Century Avenue, and the RER C does serve the library but has exceptionally poor connections to the CBD and other Right Bank destinations. It’s important to ensure the network is coherent enough to serve internal demand to a large segment of the city but also to serve travel demand to the rest of the city well.

Good transfers

Serving the entire city hinges on good transfers. The most important destination remains city center, so lines that aren’t circumferential should still aim to serve the center in nearly all cases. Internal demand should be served with strategic transfers, which may involve two lines crossing multiple times, once in or near city center and once on the wrong side of the river.

The main drawback of multiple crossings is that they are less efficient than a pure radial network with a single city center crossing between each pair of lines, provided the only distinguished part of the city is the center. Once internal travel to a geographic or demographic segment is taken into account, there are good reasons to slightly reduce the efficiency of the CBD-bound network if it drastically raises the efficiency of the secondary center-bound network. While demographic trends may come and go (will Flushing still be an unassimilated Chinese neighborhood in 50 years?), geographic constraints do not, and place identities like “Left Bank” and “Brooklyn” remain stable.

Note the qualifiers: since the CBD remains more important than any secondary center, it’s only acceptable to reduce CBD-bound efficiency if the gain in secondary center-bound efficiency is disproportionate. This is why I propose making sure there are good transfers within the particular portion of the city, even at the cost of making the radial network less perfect: this would still avoid missed connections, a far worse problem than having too many transfer points.

So what?

In New York, London, and Paris, the best that can be done is small tweaks. However, there exist smaller or less developed cities that can reshape their transit networks, and since cities tend to form on rivers and bays, segmentation is common. Boston has at least two distinguished wrong-side segments: East Boston (including Chelsea and Revere) and Greater Cambridge. East Boston can naturally funnel transit through Maverick, but in Greater Cambridge there will soon be two separate subway spines, the Red and Green Lines, and it would be worthwhile to drag a rail connection between them. This is why I support investing in rail on the Grand Junction, turning it into a low-radius circular regional rail line together with the North-South Rail Link: it would efficiently connect the Green Line Extension with Kendall.

More examples of segmented cities include the Bay Area (where the wrong-side segment is the East Bay), Istanbul (where Europe and Asia have separate metro networks, connected only by Marmaray), Stockholm (where Södermalm and Söderort are separated by a wide channel from the rest of the city, and Kungsholmen is also somewhat distinguished), and Washington (where the wrong side is Virginia). In all of these there are various compromises on metro network planning coming from the city segmentation. Stockholm’s solution – making both the Red and Green Lines serve Slussen – is by far the best, and the Bay Area could almost do the same if BART were connected slightly differently around Downtown Oakland. But in all cases, there are compromises.

Guidelines for Driverless Buses

As I’ve said a few months ago in The American Prospect, driverless bus technology does not yet appear ready for mass deployment. However, research into this technology continues. Of particular note is Google’s work at Waymo, which a source within the Bay Area’s artificial intelligence community tells me is more advanced and more serious than the flops at Uber and Tesla; Waymo’s current technology is pretty good on a well-understood closed route, but requires laborious mapping work to extend to new routes, making it especially interesting for fixed-route buses rather than cars. But ultimately, automated vehicles will almost certainly eventually be mature and safe, so it is useful to plan around them. For this, I propose the following dos and don’ts for cities and transit agencies.

Install dedicated, physically-separated bus lanes

A bus with 40 people should get 40 times the priority of a car with one person, so this guideline should be adopted today already. However, it’s especially important with AVs, because it reduces the friction between AV buses and regular cars, which is where the accident in Las Vegas reference in my TAP article happened. The CityMobil2 paradigm involves AVs in increasingly shared traffic, starting from fully enclosed circuits (like the first line in Helsinki, at the zoo) and building up gradually toward full lane sharing. Dedicated lanes are a lower level of sharing than mixed traffic, and physical separation reduces the ability of cars to cut ahead of the bus.

If there is a mixture of AV and manual buses, both should be allowed in the dedicated lanes. This is because bus drivers can be trained to know how to deal with AVs. Part of the problem with AVs in mixed traffic is that human drivers are used to getting certain cues from other human drivers, and then when facing robot drivers they don’t have these cues and misread the car’s intentions. But professional drivers can be trained better. Professional bus drivers are also familiar with their own bus system and will therefore know when the AV is going to turn, make stops, and so on.

Use Kassel curbs to provide wheelchair accessibility

Buses are at a disadvantage compared with trams in wheelchair accessibility. Buses sway too much to have the precise alignment that permits narrow enough gaps for barrier-free access on trains. However, as a solution, some German cities have reconstructed the edges of the bus lane next to the bus stop platform, in order to ease the wheels into a position supporting step-free access on low-floor buses. Potentially, AVs could make this easier by driving more precisely or by having platform extenders similar to those of some regional trains (such as those of Zurich) bridging the remainder of the horizontal gap.

Driverless trains in Vancouver and even on Paris Metro Line 14 have roll-on wheelchair access: passengers in wheelchairs can board the train unassisted. In contrast, older manually-driven trains tend to tolerate large horizontal and vertical gaps blocking passengers in wheelchairs, to the point that New York has to have some special boarding zones for wheelchairs even at accessible stations. If the combination of precision driving and Kassel curbs succeeds in creating the same accessibility on a bus as on SkyTrain in Vancouver, then the bus driver’s biggest role outside of actually driving the bus is no longer necessary, facilitating full automation.

Don’t outsource planning to tech firms

Transit networks work best when they work in tandem. This means full fare and schedule integration within and across different modes, and coordinated planning. Expertise in maintaining such networks lies within the transit agencies themselves as well as with various independent consultancies that specialize in transportation.

In contrast, tech firms have little expertise in this direction. They prefer competition to cooperation, so that there would be separate fleets within each city by company – and moreover, each company would have an incentive to arrange schedules so that buses would arrive just ahead of the other companies to poach passengers, so there wouldn’t be even headways. The culture of tech involves brazen indifference to domain expertise and a preference for reinventing the wheel, hence Uber and Chariot’s slow realization that no, really, fixed-route buses are the most efficient way of carrying passengers on the street in dense cities. Thus, outsourcing planning is likely to lead to both ruinous competition and retarded adoption of best practices. To prevent this, cities should ban private operations competing with their public bus networks and instead run their own AVs.

Most of the world’s richest cities have deep pools of tech workers, especially the single richest, San Francisco. It would be best for Muni, RATP, NYCT, and other rich-city agencies to hire tech talent using the same methods of the private sector, and train them in transit network planning so that they can assist in providing software services to the transit system in-house.

Resist the siren song of attendants

Las Vegas’s trial run involved an attendant on each bus performing customer service and helping passengers in wheelchairs. A bus that has an attendant is no more a driverless bus than a subway with computer-controlled driving and an operator opening and closing doors is a driverless train. The attendant’s work is similar to that of a bus driver. If the hope of some private operators is that relabeling the driver as an attendant will allow them to de-skill the work and hire low-pay, non-union employees, then it’s based on a misunderstanding of labor relations: transit employees are a prime target for unionization no matter whether they are called drivers.

Ultimately, the difficulty of driving a bus is not much greater than that of dealing with annoying customers, being on guard in case passengers act aggressively or antisocially, and operating wheelchair lifts. Bus drivers get back pain at high rates since they’re at the wheel of a large vehicle designed for passenger comfort for many hours a day, but this may still be a problem on AVs, and all other concerns of bus drivers (such as the risk of assault by customers) remain true for attendants. Either get everything right to the point of not needing any employee on the bus, or keep manual driving with just some computer assistance.

Resist the siren song of small vehicles

All AV bus experiments I know of (which I know for a fact is not all AV buses that are trialing) involve van-size vehicles. The idea is that, since about 75% of the cost of running a bus today is the driver’s wage, there’s no real point in running smaller vehicles at greater frequency if there’s a driver, but once the driver is removed, it’s easy enough to run small vehicles to match passenger demand and reduce fuel consumption.

However, vans have two problems. First, they only work on thin routes. Thick routes have demand for articulated buses running at high frequency, and then vans both add congestion to the bus lane and increase fuel consumption (when the vehicles are full, bigger is always more fuel-efficient). And second, they lead to safety problems, as passengers may be afraid of riding a bus alone with 3-4 other passengers but not with 20 or more (Martha Lauren rides full London buses fearlessly but would make sure to sit near the driver on nearly-empty Baltimore buses).

Medium-size buses, in the range of 20-30 seats, could be more useful on thin routes. However, passenger safety problems are likely to remain if only a handful of people ride each vehicle.

Get your maintenance costs under control

If you remove the driver, the dominant factor in bus operating costs becomes maintenance. Assuming maintenance workers make the same average annual wage and get the same benefits as transit workers in general, the wages of maintenance workers are about 15% of the total operating costs of buses in Chicago and 20% in New York.

The importance of fuel economy grows as well, but fuel today is a much smaller proportion of costs. Around 3% in Chicago and 2% in New York. European fuel costs are much higher than Americans, but so are European bus fuel economy rates: in tests, Boris buses got 4.1 km per liter of diesel, which is maybe twice as good as the US average and three times as good as the New York average.

This suggests that with the driver gone, maybe 75% of the remaining variable operating cost is maintenance. Chicago does better than New York here, since it replaces 1/12 of its fleet every year, so every year 1/12 of the fleet undergoes mid-life refurbishment and work is consistent from year to year, whereas in New York the replacement schedule is haphazard and there is more variation in work needs and thus more idle time. The most important future need for AV procurement is not electric traction or small size, but low lifecycle costs.

Update: by the same token, it’s important to keep a lid on vehicle procurement costs. New York spends $500,000 on a standard-length bus and $750,000 on an articulated bus; the Boris buses, which are bilevel and similar in capacity to an artic, cost about $500,000, which is locally considered high, and conventional artic or bilevel buses in London cost $300,000-350,000. American cities replace buses every 12 years, compared with every 15 years in Canada, and the depreciation in New York is around 6% of total bus operating costs. Cutting bus procurement costs to London levels would only save New York a small percent of its cost, but in an AV future the saving would represent around 12% of variable costs.

Plan for higher frequency

AVs represent an opportunity to reduce marginal operating costs. This means transit agencies should plan accordingly:

  • Lower marginal costs encourage running buses more intensively, running almost as much service off-peak and on weekends as at rush hour.
  • Very high frequency encourages passengers to transfer more, so the value of one-seat rides decreases.
  • Higher frequency always increases capacity, but its value to passengers in terms of reduced wait times is higher when the starting frequency is low, which means agencies should plan on running more service on less frequent routes and only add service on routes that already run every 5 minutes or less if the buses are overcrowded.

The Formula for Frequent Transit Networks

As I’m working on refining a concrete map for Brooklyn buses, I’m implementing the following formula:

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

In this post I’m going to go over what this formula really means and where it is relevant.

Operating costs

The left-hand side represents costs. The operating costs of buses are proportional to time, not distance. A few independent American industry sources state that about 75-80% of the cost of bus service is the driver’s wage; these include Jarrett Walker as well as a look at the payrolls in Chicago. The remaining costs are fuel, which in a congested city tracks time more than distance (because if buses run slow it’s because of stop-and-go traffic and idling at stops or red lights), and maintenance, which tracks a combination of time and distance because acceleration and braking cycles stress the engine.

This means that the number of service hours is fixed as part of the budget. My understanding is that the number in Brooklyn is 10,000 per weekday. I have seen five different sources about bus speeds and service provision in New York (or Brooklyn) and each disagrees with the others; the range of hours is between 9,500 and 12,500 depending on source, and the range of average speeds is between 9.7 km/h (imputed from the NTD and TransitCenter’s API) and 11 km/h (taken from schedules). The speed and hours figures are not inversely correlated, so some sources believe there are more service-km than others.

On a rail network, the same formula applies but the left-hand side should directly include service-kilometers, since rail operating costs (such as maintenance and energy) are much more distance- than time-dependent; only the driver’s wage is time-dependent, and the driver’s wage is a small share of the variable costs of rail operations.

Creating more service

Note that on a bus network, the implication of the formula is that higher speed is equivalent to more service-hours. My current belief, based on the higher numbers taken from schedules, is that 14 km/h is a realistic average speed for a reformed bus network: it’s somewhat lower than the average scheduled speed of the B44 SBS and somewhat higher than that of the B46 SBS, and overall the network should have somewhat denser stop spacing than SBS but also higher-quality bus lanes canceling out with it. The problem is that it’s not clear that SBS actually averages 14 km/h; my other sources for these two routes are in the 12-13 km/h range, and I don’t yet know what is correct. This is on top of the fact that faster transit attracts more paying riders.

Another way to create more service is to reduce deadheading and turnaround times. This is difficult. Bus depots are not sited based on optimal service. They are land-intensive and polluting and end up in the geographic and socioeconomic fringes of the city. The largest bus depot in New York (named after TWU founder Mike Quill) is in Hudson Yards, but predates the redevelopment of the area. In Brooklyn the largest depots appear to be East New York (more or less the poorest neighborhood in the city) and Jackie Gleason (sandwiched between a subway railyard and a cemetery). Figuring out how to route the buses in a way that lets them begin or end near a depot so as to reduce deadheading is not an easy task, but can squeeze more revenue-hours out of an operating cost formula that is really about total hours including turnaround time and non-revenue moves.

Service provision

The right-hand side of the equation describes how much service is provided. The network length is just the combined length of all routes. Daily frequency is measured in the average number of trips per day, which is not an easily understandable metric, so it’s better to convert it to actual frequencies:

Frequency Daily trips
15 minutes 6 am-9 pm, 30 minutes otherwise 5-1 am 70
15 minutes 24/7 96
5 minutes 7-9 am, 5-7 pm, 10 minutes otherwise 6 am-10 pm, 30 minutes 10 pm-12 am 124
5 minutes 7-9 am, 5-7 pm, 7.5 minutes otherwise 6 am-10 pm, 15 minutes 10 pm-12 am, 30 minutes overnight 164
6 minutes 6 am-10 pm, 10 minutes otherwise 5-12 am, 30 minutes overnight 188
5 minutes 6 am-10 pm, 10 minutes otherwise 5-12 am, 20 minutes overnight 228
3 minutes 7-9 am, 5-7 pm, 5 minutes otherwise 6 am-10 pm, 10 minutes otherwise 5-12 am, 20 minutes overnight 260

Daily trips are given per direction; for trips in both directions, multiply by 2. There are internal tradeoffs to each number of daily trips between peak and off-peak frequency and between midday frequency and span. But for the most part the tradeoff is between the average number of daily trips per route and the total route-length. This is the quantitative version of Jarrett’s frequency-coverage tradeoff. In reality it’s somewhat more complicated – for example, average speeds are lower at the peak than off-peak and lower in the CBD than outside the CBD, so in practice adding more crosstown routes with high off-peak frequency costs less than providing the same number of revenue-km on peaky CBD-bound buses.

It’s also important to understand that this calculation only really works for frequent transit, defined to be such that the ratio of the turnaround time to the frequency and length of each route is small. On low-frequency routes, or routes that are so short that their total length is a small multiple of the headway, the analysis must be discrete rather than continuous, aiming to get the one-way trip time plus turnaround time (including schedule padding) to be an even multiple of the headway, to avoid wasting time. On regional rail, which often has trains coming every half hour on outer tails and which is much more precisely scheduled than a street bus ever could be, it’s better to instead get the length of every route from the pulse point to the outer end to be an integer or half-integer multiple of the clockface headway minus the turnaround time.

Where is New York?

All of my numbers for New York so far should be viewed as true up to a fudge factor of 10-15% in each direction, as  my source datasets disagree. But right now, Brooklyn has about 10,500 revenue-hours per weekday (slightly more on a school day, slightly fewer on a non-school day) and an average speed of about 10.5 km/h, for a total of 110,000 revenue-km. Its bus network is 550 km long, counting local and limited versions of the same bus route as a single route but counting two bus routes that interline (such as the B67 and B69) separately; interlining is uncommon in Brooklyn, and removing it only shortens the network by a few km. This means that the average bus gets 200 runs per day, or 100 per direction.

Based on the above table, 100 runs per direction implies a frequency somewhat worse than every 5 minutes peak and every 10 off-peak. This indeed appears to be the case – nearly half of Brooklyn’s network by length has off-peak weekday frequency between 10 and 15 minutes, and the median is 12. At the peak, the median frequency, again by route-length, is 7 minutes. 7 minutes peak, 12 off-peak with some extra evening and night service works out to just less than 100 runs a day in each direction.

This exercise demonstrates the need to both shrink the network via rationalization to reduce the number of route-km and increase speed to raise the left-hand side of the equation. SBS treatments increased the speed on the B44 and B46 by 30-40% relative to the locals (not the limiteds), but just keeping the network as is would onl permit 130-140 buses per weekday per direction, which is more frequency but not a lot of frequency. The 7.5-minute standard that appears to be used in Toronto and Vancouver requires more; Barcelona’s range of 3-8 minutes implies an average of 5-6 and requires even more.

Where could New York be?

It’s definitely possible to get the number of daily frequencies on the average Brooklyn bus route to more than 200 in each direction. In Manhattan this appears true as well (the big question is whether the avenues can get two-way service), and in the Bronx 250 is easy. But even 200 in Brooklyn (which implies perhaps 350 km of network) requires some nontrivial choices about which routes get buses and which don’t, cutting some buses that are too close to other routes or to the subway. I’m not committing to anything yet because the margin calls happen entirely within the 10-15% fudge factor in my datasets.

The main reason I post this now is that I believe the formula is of general interest. In any city that wants to rationalize its transit system (bus or rail), the formula is a useful construction for the tradeoffs involved in transit provision. You can look at the formula and understand why some systems choose to branch: at the same average frequency the busiest parts of the network would get more service. You can also understand why some systems choose not to branch: at some ranges of frequency, the outer ends would get so little frequency that it would discourage ridership.

What is high frequency?

I’m using 5-6 minutes as a placeholder value beyond which there’s no point in raising frequency if there’s no capacity crunch. This isn’t quite true – on a 15-minute bus trip, going from 6 minutes between buses to 3 is a 14% cut in worst-case trip time including wait – but at this point higher frequency is at best a second-order factor. It’s not like now, when going from 15 minutes to 6 would reduce the worst-case trip time on the same bus trip by 30%.

The actual values depend on trip length. An intercontinental flight every hour is frequent; a regional train every hour is infrequent; a city bus every hour might as well not exist. One fortunate consequence is that bus trips tend to be shorter in precisely the cities that can most afford to run intensive service: dense cities with large rail networks for the buses to feed. New York’s average NYCT bus trip (excluding express buses) is 3.5 km; Chicago’s is 4.1 km; Los Angeles’s is 6.7 km. Los Angeles can’t afford to run 6-minute service on its grid routes, but trips are long enough that 10-minute service may be good enough to start attracting riders who are not too poor to own a car.

Bus Branching

There are two standard reasons why public transit should limit branching. The first is that it reduces frequency on the branches; this is Jarrett Walker’s reason, and distantly the reason why New York doesn’t interline more than two subway services anywhere except 60th Street Tunnel. The second is that it makes schedules more fragile, first because services have to be scheduled more precisely to alternate among branches, and second because delays on one branch propagate to the others. And yet, rail and bus networks still employ branching, due to benefits including better coverage and focusing frequency where demand is the highest. This is especially common on regional rail, where all services are scheduled and often interact with the mainline network, so the second problem of branching is present no matter what. Metro systems instead have less branching, often because they only serve dense areas so that the main benefits of branching are absent. But what about buses?

I posit that bus branching is more valuable in low-density areas than in high-density areas. If an area only has demand for a bus every 30 minutes, and some farther-out places only have demand for an hourly bus, then it’s fine to branch the route in two. The bus would only be useful with some timed transfers at the inner end – maybe it’s feeding a regional train station with a train every half hour – but the Zurich suburbs have half-hourly clockface schedules with timed bus/rail connections and maintain high mode share for how low their density is.

In the other direction, look at Manhattan specifically. I’ve been looking at its bus network even though I’m only supposed to redesign Brooklyn’s. I’ve mentioned before that my epistemology is that if the presence of factor A makes solution B better, then the absence of factor A should make solution B worse. I noticed that the Brooklyn bus network has very little branching: the only route numbers that branch are the B41 and B38, and the only routes with different numbers that share the majority of their lengths are the B67 and B69 (which reverse-branch). However, Manhattan has extensive branching: the M1/2/3/4 share the Madison and Fifth Avenue one-way pair, and the M101/102/103 share the Third and Lexington one-way pair. Understanding why would be useful even if I only care about Brooklyn: if there is a good reason for Manhattan buses to branch then I should consider adding branching in Brooklyn where appropriate, and even if it’s inappropriate, it’s useful to understand what special circumstances make branching good in Manhattan but not in Brooklyn.

As it is, I don’t believe the branching in Manhattan is useful for Brooklyn. This comes from several reasons, at least one of which implies it’s not really useful for Manhattan either, and by extension for other high-density regions.

Base frequency

You can run a bus that comes every half hour on a schedule, making it possible to interline two hourly routes evenly. With some discipline you can go down to 15 minutes, or possibly even 10: Vancouver runs 12-minute limited buses on 4th Avenue on a clockface schedule with on-board fare collection and shared lanes, but there is signal priority at nearly all intersections and relatively little car traffic since the West Side’s street network is rich in arterial roads and distributes cars across other routes (i.e. Broadway, 12th, and 16th Avenues).

In contrast, it’s not really feasible to run buses on a schedule when they come every 5 minutes. There can be a printed schedule, but buses won’t follow it reliably. Once frequency hits about once every 3 minutes, regular street buses bunch so much that adding more buses doesn’t increase passenger capacity, but even in the 5-10 minute range, schedules are less important than headway management, unless the bus has extensive BRT treatments reducing schedule variance. This means that if a bus comes every 10 minutes and is scheduled on headway management, then branching the route means each branch gets service every 20 minutes scheduled on headway management as well. Few passengers would want to ride such a route. This is the worst region for branching, the 7.5-15 minute range in which branches force passengers to use buses that are both infrequent and irregular.

The highest-frequency routes can branch with less risk. If a 5-minute bus branches in two, then each branch gets 10-minute service, at which point reliable schedules are still desirable but not absolutely necessary. How much service do the Manhattan bus trunks run? In the following scheme, peak means the busiest hour in the morning in the peak direction, and off-peak means the lowest frequency between the morning and afternoon peaks, which is usually around 11 am.

M1: 13 buses per hour peak (8 limited, 5 local), 5 off-peak (all local)
M2: 9 peak, 4 off-peak
M3: 6 peak, 6 off-peak
M4: 12 peak (5 limited, 7 local), 6 off-peak (all local)

M101: 6 peak, 6 off-peak (8 in the busiest off-peak hour, 2-3 pm)
M102: 5 peak, 4 off-peak
M103: 5 peak, 4 off-peak

What we see is that Manhattan branches precisely in the worst frequency range. The buses are frequent enough that it’s not possible to run them on a timetable without either much better segregation from traffic than is feasible (even waving away politics) or massive schedule padding, but they still require passengers in Upper Manhattan to wait 10-15 minutes for their specific branch. One might expect that Bus Time would make it easier on passengers by telling them where the bus is, but no, ridership has actually fallen since apps were introduced (and this fall predates the entry of app-hailed TNCs into the city). It turns out passengers like being able to rely on easily memorable clockface schedules, or else on frequencies so high that they only need to wait 5 minutes, not 15.

The street network

Even one-time visitors to New York notice that the avenues in Manhattan are all one-way. This features prominently in the Manhattan bus network, which employs consistent one-way pairs on First/Second, Third/Lex, Madison/Fifth, and Ninth/Tenth. Moreover, again as every visitor to New York knows, Central Park occupies a large blob of land in the middle, interrupting Sixth and Seventh Avenues.

The upshot is that there are more north-south routes north of 110th Street than south of it. This is roughly the branch point on the three trunks that branch (First/Second only carries the M15). In Harlem, there’s demand for buses on Lenox (i.e. Sixth) and Seventh, both of which are two-way there. There’s also commerce on an interpolating route, Manhattan/St. Nicholas, which is effectively 8.5th Avenue in most of Harlem. Farther west, Ninth/Columbus is no longer a useful through-route north of 110th, but instead Tenth/Amsterdam is two-way, and one of the two buses using the Columbus/Amsterdam one-way pair on the Upper West Side, the M11, indeed goes two-way on Amsterdam north of 110th.

This situation occurs very frequently in cities without gridded street networks. One trunk route will split in two, heading to different former villages that were incorporated into the city as it industrialized and grew. Manhattan is unusual among gridded cities in that its avenues are one-way, forcing buses into one-way pairs south of Harlem that, together with Central Park, ensure there are more useful routes north of 110th than south of it. But among cities without a planned street network this is typical.

As a check, let’s look at the bus networks in two ungridded American cities: Boston and Providence. Do they have a lot of interlining, involving one trunk route splitting in two farther out? Yes, they do!

Here is Providence. Going west of Downcity, there are two major routes to Olneyville, Westminster and Broadway, but beyond Olneyville there are four main streets, so each of the two inner corridors carries two bus routes, and one of these four routes even splits in two farther out. Going north, Charles Street carries four routes, branching off at various locations. Going east there’s a bus tunnel to College Hill carrying many routes, but even outside the tunnel, the one-way pair on Angell and Waterman carries three buses, which split in East Providence. And going south and southwest, Broad Street carries multiple routes, and one of its branches, Elmwood, carries two, splitting farther south.

Here is Boston. Unlike in Providence, buses don’t converge on city center, but on subway stations, so the map is much less clean. However, we see the same pattern of trunk routes splitting into branches. For example, going south of Ruggles, many routes go southeast to Dudley and then south on Warren Street, splitting to various destinations in Dorchester, Mattapan, and Hyde Park on the way. Going southwest of Forest Hills we see many routes use Washington Street, some staying on it and branching in Dedham and some veering west to West Roxbury and branching there. Elsewhere in the system we see the same pattern going north of Maverick and Oak Grove, northeast of Malden, west of Harvard (briefly on Mount Auburn), and northwest of Alewife.

One-seat rides and reverse-branching

I have repeatedly criticized the practice of reverse-branching on subway networks, especially New York, in which two train routes share tracks in an outlying area (such as Queens Boulevard) and then split heading into the center (such as Eighth Avenue on the E versus Sixth Avenue on the F). I did so on the same grounds that any branching is suspect: it reduces frequency on specific routes, and makes the schedule more fragile as delays propagate to more of the network. Moreover, the issue of schedule fragility gets worse if many routes share tracks at some point during their journey, whereas with conventional branching there are only two or three branches per trunk and the trunks form self-contained systems. Finally, reverse-branching lacks the main benefit of conventional branching, as it does not concentrate traffic in the core, where there’s most demand.

These issues are present on bus networks, with two modifications:

  1. The value of one-seat rides is somewhat higher. Transferring between buses is less nice than transferring between subways: in a Dutch study about location decisions, people’s disutility of out-of-vehicle time on buses was 1.5 times as high as on trains.
  2. Buses can overtake each other and, even without overtakes, run much closer together than trains. The limiting factor to capacity on buses is schedule fragility and bunching and not stopping distances. This means that reverse-branching is less likely to lead to cascading delays – buses do not have a 2-minute exclusion zone behind them in which no buses may enter.

This means that reverse-branching is more defensible on buses than on trains. However, even then, I don’t think it’s a good idea. At least in Manhattan, reverse-branching consists of avenues in Upper Manhattan that have buses going to both the East Side and the West Side: the M7 (serving the Ninth/Tenth pair) and the M102 both run on Lenox, and the M4 and M104 (running on Broadway to Midtown) both run on Broadway in Morningside Heights. These splits both reduce the frequency available to bus riders and should be eliminated. East-west service should be provided with high-quality bus routes on the main streets, especially 125th (which needs a full subway) but also 116th, 135th, 145th, and 155th.

The snag is that grids don’t work well unless they are complete. The Manhattan grid isn’t complete through Upper Manhattan, because 116th and 135th are discontinuous, without a direct connection from Central Harlem to Morningside Heights and West Harlem. However, the M7 route duplicates the 2 and 3 trains, so it’s not necessary for east-west connectivity. The M4 route doesn’t duplicate the subway, but does duplicate the M101, which runs on 125th Street and Amsterdam (and isn’t a reverse-branch because the M11 terminates shortly after 125th), so it’s not useful by itself.

Should buses branch?

There is one solid reason for buses to branch: if the street network has more major routes closer to the center than in outlying areas, then buses running on the outer arterials should come together close to the core. This is common enough on cities with haphazard street networks. It may also be reinforced if there are weak circumferential streets (Sydney is one such example). In contrast, cities with gridded street plans, even broken grids like those of Brooklyn and Tel Aviv, should have little to no bus branching.

If a bus does branch, it should ideally be extremely frequent on the trunk, so that even the branches have decent headway-based service. I’m not willing to commit to a maximum headway, but Barcelona and Toronto both have at worst 8-minute headways on their bus grids, so if that is indeed the maximum then a bus shouldn’t branch if its off-peak frequency is worse than every 4 minutes and better than every 10-20 (the more reliable the timetable is, the lower the upper limit is, since it’s possible to run on a timetable at higher frequency). In my case of interest, Brooklyn, there is exactly one bus route that comes at least every 4 minutes off-peak: the B46 on Utica runs 16 buses per hour in each direction, counting both local and limited (SBS) routes.

The area in which buses absolutely should not branch – strong interconnected networks of arterials (not necessarily grids – Paris’s network counts too), running buses every 5-15 minutes off-peak – is exactly where most strong bus networks are. It’s rare to have a bus that has extremely high frequency all day, because in most functional city such a bus would be a subway already; as it is, Utica has long been New York’s second priority for subway service, after Second Avenue. So for the most part, the places where buses are the strongest are precisely those where branching is the most deleterious. Low-frequency networks, perhaps connecting to a suburban train station with a timed transfer, should add bus branching to their planning toolkit, but high-frequency urban networks should not.

The Value of Modern EMUs

I do not know how to code. The most complex actually working code that I have written is 48 lines of Python that implement a train performance calculator that, before coding it, I would just run using a couple of Wolfram Alpha formulas. Here is a zipped version of the program. You can download Python 2.7 and run it there; there may also be online applets, but the one I tried doesn’t work well.

You’ll get a command line interface into which you can type various commands – for example, if you put in 2 + 5 the machine will natively output 7. What my program does is define functions relevant to train performance: accpen(k,a,b,c,m,x1,x2,n) is the acceleration penalty from speed x1 m/s to speed x2 m/s where x1 < x2 (if you try the other way around you’ll get funny results) for a train with a power-to-weight ratio of k kilowatts per ton, an initial acceleration rate of m m/s^2, and constant, linear, and quadratic running resistance terms a, b, and c. To find the deceleration penalty, put in decpen, and to find the total, either put in the two functions and add, or put in slowpen to get the sum. The text of the program gives the values of a, b, and c for the X2000 in Sweden, taken from PDF-p. 64 of a tilting trains thesis I’ve cited many times. A few high-speed trainsets give their own values of these terms; I also give an experimentally measured lower air resistance factor (the quadratic term c) for Shinkansen. Power-to-weight ratios are generally available for trainsets, usually on Wikipedia. Initial acceleration rates are sometimes publicly available but not always. Finally, n is a numerical integration quantity that should be set high, in the high hundreds or thousands at least. You need to either define all the quantities when you run the program, or plug in explicit numbers, e.g. slowpen(20, 0.0059, 0.000118, 0.000022, 1.2, 0, 44.44, 2000).

I’ve used this program to find slow zone penalties for recent high-speed rail calculations, such as the one in this post. I thought it would not be useful for regional trains, since I don’t have any idea what their running resistance values are, but upon further inspection I realized that at speeds below 160 km/h resistance is far too low to be of any consequence. Doubling c from its X2000 value to 0.000044 only changes the acceleration penalty by a fraction of a second up to 160 km/h.

With this in mind, I ran the program with the parameters of the FLIRT, assuming the same running resistance as the X2000. The FLIRT’s power-to-weight ratio is 21.1 in Romandy, and I saw a factsheet in German-speaking Switzerland that’s no longer on Stadler’s website citing slightly lower mass, corresponding to a power-to-weight ratio of 21.7; however, these numbers do not include passengers, and adding a busy but not full complement of passengers adds mass to the train until its power-to-weight ratio shrinks to about 20 or a little less. With an initial acceleration of about 1.2 m/s^2, the program spits out an acceleration penalty of 23 seconds from 0 to 160 km/h (i.e. 44.44 m/s) and a deceleration penalty of 22 seconds. In videos the acceleration penalty appears to be 24 seconds, which difference comes from a slight ramping up of acceleration at 0 km/h rather than instant application of the full rate.

In other words: the program manages to predict regional train performance to a very good approximation. So what about some other trains?

I ran the same calculation on Metro-North’s M-8. Its power-to-weight ratio is 12.2 kW/t (each car is powered at 800 kW and weighs 65.5 t empty), shrinking to 11.3 when adding 75 passengers per car weighing a total of 5 tons. A student paper by Daniel Delgado cites the M-8’s initial acceleration as 2 mph/s, or 0.9 m/s^2. With these parameters, the acceleration penalty is 37.1 seconds and the deceleration penalty is 34.1 seconds; moreover, the paper show how long it takes to ramp up to full acceleration rate, and this adds a few seconds, for a total stop penalty (excluding dwell time) of about 75 seconds, compared with 45 for the FLIRT.

In other words: FRA-compliant EMUs add 30 seconds to each stop penalty compared with top-line European EMUs.

Now, what about other rolling stock? There, it gets more speculative, because I don’t know the initial acceleration rates. I can make some educated guesses based on adhesion factors and semi-reliable measured acceleration data (thanks to Ari Ofsevit). Amtrak’s new Northeast Regional locomotives, the Sprinters, seem to have k = 12.2 with 400 passengers and m = 0.44 or a little less, for a penalty of 52 seconds plus a long acceleration ramp up adding a brutal 18 seconds of acceleration time, or 70 in total (more likely it’s inaccuracies in data measurements – Ari’s source is based on imperfect GPS samples). Were these locomotives to lug heavier coaches than those used on the Regional, such as the bilevels used by the MBTA, the values of both k and m would fall and the penalty would be 61 seconds even before adding in the acceleration ramp. Deceleration is slow as well – in fact Wikipedia says that the Sprinters decelerate at 5 MW and not at their maximum acceleration rate of 6.4 MW, so in the decpen calculation we must reduce k accordingly. The total is somewhere in the 120-150 second range, depending on how one treats the measured acceleration ramp.

In other words: even powerful electric locomotives have very weak acceleration, thanks to poor adhesion. The stop penalty to 160 km/h is about 60 seconds higher than for the M-8 (which is FRA-compliant and much heavier than Amfleet coaches) and 90 seconds higher than for the FLIRT.

Locomotive-hauled trains’ initial acceleration is weak that reducing the power-to-weight ratio to that of an MBTA diesel locomotive (about 5 kW/t) doesn’t even matter all that much. According to my model, the MBTA diesels’ total stop penalty to 160 km/h is 185 seconds excluding any acceleration ramp and assuming initial acceleration is 0.3 m/s^2, so with the ramp it might be 190 seconds. Of note, this model fails to reproduce the lower acceleration rates cited by a study from last decade about DMUs on the Fairmount Line, which claims a 70-second penalty to 100 km/h; such a penalty is far too high, consistent with about 0.2 m/s^2 initial acceleration, which is far too weak based on local/express time differences on the schedule. The actual MBTA trains only run at 130 km/h, but are capable of 160, given long enough interstations – they just don’t do it because there’s little benefit, they accelerate so slowly.

Unsurprisingly, modern rail operations almost never buy locomotives for train services that are expected to stop frequently, and some, including the Japanese and British rail systems, no longer buy electric locomotives at all, using EMUs exclusively due to their superior performance. Clem Tillier made this point last year in the context of Caltrain: in February the Trump administration froze Caltrain’s federal electrification funding as a ploy to attack California HSR, and before it finally relented and released the money a few months later, some activists discussed Plan B, one of which was buying locomotives. Clem was adamant that no, based on his simulations electric locomotives would barely save any time due to their weak acceleration, and EMUs were obligatory. My program confirms his calculations: even starting with very weak and unreliable diesel locomotives, the savings from replacing diesel with electric locomotives are smaller than those from replacing electric locomotives with EMUs, and depending on assumptions on initial acceleration rates might be half as high as the benefits of transitioning from electric locomotives to EMUs (thus, a third as high as those of transitioning straight from diesels to EMUs).

Thus there is no excuse for any regional passenger railroad to procure locomotives of any kind. Service must run with multiple units, ideally electric ones, to maximize initial acceleration as well as the power-to-weight ratio. If the top speed is 160 km/h, then a good EMU has a stop penalty of about 45 seconds, a powerful electric locomotive about 135 seconds, and a diesel locomotive around 190 seconds. With short dwell times coming from level boarding and wide doors, EMUs completely change the equation for local service and infill stops, making more stops justifiable in places where the brutal stop penalty of a locomotive would make them problematic.

How Deinterlining Can Improve New York City Transit

New York is unique among the major subways of the world in the extent of interlining its network has. All routes share tracks with other routes for part of the way, except the 1, 6, 7, and L. The advantage of this system is that it permits more one-seat rides. But the disadvantages are numerous, starting with the fact that delays on one line can propagate to nearly the entire system, and the fragile timetables lead to slower trains and lower capacity. New NYCT chief Andy Byford just released a plan calling for investment in capacity, called Fast Forward, focusing on accessibility and improved signaling, but also mentioning reducing interlining as a possibility to increase throughput.

I covered the interlining issue more generally in my article about reverse branching, but now I want to explain exactly what it means, having learned more about this issue in London as well as about the specifics of how it applies to New York. In short, New York needs to reduce the extent of reverse branching as much as possible to increase train speed and capacity, and can expect serious gains in maximum throughput if it does so. It should ultimately have a subway map looking something like this:

Lessons from London

In London, there is extensive interlining on the Underground, but less so than in New York. The subsurface lines form a complex interconnected system, which also shares tracks with one branch of the Piccadilly line, but the Northern, Central, Victoria, Jubilee, and Waterloo and City lines form closed systems (and the Bakerloo line shares tracks with one Overground line). The Northern line reverse-branches: it has two central trunks, one through Bank and one through Charing Cross; one southern segment, with through-trains to both trunks; and two northern branches, each sending half its trains to each trunk. The other closed systems have just one trunk each, and as a result are easier to schedule and have higher capacity.

As the Underground moves to install the same high-capacity signaling on more and more lines, we can see what the outer limit of throughput is on each system. The Northern line’s new moving-block signaling permits 26 trains per hour on the Bank trunk and 22 on the Charing Cross trunk. When the Battersea extension opens, reverse branching on the south will end, pairing the older line to Morden with Bank and the new extension with Charing Cross, and capacity will rise to 32 tph per trunk. Planned improvements to transfer capacity at Camden Town, the northern branch point, will enable TfL to permanently pair each northern branch with one central trunk, raising capacity to 36 tph per trunk. Moreover, TfL expects moving block signaling to raise District line capacity from 24 tph to 32, keeping the current reverse branching. The Victoria line already runs 36 tph and the Jubilee line soon will too, while the Central line runs 35 tph. So 36 vs. 32 seems like the difference coming from the final elimination of reverse branching, while more extensive reverse branching reduces capacity further.

The reason complex branching reduces capacity is that, as delays propagate, the schedule needs to incorporate a greater margin of error to recover from unexpected incidents. It also slows down the trains, since the trains are frequently held at merge points. The general rule is that anything that increases precision increases capacity (such as automation and moving block signaling) and anything that reduces precision reduces capacity; reverse branching reduces timetable precision, because each train can be delayed by incidents on more than one line, making delays more common.

What deinterlining in New York entails

NYCT has its work cut out for it when it comes to deinterlining. There are eight different points in the system where reverse-branching occurs – that is, where lines that do not share track in Manhattan (or on the G trunk outside Manhattan) share tracks elsewhere.

  1. The 2 and 5 trains share tracks on the Nostrand Avenue Line.
  2. The 2 and 5 also share tracks in the Bronx.
  3. The A and C trains share tracks on the two-track narrows through Lower Manhattan and Downtown Brooklyn.
  4. The A and D share the express tracks on Central Park West while the B and C share the local tracks.
  5. The E and F share the express tracks on Queens Boulevard, while the M and R share the local tracks, the E and M share the tunnel from Queens to Manhattan, and the N, R, and W share a different tunnel from Queens to Manhattan.
  6. The B and Q share tracks in Brooklyn, as do the D and N.
  7. The F and G share tracks in South Brooklyn.
  8. The M shares the Williamsburg Bridge tracks with the J/Z but runs in Manhattan on the same tracks as the F.

NYCT should work to eliminate all of the above reverse branches. The easiest to start with is #6: the junction at DeKalb Avenue should be set to keep the B and D trains together and to keep the N and Q together rather than to mix them so that the B shifts to the Q tracks and the D to the N tracks. This requires no changes in physical infrastructure, and has especially high benefits as the junction delays trains by several minutes in each direction. Moreover, the loss of one-seat rides is minimal: the BDFM and NQRW run closely parallel in Manhattan and intersect with a transfer at Herald Square in addition to the inconveniently long BQ/DNR transfer at Atlantic Avenue.

Another relatively easy reverse branch to eliminate is #8, a recent introduction from the 2010 service cuts. Previously, today’s M route in Queens and Manhattan was covered by the V train, which turned on the Lower East Side, while the M ran the same route as the J/Z, merging onto the R and thence the N in Brooklyn at rush hour. Today’s route is thus an M-V merger, which railfans including myself hoped would help decongest the L by creating an alternative route from Williamsburg to Midtown. Unfortunately, such decongestion has not happened, perhaps because gentrification in Williamsburg clusters near the L and not near the J or M.

Harsh decisions

Fixing the reverse-branching at DeKalb Avenue and on the Williamsburg Bridge is painless. The other reverse branches require a combination of hard decisions and new infrastructure.

Fixing reverse branches #3 and #4 requires no capital investment, just political will. Reverse branch #4 is there because there’s demand for two routes’ worth of capacity in the tunnel from Brooklyn but there’s only one express line on Eighth Avenue, and that in turn is the result of reverse branch #3; thus these two issues should be tackled together.

NYCT should decide between having the A and C trains run express between 145th and 59th Streets and the B and D trains run local, or the other way around. This is not an easy decision: either Washington Heights or Grand Concourse would get consigned to local trains. North of 145th the total number of boardings is 102,000 at B/D stations compared with 79,000 on the A/C, but conversely Concourse riders can change to the express 4 trains whereas Washington Heights’ only alternative is the local 1. However the A and C run, express or local, the E should run the opposite in Manhattan – it can merge to either the local or express tracks – and the express trains should continue to Brooklyn. The map I made doesn’t distinguish local from express service, but my suspicion is that Washington Heights should get express trains, on account of its long commutes and lack of fast alternatives.

The same problem of harshness occurs in reverse-branch #5. In theory, it’s an easy fix: there are three track pairs in Queens (Astoria, Queens Boulevard local, Queens Boulevard express) feeding three tunnels to Manhattan (63rd, 60th, and 53rd Streets). In practice, the three Manhattan trunks have astonishingly poor transfers between them in Midtown. Nonetheless, if it does nothing else, NYCT should remove the R from Queens Boulevard and route all 60th Street Tunnel trains to Astoria; together with fixing DeKalb Avenue, this would separate the lettered lines into two closed systems, inherited from the BMT and IND.

However, undoing the connection between the BMT and the IND probably requires constructing a transfer station in Long Island City between Queensboro Plaza and Queens Plaza, which involves a few hundred meters of underground walkway. Even then, the connection cannot possibly be convenient. The saving grace is that Eighth Avenue, Sixth Avenue, and Broadway are close enough to one another that passengers can walk to most destinations from any line.

Subsequently, NYCT should make a decision about whether to send express Queens Boulevard trains to 63rd Street and Sixth Avenue and local trains to 53rd and Eighth, as depicted in the above map, or the other way around. The problem is that the merge point between 53rd and 63rd Street Tunnels is one station east of Queens Plaza, at a local station, and thus the true transfer point is Roosevelt Avenue, far to the east. Riders on the local stations west of Roosevelt would get no choice where to go (though they get little choice today – both the E and M serve 53rd Street, not 63rd). The argument to do things as I depict them is to give the local stations access to 53rd Street; the argument to switch the lines is that there is more demand on 53rd than 63rd and also more demand on the express tracks than the local tracks, so the busiest lines should be paired. However, this in turn runs into turnback capacity limitations on the E in Manhattan, at the World Trade Center bumper tracks.

Potentially, NYCT could try to convert 36th Street into an express station, so that passengers could connect cross-platform. But such a dig would be costly and disruptive to operations. There were plans to do this at 59th Street on the 1/2/3 a few decades ago, for the transfer to the A/B/C/D, but nothing came of them.

Where new infrastructure is needed

The remaining reverse branches get increasingly more difficult. Already #7 requires new turnouts. The South Brooklyn trunk line has four tracks, but there’s not enough demand (or space in Manhattan) to fill them, so only the local tracks are used. There are occasional railfan calls for express service using the F, but it’s better to instead use the express tracks to segregate the G from the F. The G could be turned at Bergen Street on the local tracks, while the F could use the express tracks and then transition to the locals on new turnouts to be constructed at Carroll Street.

Also in the category of requiring new turnouts is #1: Rogers Avenue Junction is set up in a way that briefly forces the 2, 3, and 5 trains to share a short segment of track, limiting capacity. This can be resolved with new turnouts just east of the junction, pairing Nostrand Avenue Line with the local tracks and the West Side and the portion of the Eastern Parkway Line east of Nostrand with the express tracks and the Lexington Avenue Line. Trains on Eastern Parkway could either all go local, or keep the current mixture of local trains to New Lots (currently the 3) and express trains to Utica (currently the 4), skipping a total of two stations. This fix also reduces passengers’ access to one-seat rides, but at least there is a reasonable cross-platform transfer at Franklin Avenue, unlike on Queens Boulevard or at 145th Street and St. Nicholas.

And then there is #2, by far the most difficult fix. Demand on the White Plains Road branch in the Bronx is too strong to be a mere branch: the combined number of boardings at all stations is 166,000 per weekday, and besides, the line branches to Dyre Avenue near its outer end and thus needs the frequency of either a trunk or two branches to ensure adequate service to each other branch. This is why it gets both the 2 and 5 trains. There is unfortunately no infrastructure supporting a switch eliminating this track sharing: the 4 and 5 trains could both use this line, but then the 2 has no way of connecting to Jerome Avenue Line without new tunnels.

On the map, I propose the most obtrusive method of fixing this problem: cutting the 3 trains to a shuttle, with a new pocket track at 135th Street, letting passengers transfer to the 2, ideally cross-platform. With all through-trains running on the 2, there is no need (or space) for the 5 on White Plains Road, and instead the 5 should help boost the frequency on Jerome Avenue. In addition, some work is required at Woodlawn, which currently has bumper tracks, fine for a single branch but not for a non-branching trunk line (the bumper tracks on the L limit throughput to 26 tph no matter how good the electronics are).

Additional infrastructure suggested by deinterlining

Deinterlining is a service increase. Lines that today only get half or two-thirds service would get full trunk frequency: Second Avenue Subway would get the equivalent of the Q and N trains, the Astoria Line would get the entirety of 60th Street Tunnel’s capacity, Eighth Avenue would get more express trains, and 63rd Street Line and the South Brooklyn Line would get more than just the half-service of the F. With six track pairs on the lettered lines through Midtown and six north and east (Central Park West*2, Second Avenue, Astoria, Queens Boulevard*2), there is no room for natural branching to give more service to busy areas than to less busy ones.

One solution to this situation is targeted development on weak lines. Even with half service, South Brooklyn has underfull F trains, and Southern Brooklyn’s B, D, N, and Q trains aren’t much busier, making this entire area an attractive target for upzoning.

However, it’s more interesting to look at lines with extensions that suggest themselves. Second Avenue Subway has the obvious extension north to Harlem in phase 2, and a potential subsequent extension under 125th Street to Broadway, which is less obvious but popular among most area railfans (including one of my inside sources at NYCT). The Astoria Line has a natural extension to LaGuardia, ideally elevated over Ditmars to capture local ridership on Astoria as well as airport traffic; while the steel el structures in New York are soundboxes, it is possible to build quieter els using concrete (as on the 7 el over Queens Boulevard in Sunnyside) or a mixture of concrete columns and a steel structure (as on the Metro 2 and 6 els here in Paris).

The Nostrand Avenue Line provides an especially interesting example of a subway extension suggested by deinterlining. The terminal, Flatbush Avenue, was intended to be temporary, and as a result has limited turnback capacity. To prevent it from constraining the entire 2 route, which became the city’s most crowded even before Second Avenue Subway began decongesting the 4 and 5, it would be prudent to extend the line to Sheepshead Bay as the city intended when it planned the line in the 1910s.

In contrast, a subway extension under Utica, a stronger bus corridor than Nostrand with a strong outer anchor at Kings Plaza, loses value under deinterlining. It could only get a branch and thus have lower capacity than Nostrand. It would also definitely force branching on the express trains, whereas without such an extension they could run as a single unbranched line between Woodlawn and New Lots Avenue via Jerome Avenue, Lexington Avenue, and Eastern Parkway. A Utica subway should wait until there is political will to fund an entirely new crossing into Manhattan, presumably via Williamsburg to help decongest the L.

A second extension I have occasionally mooted, a subway under Northern, loses value even more. Such a subway would be a fourth trunk line in Queens and have to come at the expense of capacity on Queens Boulevard. It is only supportable if there is an entirely new tunnel to Midtown, passing under the mess that is the tracks in Long Island City.

A deinterlined New York City Subway

Fast Forward proposes moving block signaling on the most crowded subway segments, but typically only on trunks, not branches, and in some cases not even entire trunks. But in the long term, New York should transition to moving blocks and automation on all lines – at the very least the highly automated system used on the L, but ideally fully driverless operation, in recognition that wages are going up with economic growth but driver productivity isn’t. Simultaneously, deinterlined operations should allow tph counts in the mid 30s or even more (Metro 13 here runs 38 tph and Metro 14 runs 42).

Instead of the potpourri of lines offered today, there would be fewer, more intense lines. Nomenclature would presumably change to deal with the elimination of some services, clarifying the nature of the subway as a nine-line system in which five lines have four tracks and four lines have two. Each of these fourteen track pairs should be able to support a train every 90-105 seconds at the peak; not all lines have the demand for such frequency, and some have capacity-limiting bumper tracks that aren’t worth fixing (e.g. the 1 at Van Cortlandt Park), but many lines have the infrastructure and the demand for such capacity, including the express lines entering Midtown from Uptown or Queens.

Off-peak, too, service would improve. There is ample capacity outside rush hour, but turning the system into one of lines arriving every 4-5 minutes with strategic transfers rather than every 8-10 minutes would encourage people to take the trains more often. The trains would simultaneously be faster and more reliable, since incidents on one line would wreck service on other trains on the same line but leave the rest of the network unaffected.

With service improvements both during and outside rush hour, New York could expect to see substantial increases in ridership. Raising peak frequency from the current 24 tph to 36 tph on the busiest lines (today’s 2/3, 4/5, A/D, and E/F) is equivalent to building an entirely new four-track subway trunk line, and can be expected to produce similar benefits for passengers. The passups that have become all too familiar for riders on the 4, L, and other busy trains would become a thing of the past unless ridership rose 50% to match the increase in capacity.