Jarrett has a good post about the new Auckland bus redesign, which he had been involved in when he worked for international consultancy MRCagney, before he opened his own. He mentions one peculiar aspect of Auckland – namely, that it is so divided by water boundaries that different areas of it have independent surface transit networks – that facilitates gradual implementation. In contrast, in a city with a more connected street network, every route affects every other route, so redesign has to be implemented together, without any intermediate phases. He brings up Brooklyn (together with Queens) as one example of such a connected network, and I feel like I need to explain why a phased approach is appropriate there.

But this is not just about Brooklyn. The question of whether to implement changes abruptly or gradually generalizes to every scale, up to and including the type of regime (democratic, militaristic, communist, etc.). The scope of this post concerns bus networks anywhere. The arguments I bring up in favor of a phased approach in Brooklyn should also give correct answers in other cities, regardless of whether they end up recommending gradualism.

Sharp edges

Jarrett brings up one factor influencing whether phased implementation is appropriate: sharp edges between different parts of the city. In New York, the East River has few road crossings and many rail crossings; only one local bus crosses it in Brooklyn, the half-hourly B39, and only four cross it in Queens.

But even edges that look less sharp than the East River or the Hudson can be so stark so as to permit separate planning on their two sides. The Harlem River is one example: many Bronx buses cross it, but their routes in Manhattan are constrained based on which avenue or street the bridge connects to, so there’s not much scope for creative recombination.

Brooklyn itself has few internal sharp edges. The closest thing to a sharp edge is the combination of Greenwood Cemetery and Prospect Park, separating on one side Park Slope and South Brooklyn and on the other side Flatbush and Southern Brooklyn. A few marginal neighborhoods are sharply divided from the rest of the borough, especially Red Hook. But for those neighborhoods, the question of where in the rest of the borough they should connect to depends on the shape of the rest of the system.

That said, it’s plausible to talk about how the new network would look in various neighborhoods, if there are choke points or generally agreed upon spines. Red Hook is an especially good example, since it has a strong connection to Manhattan via the Brooklyn-Battery Tunnel (hence, our proposed tunnel bus to Lower Manhattan). But as the arguments in comments here over Williamsburg show (and as my constant refrain about the north-south Bed-Stuy routes shows), it’s possible to discuss individual neighborhoods even if they’re more strongly connected, as long as it’s clear that it’s in the context of a greater network.

However, in one aspect, Jarrett and the MTA make a mistake: they treat the edge between Brooklyn and Queens as less sharp than it really is. In the north, the Newtown Creek choke point forces buses to all go up to Long Island City along a single bridge. In the center, a few route mergers passing through Bushwick and Ridgewood (especially the B54/Q55 on Myrtle) are reasonable, but fully integrated planning would not create very many connections. It’s possible to design the network for Brooklyn alone and then notate where Queens connections would happen, just as it’s possible to design a Manhattan network and point out that the M60 goes into Queens.

The subtle issue regarding Brooklyn and Queens concerns what happens in the south. At TransitCenter we were asked about connections to Howard Beach, but when I looked, I ran across a subtle geographic divide. The southeastern margin of Brooklyn and Queens is a series of small peninsulas with weak connections between them: Gerritsen Beach, Mill Basin, Bergen Beach, Canarsie, Starrett City, Spring Creek, Howard Beach, Old Howard Beach. When I crayoned a metro network for Lagos, which has the same problem in the west and northwest, I had to assume new metro bridges connecting various neighborhoods. On a surface transit network in a developed country, such bridges are unlikely to happen, forcing buses to use the main through-routes today, like Flatlands and Linden.

Is it good enough today?

The entire reform versus revolution discourse depends on how bad things are today. It’s unavoidable in discussions of socialism and Marxism. Socialists and even some social democrats hold that mid-20th century social reforms (like the New Deal) saved capitalism from itself, by making the working class’s situation less desperate. As a result, there is a contingent of leftists who call themselves accelerationists, who prefer to make things as bad as they can be (for example, by refusing to back the center-left against the far right) hoping that this would accelerate the revolution.

The “is it good enough today?” principle scales down to any level. When it comes to bus networks, it really asks, how much would the optimal route network differ from today’s situation?

The highly radial buses of San Jose today, Houston before Jarrett’s redesign, and Barcelona before Nova Xarxa all differ greatly from the redesigned networks. This encourages abrupt implementation, in two ways. First, the old routes are generally weak, increasing the pressure to get rid of them. And second, the old routes don’t feed the new grid trunk lines well, whereas the grid trunks feed one another. Nova Xarxa (which is a six-year process, retaining many old lines) has seen its phase 1 lines grow in ridership as each subsequent phase was implemented, making the early stages much less useful than the entire system.

In contrast, Brooklyn is firmly in the good enough basket. This does not mean its current network design is objectively good; it isn’t. But it does mean that most of its key trunk lines should survive redesign with at most light modifications. Among the 15 busiest Brooklyn routes today measured by ridership per km, only three see big changes: the B1 (straightened into a Southern Brooklyn grid), the B82 (cut to Kings Highway, its tails on both sides given to the B6), and the B41 (cut north of the B/Q subway connection at Prospect Park). A few more are merged into longer routes, like the B42 and the B60, but maintain their current route, just with through-service elsewhere. Key grid routes like Lafayette, Church, Nostrand, Avenue M, and Myrtle survive almost unchanged.

The Brooklyn redesign is not predominantly about starting from scratch, since the network today already has the characteristics of an imperfect grid. It’s about consolidating weak and weak-ish routes, straightening some buses that are too circuitous, and switching around buses to serve destinations that have grown stronger since the 1970s redesign. The East New York network in particular has a lot of meanders that should be fixed regardless of what happens anywhere else; the rest of the bus and subway network is good enough that people from East New York can then transfer to it even if increasing trunk frequency happens later.

Future changes

Bus redesigns are not immutable, to be done once in a few decades with long periods of stasis in between. Cities change, and the optimal bus network for 2025 may be different from that for 2019 in some situations. In a city where there’s relative stasis in development intensity, traffic, and any rail trunk, an abrupt change makes more sense. Realistically, such a change would come not when the first phase of a gradual implementation would have been done but when the middle or last phases would have. Thus, if the redesign is a long-lasting product it’s easier to wait for the first phase (which in an abrupt implementation is also the last phase) and not change much afterward.

This relates to California Transit Twitter’s biggest criticism of Jarrett’s San Jose redesign: that it does not incorporate the recent BART extension to Warm Springs. Jarrett unveiled his redesign for VTA in the spring of 2017, expecting BART to be extended from Warm Springs to the San Jose Flea Market at Berryessa by the end of the year, as BART had projected. Based on this expectation, he designed the network around an abrupt implementation, to go into effect shortly after trains would start running to Berryessa. Since then, BART has announced delays to the extension, talking about opening it only at the end of 2019. Trusting BART’s early promises of 2017 opening is an understandable error; Jarrett did not cause the BART timetable slip. But the outcome is that the VTA bus redesign is delayed.

The upshot is that in a city with a rapidly-growing rapid transit network, bus redesigns should be done on a continuous basis, tweaked every time a new subway line opens. The Bay Area is not generally such a city, but BART is expanding into San Jose, so in that part of the region, phased implementation with updates every few years is warranted. By the same principle, a city with rapid changes in where people live and work should expect recurrent changes to its surface transit network; this is less relevant to San Jose, since the growth nodes are the CBD (e.g. the upcoming Google building) and the Apple headquarters in Cupertino, but it’s relevant to cities in which residential areas are commercializing, such as San Francisco with SoMa.

New York, of course, has a static subway system, courtesy of extreme construction costs. It also has a relatively static workplace geography. However, in one respect, it is undergoing rapid change: it is gradually making its subway network accessible. When I say that the optimal networks for 2018, 2022, and 2026 are all different, I say this in reference to upcoming subway accessibility upgrades, as well as potential changes (i.e. de-interlining) that would increase subway frequency at the cost of one-seat rides. In Brooklyn, our plan to get rid of the B25 depends on upcoming accessibility upgrades for Broadway Junction, without which the bus should probably stay as an accessible alternative to the A and C trains. Likewise, our plan to retain the B63 comes from plans to only make the outermost R stations accessible but not the ones in Sunset Park or South Slope.

What about Nova Xarxa?

On two out of three metrics, Barcelona’s layout recommends an abrupt approach: it lacks internal sharp edges, and its preexisting network was too radial to be useful. On the third, it does not: it is rapidly expanding its metro network; however, the implementation of Nova Xarxa as far as I can tell has not been timed for the opening of L9/L10. So why is it phased there?

The fact that the early-phase lines of the network have seen further increases in ridership as the rest of the network has come online suggests that, on purely technical criteria, gradual implementation was not the right choice in Barcelona. However, in political reality, Nova Xarxa could not replace the entire radial network. Most bus routes in Barcelona today are still not Nova Xarxa. The system’s characteristic as an overlay that took over old lines that became superfluous forced it to be done in phases.

Conflicting excuses

In comments, people here have warned that a phased implementation can be an excuse to do nothing: put the few things everyone agrees on in the first phase, do that, and then postpone future phases indefinitely. This is a real risk. However, abrupt change has its own risks as well: it can be used as an excuse not to do low-cost or negative-cost things that can be implemented fast, such as merging the two Myrtle routes, redoing the East New York bus network in advance of the L train shutdown, and opening the Red Hook-Lower Manhattan route.

The upshot is that the question of gradualism seems independent from the question of obstructive bureaucrats and apparatchiks. There may well arise a local situation in which one answer to the main question is less vulnerable to political sabotage than the other, but it depends on idiosyncratic factors and is unlikely to be the case in general.

With the political criteria uncertain, the answer to whether network redesign should be done in one go or in stages should depend only on technical criteria. These differ from city to city and from region to region depending on local physical and urban geography. In New York, they suggest a phased implementation would work; elsewhere, they may not.

About two weeks ago, Eric Goldwyn and I unveiled our Brooklyn bus redesign. It consolidates the borough from 550 route-km to about 350, and cuts the number of stops along the surviving lines from 1580 to 706; the increase in speed coming from stop consolidation and other treatments (i.e. bus lanes and prepayment) and the route consolidation together permit doubling the frequency with the same resources available today, guaranteeing that each bus route have at worst 6-minute frequency between 6 am and 10 pm. The first version we released was 1.0, and the version I blogged was 1.1. In this post I’d like to introduce changes as well as explain why we made certain decisions that have been criticized in comments here and elsewhere.

Version 1.2

V1.2 differs from v1.1 in just two ways. First, it was pointed out to me that we made a mistake in the map: the route we proposed for the B6 to take across the structure of the Brighton Line of the subway, at Avenue H, was not in fact a street crossing. At Avenue H the structure goes from trenched to the north to elevated in the south, and as a result the street does not go through. We fixed this error by restoring the present-day route, and also slightly changing the route of the B11 to follow what must be a high-quality bus lane.

And second, months ago, in arguments with former MTA planner Allan Rosen (who comments on blogs by the name BrooklynBus and has his own proposed redesign), there came the question of the route of the B9. Allan was supportive of the idea of running the B9 on Veterans Avenue, taking over what is now a B41 branch, rather than going to Kings Plaza as it does today, legacy of an era when Kings Plaza was a more important shopping destination. I also asked about straightening the route, which currently goes on a combination of Avenues L and M; Avenue M provides a straighter route connecting to the important destinations (the eastern end of the route, and the main drag in Midwood at Avenue M). Allan explained that no, a reroute to Avenue M is not feasible, as east of the heart of Midwood it’s a narrower residential street, forcing the bus to use the wider Avenue L. The only reason the straighter Avenue M route appeared on v1.0 and v1.1 is that I forgot to change it; after we went public with the map, he reminded us.

There are some associated changes to the stop spacing to accommodate the new routes (or, rather, the retention of old routes that we were wrong to try to change before), but overall there is practically no impact on overall trip times. The B9 is a few hundred meters longer than in v1.0 and v1.1, but the cost in on the order of 20 service-hours per weekday, which by itself is a lot lower than my uncertainty in the underlying numbers (which is about 100 hours).

Service-hours vs. fleet requirement

When putting together the redesign, we aimed at one cost metric: service-hours. This is the correct metric for variable bus operating costs, as they are dominated by the driver’s wage (which is hourly, not per km) and to a lesser extent maintenance costs (which are partly distance-based and partly time-based, as the frequent acceleration cycles common to slow bus traffic stress the engine). The MTA costs buses by distance and not time, which is not a bad approximation when all buses are about equally fast, but generates wrong results when the subject of the discussion is speeding up the buses, as we propose.

But there’s one more metric we did not consider: fleet requirement. Our redesign actually saves money there, which should not be a surprise, as it has more off-peak service, which implies less service at the peak. Our 10,000-hour schedule requires a fleet of 1,007 buses, which compares with 1,129 today excluding the MTA Bus-operated B100 and B103 (which look like they require about 40 vehicles between them). Our proposed v1.2 schedule has 7.5% fewer service-hours than today – not because we propose a cut but because we expect future additions and politicized slowdowns to add hours – but 14% fewer buses. The smaller fleet is to be used more intensively and somewhat more efficiently thanks to the removal of short, infrequent routes.

Since the goal is to keep the redesign roughly cost-neutral, it’s likely that overall service-hour figures will rise: higher operating costs will be balanced by slightly lower capital costs, as the MTA will need to procure slightly fewer buses and not need to expand depots for them as much. In 2008-11, the MTA spent $500,000 per bus on procurement; in 2014, this was the cost per standard bus (which is the vast majority of the MTA Bus and NYCT fleet), while articulated buses were $750,000. This is a premium of about 50% over London bus costs.

Overall the fleet requirement looks like a small proportion of the cost. A $500,000 bus, say $600,000 at today’s higher prices, operates for 12 years, and requires a team of about five drivers, each earning around $140,000 a year with benefits. This is just about market wage – San Francisco and Boston, which pay about the same, have trouble finding and retaining drivers; high bus driver wages should be viewed as similar to high wages for oil rig workers, compensating for poor work conditions. Excluding the costs of depot enlargement, the overall exchange rate seems to be about one bus = 40-45 daily service-minutes. At best, our redesign can squeeze maybe 100 extra daily hours out of better fleet utilization.

The Williamsburg issue

As Eric and I have always emphasized in our communications, our redesign is necessarily win-lose – it’s just that there’s overall much more winning than losing. This is true across neighborhoods as well as within neighborhoods. The diciest case is that of Williamsburg, where we are proposing to consolidate a number of routes into 1.5 north-south trunk lines: one is a continuation of the B44 running up Bedford, and the other goes up Graham and thence either Manhattan Avenue (connecting to the G) or McGuinness (a straighter route on a wider street). This guts service to South Williamsburg, especially west of the BQE, where the only remaining stops are the Marcy Avenue J/M/Z subway stop and another stop on Broadway at Bedford.

It’s not an optimal situation. However, it’s a necessary cut, for a number of reasons:

1. The existing north-south lines in Williamsburg are for the most part quite weak. The average weekday ridership per route-km in Brooklyn is about 1,100. The Williamsburg routes are at 945 (B43), 613 (B62), 414 (B67), 358 (B48), 225 (B24), and 152 (B32). The strongest two run along the routes that we are retaining for north-south service, but the rest are so weak that consolidation is required; for the same reason, we are replacing the B48 and B69 (which is at 453) in Clinton Hill with a compromise route on Washington.
2. The Williamsburg routes are not just weak but also wasteful, measured in ridership per service-hour. Borough average is 55, and the overall strong routes cluster in the 60s, with high ridership balanced by high service. The top three routes are the B74 (98), B1 (82), and B36 (70), serving short-hop trips in Southern Brooklyn. Among the Williamsburg, only the B43 (49) holds up; the B62 (42), B67 (39), B32 (35), B24 (35), and B48 (32) are weak, the last three all falling in the borough’s bottom six.
3. The main north-south route in South Williamsburg west of the BQE is Bedford. Unfortunately, a continuous route up Bedford misses the all-important connection to the subway at Marcy. The B62 resolves this issue by detouring to serve Marcy, which slows down through-riders.
4. Williamsburg streets are narrow. Even Bedford is only 18 meters wide, comparable to a Manhattan street. Bus speeds are unlikely to be high in such a situation, and bus lanes are guaranteed to be contentious due to the removal of on-street parking and loading access.
5. The eastern margins of Williamsburg and Greenpoint are awkwardly just too far away for some people to walk to the subway (Meeker Avenue’s easternmost residential area, at Van Dam, is 960 meters from the nearest bus stop in our plan and 1,370 from the G train), but just close enough that most people will still walk rather than take a bus unless the bus is extremely frequent. Without the travel intensity found in Coney Island and at Kingsborough Community College, there is no hope for the travel volumes justifying very high frequency on the routes there, especially the B1. A frequency-ridership spiral is unavoidable, helping explain the poor performance of the B24 and B48.

The only possible compromise is to keep the B44’s current route on Lee, which in our plan we slightly straightened to reach the Marcy subway station faster. Keeping the northbound direction on Bedford, which serves South Williamsburg more centrally than Lee, is out of the question: south of Flushing Avenue, Nostrand is unambiguously more important, and the northern tail of the B44 is too weak to be allowed to drive the placement of the entire route. The cost of restoring the Lee/Taylor bus stop is small, around 12 daily service-hours, and this can be incorporated into the next version. However, it still only serves the area peripherally, and slows through-riders by around 1.5 minutes each way.

Brooklyn-Queens connections

People have told us that interborough connections are the new hot thing, to replace the borough-by-borough bus planning that currently exists. We are not depicting any on our map beyond what currently exists: one route to JFK, the aforementioned north-south Williamsburg route to Long Island City, and a bunch of east-west routes through Bed-Stuy terminating slightly east of the borough line. We are willing to be convinced otherwise, but so far it seems like adding more connections is difficult, for several unrelated reasons.

Hard boundaries

The Brooklyn-Queens border may not be as stark as the East River or the Harlem River, but it is nonetheless mostly hard. East of the Greenpoint/LIC border, the border follows a polluted industrial creek; the B24 crosses it twice and is very weak, and there’s no good route until the cluster of Grand, Metropolitan, and Flushing around Ridgewood. Metropolitan and Grand do go through, and we indicate them on our map. Flushing doesn’t; there’s no good route in Queens to connect it to except maybe a hybrid of the Q18 and Q47 to LaGuardia, and even that is uncertain.

Beyond Ridgewood, there is another hard boundary consisting of several cemeteries. The B13 goes through today, but is a weak route (473 riders/km, 38/hour) and should be cut to just a north-south subway feeder. To the immediate south of the cemeteries, several Queens buses go through to key connection points in Brooklyn. Only the southernmost zone, around Howard Beach, has weak connections.

Queens is not Brooklyn

Brooklyn is relatively uniformly dense, making a grid with uniformly high frequency tenable. Queens is not. East Elmhurst is several times denser than Queens Village. Central and Eastern Queens have a street hierarchy, in which the list of which streets get bus routes is preordained: Lefferts, Jamaica, Union Turnpike, Main, etc.; it’s not the relatively flat grid hierarchy that characterizes most of Brooklyn. There are multiple town centers to serve, with too sparse a rail network for buses to work purely as a rail feeder. The LIRR has so many stations that there are two distinct optimal maps, one assuming fare and schedule integration with commuter rail and one assuming today’s lack of integration.

What this means is that maybe a uniform 6-minute frequency is not right for Queens. Maybe the larger geographic size of Queens, with longer bus routes, permits slightly lower frequency, say every 8 minutes at the base (maybe even every 10). Combining routes is not always the right approach in this situation; there are going to be frequency-based seams.

Depot locations

There are some potential combinations of Brooklyn and Queens bus routes, most obviously on Avenue, which hosts the B54 and Q55. The B12 could even be combined with the Q56 and Q24 as branches. The Q58, an extremely strong circumferential, could be combined with the B38, the busiest Brooklyn route near its terminus. The problem is that the break points today tend to be very close to bus depots, and often they’re major destinations in their own right, such as the subway connection point at Broadway Junction or at Myrtle/Wyckhoff.

The B54/Q55 combination seems relatively easy, but the rest are more strained. At East New York Depot especially the loss of the easy pullout is unlikely to justify cutting the transfer to the few through-riders.

The City Line problem

At TransitCenter, we were asked specifically about the southernmost part of the Brooklyn/Queens border, covering City Line and Spring Creek on the Brooklyn side and Lindenwood and Howard Beach on the Queens side. The bus network there today is glaring in its gaps: there is no east-west connection south of the Q7 (the B15 looks like a connection on a map, but runs nonstop from Brooklyn to JFK). The street network itself is poorly connected, but even the existing connection at Linden doesn’t host local buses.

And yet, there’s not much room for serious improvements. The B15 could make a stop just over the border on the Queens side, but its route to the airport takes it through a highway with nowhere to stop; a BRT lane with some stops at north-south arteries like Woodhaven might be possible, but would not be a pleasant place to transfer at.

Worse, going on Linden and then southeast toward Howard Beach raises a difficult question: where does such a route go on the Brooklyn side? There are too many options: Gateway Center, New Lots on the 3, Euclid on the A/C. Reverse-branching is out of the question. Of those, probably the best is New Lots – Euclid serves a subway line that Howard Beach can get to more easily without the bus, and Gateway will always be too circuitous compared with driving on the Belt Parkway.

Tweaks vs. redesign

There are tweaks that improve Brooklyn-Queens connectivity, like merging the two Myrtle routes, giving the Brooklyn-JFK route dedicated lanes to facilitate a stop at Woodhaven, and changing the Metropolitan and Grand routes slightly to improve intra-Williamsburg east-west service (already depicted on our map). However, this is not the same as a redesign. In some parts of Brooklyn our proposal is a tweak, for example the east-west routes in Bed-Stuy, but in Southern Brooklyn and East New York we are rationalizing nearly everything into a grid, and in Bushwick and Canarsie we are proposing extensive changes.

Additional routes?

Based on the shape of our proposal, there are a few potential additions. One involves a 16th Avenue north-south route, possibly veering east to follow Cortelyou and Beverly. Another involves an Ocean Parkway bus to Church. A third involves extending the B17 up through Bed-Stuy to provide a second interpolating route between Nostrand and Malcolm X, which is available today (as the B15 and B43) but not on our map. A fourth involves going up Smith Street between Red Hook and Downtown Brooklyn until the subway stops in South Brooklyn are made wheelchair-accessible.

However, all of those add a hefty number of service-hours. Whether they’re tenable depends on how strictly NYC DOT implements our recommendations for dedicated lanes on every bus route. If no bus routes are added on top of the ones that exist today, v1.2 requires 11,050 revenue-hours and 1108 buses. This is still more or less achievable with current resources (it requires about a 1-1.5% increase in costs), but there is no room for any additional routes, or for restoring the B25. And that’s without taking into account compromises on bus stop spacing and bus route reliability.

In contrast, things are rosier if the reliability improvements we prescribe are implemented, and if every bus that needs a dedicated lane (i.e. nearly all of them) gets it even if motorists complain. There’s room in the budget for additional service. The above bus routes, excluding B25 restoration, total about 30 km including some possible tie-ins elsewhere in the system, creating nearly 800 new service-hours, bringing the system to the same place it is today, maybe just 1% short given additional efficiency and fleet savings.

And if higher ridership brings in more revenue for the same expense, there should be room for more service increases. The network in v1.2 could support maximum 5-minute peak headways on all routes for 210 more hours, which should not be hard to accommodate even with more routes. Going down to 4-minute peak headways requires another 370 hours, and going to 5-minute off-peak headways requires another 890.

To do all of this, another 1,300 hours or so are needed net of efficiency gains. To keep the subsidy per rider constant, this requires a 12% gain in overall linked trips, which isn’t outlandish (it would still leave Brooklyn with less bus ridership than at the 2002 peak). Making such expansion cost-neutral is harder: a linked trip nets about $2 in revenue, and this expansion would cost about $95 million annually, and then the required growth in ridership, 47.5 million, is 25% over Brooklyn’s unlinked bus ridership. It still looks achievable but very ambitious, relying on a positive frequency-ridership spiral.

Will this happen?

Some variant of a bus redesign will definitely happen. It’s in vogue in the US right now, and the MTA is taking this as an excuse to rationalize its bus service, which has accumulated a lot of oddities and historical artifacts that no longer make much sense.

The question is, will a good redesign happen? That I don’t know. I believe our redesign is good. The conversations I’ve had with bus planners at the MTA have been positive and suggest to me that, barring political interference, they are likely to come up with good redesigns as well, sharing the same overall characteristics as ours. We are working from the same set of best practices, for the most part.

But then the political question looms large. Physically separated bus lanes and signal priority require the city to give a damn about bus riders. Stop consolidation requires the MTA to stick to a long interstation even if minority of people who are hurt by it (e.g. by having high walk penalties and low wait penalties) complain. All of this requires political appointees at DOT and the MTA to consciously think how they can provide better public transit to the city they serve. Will they deliver?

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.

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.

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.