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.