# Where is Electrification Warranted?

At the beginning of the month, I published a piece in Voice of San Diego calling for medium-speed rail investment in the Los Angeles-San Diego corridor, centering electrification. This was discussed in a 500-comment thread on California HSR Blog, in which area rail activist Paul Dyson ripped into my plan, arguing (among other things) that electrification is costlier and less useful than I think. Instead of reopening the debate on that particular corridor, I want to discuss a more general set of guidelines to when rail lines should be electrified.

I haven’t said so in these exact words, but I think North American rail authorities and activists underrate electrification. As a result, I find myself persistently prescribing electrification and defending it when it’s already on the table, even as I attack other rail investments as wasteful. On social media and in blog comments I find myself having to constantly explain to people that no, a $20 billion New York regional rail plan should not use dual-mode locomotives but rather spend$250 million on New Jersey-side electrification.

A year and a half ago I wrote about why small, dense countries should fully electrify. The reasons laid out in that post are included in the guidelines below, but there are some additional circumstances justifying electrification.

Narrow stop spacing

Each train has a stop penalty – a total amount of time it loses to making each stop. The penalty is based on dwell time, line speed, and train acceleration and braking performance. If the line speed is 130 km/h, then the penalty excluding dwell time is about 35 seconds for a FLIRT and 80 seconds for a diesel GTW. This 45-second difference per stop is the same if there is a stop every 3 km or if there is a stop every 50 km.

Stop spacing is narrower on commuter lines than on intercity lines, so electrification usually starts from commuter rail. The first mainline electrification in the world was in Paris on the commuter lines serving Gare d’Orsay; subsequently the commuter lines in Paris, London, Tokyo, Berlin, New York, Philadelphia, and other major cities were wired. In many of these cases, commuter rail was electrified decades before intercity mainlines: for example, Japan started electrifying Tokyo’s innermost commuter lines in the 1900s and completed them in the 1920s and early 30s, but took until 1956 to electrify the first intercity line, the Tokaido Line.

However, in some dense regions, even the intercity lines have many stops. Cities in Israel, Belgium, the Netherlands, and Switzerland are just not very far apart, which blurs the distinction between regional and intercity lines somewhat. Switzerland is all-electrified, and my post from 2015 argued that the first three should be, too. In the US, there are specific regions where continuous sprawl has led to the same blurring: the Northeast Corridor, Southern California, Central and South Florida, New England. All are characterized by high population density. New England has closely spaced cities, whereas the LA-San Diego corridor and corridors within Florida have so much sprawl that there have to be several stations per metro area to collect people, reducing stop spacing.

Frequent sharp curves between long straight segments

Electric multiple units (EMUs) can make use of their high acceleration not at stations, but also at slow restrictions due to curves. They are also capable of higher cant deficiency than top-heavy diesel locomotives, since they have low center of gravity, but the difference for non-tilting trains is not so big. A uniformly curvy line does not offer EMUs much advantage, since all trains are slow – if anything, the lower the top speed, the less relevant acceleration is.

The big opportunity to accelerate is then when a mostly straight line is punctured by short, sharp curves. Slowing briefly from 130 km/h to 70 km/h and then speeding back up costs a FLIRT on the order of 15 seconds. A diesel train, whether powered by a locomotive or by diesel multiple units (DMUs), can’t hope to have the required power-to-weight ratio for such performance.

Mountains

EMUs’ better acceleration profile makes them better-suited for climbing hills and mountains. Modern EMUs, especially low- and medium-speed ones optimized for high acceleration, can effortlessly climb 4% grades, at which point DMUs strain and diesel locomotives require helper engines. When the terrain is so mountainous that tunnels are unavoidable, electric trains do not require ventilation in their tunnels. As a result, some long rail tunnels were electrified from the start. The combination of uphill climbs and tunnels is literally toxic with diesels.

Cheap, clean electricity

Electrification has lower operating costs and lower greenhouse gas emissions in areas where the electricity is powered by cheap hydro or geothermal power than in areas where it is powered by fossil fuels. Switzerland became the only country with 100% rail electrification because it had extensive hydro power in the middle of the 20th century and was worried about relying on coal shipments from Nazi Germany during the war.

This is especially useful in far northern countries, like Sweden and Canada, which have low population density and little evaporation, leading to extensive hydro potential per capita. Despite its low density, Sweden has electrified about two thirds of its rail network. In the US, this is the most relevant to the Pacific Northwest.

But in the future, the falling cost of solar power means that clean electricity is becoming more affordable, fast. This favors electrification in more places, starting from sunny regions like most of the US.

Small installed diesel base

A rich or middle-income country building railroads for the first time, or expanding a small system, needs to build new yards, train maintenance crews, and procure spare parts. It should consider electrifying from the start in order to leapfrog diesel technology, in the same manner many developing countries today leapfrog obsolete technologies like landline phones. In contrast, a larger installed base means electrification has to clear a higher bar to be successful, which is why Japan, France, and other major core networks do not fully electrify.

The US situation is dicey in that it does have a lot of diesel equipment. However, this equipment is substandard: reliability is low, with mean distance between failures (MDBF) of about 45,000 km on the LIRR compared with 680,000 on new EMUs (source, pp. 30-31); the trains are very heavy, due to past FRA regulations; and the equipment is almost universally diesel locomotives rather than DMUs, which makes the acceleration problem even worse than it is for GTWs. Total acceleration and deceleration penalty on American diesel locomotives is not 80 seconds but 2-2.5 minutes.

Because North America underrates electrification, some people who self-identify as forward-thinking propose DMUs. Those require new maintenance regimes and facilities, creating an entire installed base from scratch instead of moving forward to EMUs.

Globally, the installed diesel base for high-performance lines is vanishingly small. The technology exists to run diesel trains at more than 200 km/h, but it’s limited in scope and the market for it is thin.

Through-service to electric lines

Whenever a diesel line is planned to run through to an electric line, it should be a prime candidate for electrification. Dual-mode locomotives exist, but are heavy and expensive; dual-mode multiple units are lighter, but are still boutique products.

This is especially true for the two biggest investments a network can make in passenger rail: RER tunnels, and HSR. RER tunnels involve expensive urban tunneling. When a kilometer of urban subway costs $250 million and a kilometer of catenary costs$2 million, the economics of the latter become stronger. Not to mention that RERs are typically short-hop commuter rail, with frequent stops even on the branches. HSR is a different beast, since it’s intercity, but the equipment is entirely electric. Running through to a diesel branch means towing the train behind a diesel locomotive, which means the expensive HSR traction equipment is idle for long periods of time while towed; this is at best an interim solution while the connecting legacy line is wired, as in the line to Sables d’Olonne.

Nearly complete electrification

Areas where the rail network is almost completely electrified benefit from finishing the job, even if individually the diesel lines are marginal candidates for electrification. This is because in such areas, there is a very large installed electric base, and a smaller diesel base. In small countries the remaining diesel base is small, and there are efficiencies to be had from getting rid of it entirely. This is why the Netherlands and Belgium should finish electrification, and so should Denmark and Israel, which are electrifying their main lines.

This is somewhat less applicable to larger countries, such as Sweden, Poland, and especially Japan. However, India is aggressively electrifying its rail network and planning even more. Note that since networks electrify their highest-trafficked lines first, the traffic can be almost completely electrified even if the trackage is not. For example, Russia is about 50% electrified, but 86% of freight tonnage is carried on electric trains, and the share of ton-km is likely higher since the Trans-Siberian Railway is electrified.

This also applies to networks smaller than an entire country. Commuter rail systems that are mostly electrified, such as the LIRR, should complete electrification for the same reason that mostly electrified countries should. In New England and Southern California, regional rail electrification is desirable purely because of the acceleration potential, and this also makes full electrification desirable, on the principle that a large majority of those two regions’ networks have enough potential traffic to justifying being wired without considering network effects.

Recommendations

Every place – a country, an isolated state or province, a commuter rail system – that is at least 50-60% electrified should consider fully electrifying. The majority of the world that is below that threshold should still wire the most important lines, especially regional lines. Capital-centric countries like Britain and France often get this wrong and focus on the intercity lines serving the capital, but there are low-hanging fruit in the provincial cities. For example, the commuter rail networks in Marseille, Lyon, and Bordeaux are almost entirely electrified, but have a few diesel lines; those should be wired.

In North America, electrification is especially underrated. Entire commuter rail networks – the MBTA, Metra, Metrolink, MARC/VRE, GO Transit, AMT, tails on the New York systems – need to be wired. This is also true of short-range intercity lines, including LA-San Diego, Chicago-Milwaukee, Boston-Portland, Toronto-Niagara Falls, and future New York-Scranton. It is important that good transit activists in those regions push back and support rail electrification, explaining its extensive benefits in terms of reliability and performance and its low installation cost.

# What the RER A vs. C Contrast Means for New York Regional Rail

A few weeks ago, I published a piece in City Metric contrasting two ways of through-running regional rail, which I identify with the RER A and C in Paris. The RER C (or Thameslink) way is to minimally connect two stub-end terminals pointing in opposite directions. The RER A (or Crossrail) way is to build long city-center tunnels based on urban service demand but then connect to legacy commuter lines to go into the suburbs. Crossrail and the RER A are the two most expensive rail tunnels ever built outside New York, but the result is coherent east-west regional lines, whereas the RER C is considerably more awkward. In this post I’d like to explain what this means for New York.

As I said in the City Metric piece, the current plans for through-running in New York are strictly RER C-style. There’s an RPA project called Crossrail New York-New Jersey, but the only thing it shared with Crossrail is the name. The plan involves new Hudson tunnels, but service would still use the Northeast Corridor and LIRR as they are (with an obligatory JFK connection to get the politicians interested). I alluded in the piece to RER A-like improvements that can be done in New York, but here I want to go into more detail into what the region should do.

Regional rail to Lower Manhattan

Regional rail in New York should serve not just Midtown but also Lower Manhattan. Owing to Lower Manhattan’s intense development in the early 20th century already, no full-size train stations were built there in the era of great urban stations. It got ample subway infrastructure, including by the Hudson Tubes (now PATH), but nothing that could be turned into regional rail. Therefore, regional rail plans today, which try to avoid tunneling, ignore Lower Manhattan entirely.

The Institute for Rational Urban Mobility, longtime opponent of the original ARC project and supporter of through-running, even calls for new tunnels between Hoboken and Midtown, and not between Hoboken and Lower Manhattan. I went to an IRUM meeting in 2009 or 2010, when Chris Christie had just gotten elected and it was not clear what he’d do about ARC, and when people pitched the idea, I asked why not go Hoboken-Lower Manhattan. The reply was that it was beyond the scope of “must connect to Penn Station” and at any rate Lower Manhattan wasn’t important.

In reality, while Midtown is indeed a bigger business district than Lower Manhattan, the job density in Lower Manhattan is still very high: 320,000 people working south of Worth Street in 1.9 km^2, compared with 800,000 in 4 km^2 in Midtown. Nothing in Ile-de-France is this dense – La Defense has 180,000 jobs and is said to have “over 800 jobs/ha” (link, PDF-p. 20), and it’s important enough that the RER A was built specifically to serve it and SNCF is planning a TGV station there.

Regional trains to Lower Manhattan are compelled to be more RER A-style. More tunnels are needed than at Penn Station, and the most logical lines to connect create long urban trunks. In a post from two years ago, I consistently numbered the regional lines in New York 1-5 with a non-through-running line 6:

1. The legacy Northeast Corridor plus the Port Washington Branch, via the existing Hudson tunnels.
2. More lines in New Jersey (some Northeast Corridor, some Morris and Essex) going to the New Haven Line via new Hudson tunnels and Grand Central.
3. Some North Side LIRR lines (presumably just Hempstead and the Central Branch) to the Hudson Line via Penn Station and the Empire Connection; some LIRR trains should terminate at Penn Station, since the Hudson Line can’t support as much traffic.
4. The Harlem Line connecting to the Staten Island Railway via Lower Manhattan and a Staten Island-Manhattan tunnel, the most controversial piece of the plan judging by comments.
5. The New Jersey lines inherited from the Erie Railroad (including the Northern Branch) to the South Side LIRR (to Far Rockaway, Long Beach, and Babylon) via Lower Manhattan.
6. More North Side LIRR lines (probably the Ronkonkoma and Port Jefferson branches) to Grand Central via East Side Access.

The Lower Manhattan lines, numbered 4 and 5, have long trunks. Line 4 is a basic north-south regional line; it’s possible some trains should branch to the Hudson Line, but most would stay on the Harlem Line, and it’s equally possible that the Hudson Line trains to Grand Central should all use line 2. Either configuration creates very high all-day frequency between White Plains and St. George, and still high frequency to both Staten Island branches, with many intermediate stations, including urban stops. Line 5 goes northwest-southeast, and has to have, at a minimum, stops at Pavonia, Lower Manhattan, Downtown Brooklyn, and then all the LIRR Atlantic Branch stops to and beyond Jamaica.

More stops within new tunnels

Even new tunnels to Midtown can be built with the RER A concept in mind. This means more stations, for good connections to existing subway and bus lines. This is not superficially obvious from the maps of the RER A and C: if anything, the RER C has more closely-spaced stops within Paris proper, while the RER A happily expresses from La Defense to Etoile and beyond, and completely misses Metro 5 and 8. Crossrail similarly isn’t going to have a transfer to every Underground line – it’s going to miss the Victoria and Piccadilly lines, since connecting to them would have required it to make every Central line stop in the center of London, slowing it down too much.

However, the important feature of the RER A is the construction of new stations in the new tunnels – six of them, from La Defense to Nation. The RER C was built without any new stations, except (later) infill at Saint-Michel, for the transfer to the RER B. The RER C’s urban stations are all inherited legacy stations, even when underground (as some on the Petite Ceinture branch to Pontoise are), since the line was built relatively cheaply, without the RER A’s caverns. This is why in my City Metric piece, I refer to the RER B as a hybrid of the RER A and C approaches: it is a coherent north-south line, but every station except Saint-Michel is a legacy station (Chatelet-Les Halles is shared with the RER A, Gare du Nord is an existing station with new underground platforms).

With this in mind, there are several locations where new regional rail tunnels in New York could have new stations. I wrote two years ago about Bergenline Avenue, within the new Hudson tunnels. The avenue hosts very high bus and jitney frequency, and today Manhattan-bound commuters have to go through Port Authority, an obsolete structure with poor passenger experience.

Several more locations can be identified. Union Square for line 4 has been on the map since my first post on the subject. More stations on line 5 depend on the alignment; my assumption is that it should go via the approach tracks to the Erie’s Pavonia terminal, but if it goes via Hoboken then there should be a station in the Village close to West 4th Street, whereas if it goes via Exchange Place then there should be a station at Journal Square, which is PATH’s busiest New Jersey station.

On lines 4 and 5, there are a few additional locations where a station should be considered, but where there are strong arguments against, on the grounds of speed and construction cost: Brooklyn Heights, Chinatown (on line 5 via Erie, not 4), a second Lower Manhattan station on line 4 near South Ferry (especially if the main Lower Manhattan station is at City Hall rather than Fulton Street).

There are also good locations for more stations on the Metro-North Penn Station Access routes, both the New Haven Line (given to line 1) and the Hudson Line (given to line 3). Current plans for Penn Station Access for the New Haven Line have four stations in the Bronx, but no connection to Astoria, and a poor connection to the Bx12 buses on Fordham Road. A stop on Pelham Parkway would give a stronger connection to the Bx12 than the Coop City station, which the Bx12 reaches via a circuitous route passing through the 6 train’s northern terminus at Pelham Bay Parkway. Astoria has been studied and rejected on two grounds: one is construction difficulties, coming from the constrained location and the grade; the other is low projected ridership, since current plans involve premium fares, no fare integration with the subway and buses, and low off-peak frequency. The first problem may still be unsolvable, but the second problem is entirely the result of poor industry practices.

On the Empire Connection, there are plans for stops at West 62nd and West 125th Street. It is difficult to add more useful stations, since the line is buried under Riverside Park, far from Upper West Side and Washington Heights development. The 125th Street valley is one of few places where urban development reaches as far west as the Empire Connection. That said, Inwood is low-lying and it’s possible to add a station at Dyckman Street. In between, the only semi-plausible locations are 145th Street or 155th-158th (not both, they’re too close), and even those are marginal. All of these neighborhoods, from West Harlem north, have low incomes and long commutes, so if it’s possible to add stations, Metro-North should just do it, and of course make sure to have full fare integration with the subway and buses. The one extra complication is that there are intercity trains on this line and no room for four-tracking, which limits the number of infill stops that can support high frequency (at worst every 10 minutes).

Infill stops on existing lines

The existing regional lines in New York have very wide stop spacing within the city. It’s a general feature of North American commuter rail; I wrote about it 5 years ago in the context of Chicago, where Metra is even more focused on peak suburb-to-CBD commutes than the New York operators. In most North American cities I heartily endorse many infill stops on commuter rail. I have a fantasy map for Los Angeles in which the number of stops on inner commuter rail lines triples.

However, New York is more complicated, because of the express subway lines. In isolation, adding stops to the LIRR west of Jamaica and to Metro-North between Harlem and Grand Central would be a great idea. However, all three lines in question – Metro-North, the LIRR Main Line, and the Atlantic Branch – closely parallel subway lines with express tracks. It’s still possible to boost urban ridership by a little by having a commuter rail stop for each express subway stop, which would mean 86th and 59th Streets in Manhattan and Utica Avenue in Brooklyn, but the benefits are limited. For this reason, my proposed line 4 tunnel from Grand Central down to Lower Manhattan has never had intermediate stations beyond Union Square. For the same reason, while I still think the LIRR should build a Sunnyside Junction station, I do not endorse infill elsewhere on the Main Line.

That said, there are still some good candidates for infill. Between Broadway Junction and Jamaica, the LIRR parallels only a two-track subway line, the J/Z, which is slow, has poor connections to Midtown (it only goes into Lower Manhattan), and doesn’t directly connect Jamaica with Downtown Brooklyn. The strongest location for a stop is Woodhaven Boulevard, which has high bus ridership. Lefferts is also possible – it hosts the Q10 bus, one of the busiest in the borough and the single busiest in the MTA Bus system (most buses are in the New York City Transit bus division instead). It’s 4.7 km from Woodhaven to Broadway Junction, which makes a stop around Logan or Crescent feasible, but the J/Z is much closer to the LIRR west of Crescent Street than east of it, and the A/C are nearby as well.

Another LIRR line that’s not next to a four-track subway is the inner Port Washington Branch. There are no stops between the Mets and Woodside; there used to be several, but because the LIRR had high fares and low frequency, it could not compete once the subway opened, and those stations all closed. There already are plans to restore service to Elmhurst, the last of these stations to be closed, surviving until 1985. If fares and schedules are competitive, more stations are possible, at new rather than old locations: Queens Boulevard with a transfer to a Triboro RX passenger line, and two Corona stops, at Junction Boulevard and 108th Street. Since the Port Washington Branch is short, it’s fine to have more closely-spaced stops, since no outer suburbs would suffer from excessive commutes as a result.

Beyond Jamaica, it’s also possible to add LIRR stops to more neighborhoods. There, the goal is to reduce commute length, which requires both integrated fares (since Southeast Queens is lower middle-class) and more stops. However, the branches are long and the stop spacing is already not as wide as between Jamaica and Broadway Junction. The only really good infill location is Linden Boulevard on the Atlantic Branch; currently there’s only a stop on the Montauk Line, farther east.

In New Jersey, the situation is different. While the stop spacing east of Newark is absurdly long, this is an artifact of development patterns. The only location that doesn’t have a New Jersey Transit commuter rail stop that could even support one is Harrison, which has a PATH station. Additional stations are out of the question without plans for intense transit-oriented development replacing the warehouses that flank the line. A junction between the Northern Branch and line 2, called Tonnelle in my post on The Transport Politic from 2009, is still feasible; another stop, near the HBLR Tonnelle Avenue station, is feasible on the same grounds. But the entire inner Northern Branch passes through hostile land use, so non-junction stations are unlikely to get much ridership without TOD.

West or south of Newark, the land use improves, but the stop spacing is already quite close. Only two additional locations would work, one on the Northeast Corridor near South Street, and one on the Morris and Essex Lines at the Orange Street stop on the Newark Subway. South Newark is dense and used to have a train station, and some area activists have hoped that plans to extend PATH to the airport would come with a South Street stop for additional urban service. At Orange Street the land use isn’t great, since a highway passes directly overhead, but the Newark Subway connection makes a station useful.

Finally, in Manhattan, the East River Tunnels have four tracks, of which Amtrak only needs two. This suggests an infill East Side station for the LIRR. There are strong arguments against this – namely, cost, disruption to existing service, and the fact that East 33rd Street is not really a prime location (the only subway connection there is the 6). On the other hand, it is still far denser than anywhere in Brooklyn and Queens where infill stations are desirable, and the 6’s ridership at 33rd Street is higher than that of the entire Q10 or Bx12.

Conclusion

The RER A and Crossrail are not minimal tunnels connecting two rail terminals. They are true regional subways, and cost accordingly. Extracting maximum ridership from mainline rail in New York requires building more than just short connections like new Hudson tunnels or even a Penn Station-Grand Central connection.

While some cities are blessed with commuter rail infrastructure that allows for coherent through-service with little tunneling (like Boston) or no tunneling at all (like Toronto), New York has its work cut out for it if it wants to serve more of the city than just Jamaica and the eastern Bronx. The good news is that unlike Paris and London, it’s possible to use the existing approaches in Brooklyn and New Jersey. The bad news is that this still involves a total of 30 km of new tunnel, of which only about 7 are at Penn Station. Most of these new tunnels are in difficult locations – underwater, or under the Manhattan CBD – where even a city with reasonable construction costs like Paris could not build for $250 million per km. The RER A’s central segment, from Nation to Auber, was about$750 million/km, adjusted for inflation.

That said, the potential benefits are commensurate with the high expected costs. Entire swaths of the city that today have some of the longest commutes in the United States, such as Staten Island and Eastern Queens, would be put within a reasonable distance of Midtown. St. George would be 6 minutes from Lower Manhattan and perhaps 14 from Grand Central. Siting infill stations to intersect key bus routes like Bergenline, Woodhaven, and Fordham, and making sure fares were integrated, would offer relatively fast connections even in areas far from the rail lines.

The full potential of this system depends on how much TOD is forthcoming. Certainly it is easier to extract high ridership from rapid transit stations that look like Metrotown than from ones that look like typical suburban American commuter rail stops. Unfortunately, New York is one of the most NIMBY major cities in the first world, with low housing growth, and little interest in suburban TOD. Still, at some locations, far from existing residential development, TOD is quite likely. Within the city, there are new plans for TOD at Sunnyside Yards, just not for a train station there.

The biggest potential in the suburbs is at White Plains. Lying near the northern terminus for most line 4 trains, it would have very good transit access to the city and many rich suburbs in between. It’s too far away from Manhattan to be like La Defense (it’s 35 km from Grand Central, La Defense is 9 km from Chatelet-Les Halles), but it could be like Marne-la-Vallee, built in conjunction with the RER A.

Right now, the busiest commuter lines in New York – both halves of the Northeast Corridor and the LIRR Main Line – are practically intercity, with most ridership coming from far out. However, it’s the inner suburbs that have the most potential for additional ridership, and middle suburbs like White Plains, which is at such distance that it’s not really accurate to call it either inner or outer. The upper limit for a two-track linear route with long trains, high demand even in the off-peak hours, and high ridership out of both ends, is around a million riders per weekday; higher ridership than that is possible, but only at the levels of overcrowding typical of Tokyo or Shanghai. Such a figure is not out of the question for New York, where multiple subway lines are at capacity, especially for the more urban lines 4 and 5. Even with this more limited amount of development, very high ridership is quite likely if New York does commuter rail right.

# Boston NightBus: Planning Around Timed Connections

Over the last year, several people at the Boston advocacy group TransitMatters have been working on a plan to restore night bus service in the area, which is one of few big US cities with no transit between 1 and 5 am. See here for the original concept, from March of last year. The TransitMatters plan assumes limited financial resources, designing the plan around eight or nine routes, all running on an hourly takt schedule, meeting at one central location for a pulse, currently planned to be Copley Square. This seems fairly standard: in Vancouver, too, the daytime bus grid is replaced with a pulse-based system at night, with 30-minute headways on most lines.

So far, so good. The problem is that after additional work, including checking travel times on Google Maps but also some nighttime test drives, TransitMatters found that the original map would not work with an hourly takt. Hourly service with one vehicle per route requires one-way travel time to be 30 minutes minus turnaround time. Double-length routes, at one hour minus turnaround times, can also fit into the system, with two vehicles, but nothing in Boston is that long. Several of the routes turn out to be just a hair too long, and the plan evolved into one with 75-minute headways, too long and irregular for customers. In meetings with stakeholders, the relevant members of Transit Matters were told as much, that 75 minutes was too low a frequency.

I started doing work on this plan around then. Since I think a clockface schedule is important – especially if there’s money for more buses, because then the headways would be 30 minutes and not an awkward 37.5 minutes – I started to sketch ideas for how to reduce travel time. The revisions center the schedule, fitting route choices around the need for buses to complete the roundtrip in an hour minus two turnaround times; this is what I came up with. Time is saved by avoiding detours, even to relatively major destinations, and by not going as far as would be ideal if there were no need to maintain the takt. Many of the design principles are generally useful for designing takt-based schedules, including for commuter rail and for rail-bus connections.

Schedule padding should be based on expected punctuality

This is a point I’ve made before in talking about LIRR scheduling, where fragile timetabling contributes to high schedule padding. Overall, punctuality depends on the following possible attributes of transit services:

• Rail is more punctual than buses, and electric service is more punctual than breakdown-prone diesels.
• Grade-separated transit is more punctual than surface transit.
• Services are more punctual when there are fewer riders, especially buses, which only stop when riders request it.
• Surface transit is more punctual if it has dedicated lanes, or if (as on some Vancouver routes) it runs on a street with signal priority over intersecting traffic.
• Surface transit is more punctual off-peak, especially at night, when there’s no congestion.
• Transit service is more punctual the shorter the span is: a system that’s only supposed to run for 5 night hours has less room for schedule slips than one that’s supposed to run for 21 daytime hours. (This I credit to Ant6n.)

While NightBus involves surface buses running in shared traffic lanes using on-board fare collection, the expected traffic is so low that travel time is likely to be close to the travel time depicted on Google Maps without traffic, and significant variations are unlikely. This means it’s possible to get away with less schedule padding, even though the plan requires 8 routes to converge at one pulse point. The maximum one-way travel time should be taken to be around 26 minutes. 24 minutes is better, and ideally not all routes should be 26 (they’d wait for one another at the pulse point, so it matters how many routes are near the maximum and not just what the maximum is).

Routes should run as fast as necessary and as far as possible

Sometimes, the optimal routing is already the fastest – for example, maybe it really is optimal to link two nodes with a nonstop route. Usually, it is not: on rapid transit there are intermediate stops, on surface transit there are detours and slower segments when freeways are available. When the schedule is tight, there is a plethora of tradeoffs that must be made about travel time. A detour to a major destination, so important that in isolation it would improve service despite the slowdown for through-passengers, must be weighed against other detours. On fast commuter rail line, where there is a significant stop penalty, the equivalent is the intermediate stop; I discussed this 5 years ago in the context of the Lowell Line. The overall length of the route is also a variable: when possible, the outer end should be as far as possible while maintaining the takt.

In the context of NightBus, I used this rule for all routes:

• The N17, running parallel to the Red Line to Ashmont, runs straight on Dorchester Avenue, whereas in the original plan it detoured to serve Kane Square; there is no time to detour to Kane Square, so in the revised plan it skips it, and passengers going there would need to walk 500 meters.
• The N28, running on Washington Street and Blue Hill Avenue, terminates at the future Blue Hill Avenue commuter rail stop, and not the Mattapan trolley stop. At night the trolleys don’t run, so the connection isn’t important, and the few hundred meters cut from the route give the buses 2 crucial minutes with which to make the 26-minute one-way schedule.
• The N32/39 cannot go on Huntington (N39) and thence to Hyde Park (N32); it can either go on Huntington to less valuable Roslindale or on a route parallel to the Orange Line to Hyde Park. I believe the latter option is better, but this is up for debate.
• The N57 follows the Green Line B Branch to Boston College (taking 20 minutes), not the 57 into Watertown (which would take about 27); I think this is also the optimal decision independently of the need to make the pulse, but the pulse makes it far better. Note that this means the route would have to use unmarked bus stops, since in the daytime there is no bus paralleling the B Branch.
• The N1 terminates at Davis Square, without going farther into Cambridge or into Arlington (as N77).
• The N82 and N110 use Storrow Drive to skip Downtown Boston’s slow streets. The buses run on a pulse, so there is no need for more than one bus to serve the same route – they’d be scheduled to bunch, rather than overlying to provide higher frequency. The N111 to East Boston, Chelsea, and Revere serves Downtown Boston instead. This cuts service from Downtown to Malden and Medford, but Downtown is a 9-5 neighborhood, so there’s less need to connect it in every direction at night.
• The N111 terminates in central Revere and not in North Revere.

Not all transit services are meant for all social classes

At night, buses go at approximately the same speed as cars, provided cars can’t take freeways. If the cars are carrying multiple passengers, as ride-sharing counterproposals plan to, then they probably can’t take freeways. In theory, this means buses would be for everyone, since they were as fast as taxis. In practice, this is only true for people using one route – diagonal trips are still faster by taxi. But worst, the hourly frequency is brutal. People who can plan their night travel around the schedule would use the bus; so would people who can’t afford taxis. But people in the top two-thirds of the income distribution are unlikely to use NightBus, or any ride-sharing alternative (if ride-sharing can afford more vehicles for higher frequency, so can buses).

What this means is that the service needs to be designed around the needs of low-income riders. As a note of caution, in popular parlance there’s a tendency to conflate low-income riders with other groups, such as elderly riders, and pit their needs against good transit practices like wider stop spacing, off-board fare collection, frequent grids, and so on. Those practices are applicable to everyone, and if they appear to favor middle-class riders, it’s because when the buses are too slow, the middle class drives and the poor keep taking the bus, so faster buses have higher proportions of richer riders.

With that caveat in mind, what I mean when I talk about low-income riders is the distribution of origins and destinations. The various draft plans proposed by Transit Matters members all focused on serving lower-income neighborhoods. This is why it’s not such a problem that the N1 only goes as far as Davis Square: that is the favored quarter of the Boston area, and the areas cut off from service, such as Arlington, are rich enough that few would ride an hourly or even half-hourly bus. Additional decisions made based on this principle include,

• The N32/N39 route serves Hyde Park and not Roslindale. At equal incomes, I’d probably suggest serving Roslindale, which makes for a shorter route, and allows the route to use the extra time gained to get to Forest Hills via a longer route on Huntington and pass near Longwood. But incomes are not equal: Roxbury is much poorer than Longwood and Jamaica Plain, and Hyde Park is poorer than Roslindale.
• The N57 serves Boston College, which is middle-income but still poorer than Watertown.
• The N111 serves Chelsea, and probably would regardless of average incomes, but it could instead go parallel to the Blue Line, serving somewhat less poor and less dense areas.

The schedule’s importance is higher at lower frequency

None of the above principles really matters to a subway with 2-minute peak headways and 4-minute off-peak headways. Some of these subways don’t even run on a fixed schedule: it’s more important to maintain even headways than to have trains come when the nominal schedule says they will.  The point where clockface scheduling starts to become important seems contentious among transit planners. Swiss planners use clockface schedules down to (at highest) 7.5-minute headways, and say that 11-minute headways are a recipe for low ridership. In Vienna and Berlin, timed transfers are offered on the U-Bahn on 5-minute trains. At the opposite end, hourly and even half-hourly services must be designed around a schedule with quick connections, to prevent passengers from having to wait the full headway.

In borderline cases – the 7.5-15 minute range – transfers can be timed, and at the less frequent end some overtakes, but there is no real need to design the rest of the schedule around the headway. The main reason to operate with tight turnarounds is to reduce fleet and crew requirements. Any looseness in the schedule, beyond the minimum required for punctuality and crew comfort, should be thought of as a waste. However, the waste is capped by the overall headway. Concretely, if your favorite transit route takes 31 minutes one-way after factoring in turnaround time and schedule padding, then it needs 2 vehicles to provide hourly service, lying idle half the time; to provide 10-minute service, it needs 7 vehicles, lying idle only 11% of the time. So if frequency is high enough, the route should be designed without regard to turnaround times, because the effect is reduced.

But NightBus is hourly; 30-minute service is aspirational. This means that the schedule is more important than anything else. Even if a single neighborhood feels genuinely screwed over by the decisions made to keep the routes at or under 26 minutes – for example, if Revere and Mattapan prefer service going farther out even at the cost of 70- or 75-minute frequency – good transit activists must think in systemwide terms. Maintaining the hourly takt throughout the service area is more important than North Revere and the last few hundred meters in Mattapan.

Ultimately, buses and trains are not all that different

There are major differences between buses and trains in capital costs, operating costs, reliability, and so on, leading to familiar tradeoffs. Even at medium-size transit systems such as the MBTA, frequent bus networks are convoluted and at times fully gridded, while rapid transit networks are invariably radial at least to some extent,. Buses also can’t consistently use timed transfers at high frequency.

However, there are many similarities, especially with small bus networks, which are designed around a pulse rather than a grid:

• Public transit works with transfers and central dispatching. This makes it better at pulse-based network than any taxi (including ride-hailing apps) or ride-sharing service.
• Vehicles are large – not to the same extent of course, but relatively speaking (trains in large cities, buses in small ones or at night). There’s less room for the everywhere-to-everywhere one-seat rides that taxis provide at higher cost. If there’s budget for more service-hours, it’s spent on higher frequency or longer routes and not on adding more one-seat rides.
• Routes are centrally planned, with decisions made about one area affecting service in other areas. It is not possible for routes to evolve by private spontaneous action except in the thickest markets, far bigger than what small bus networks can support.
• The importance of the schedule and of timed transfers is proportional to the headway, and inversely proportional to frequency.

This is good news, because it means that the large body of good industry practices for rail planning, inherited from such countries as Switzerland and Japan, can be adapted for buses, and vice versa. I did not invent the principle of running trains as fast as necessary; it’s a Swiss planning principle, which led the country to invest in rail just enough to enable trains to go between Zurich, Basel, and Bern in one hour minus turnaround and transfer time. Nor did I expect, when I started getting involved in Transit Matters, that this would be so helpful in designing a better bus plan.

# When Buses are a Poor Guide to Corridor Demand

Vancouver is going to open the Evergreen Line at the end of the year, an 11-km SkyTrain branch to Coquitlam with a projected ridership of 70,000 per weekday; current ridership on the B-line bus paralleling the route, the 97, is 11,000, the 20th busiest citywide (see data here).

New York is going to open the first phase of Second Avenue Subway at the end of the year or early next year, a total of 4 km of new route with projected ridership of 200,000 per day (see pp. 2-3). The bus running down First and Second Avenues, the M15, has 46,000 weekday riders, trading places with two other routes for first citywide, but first phase only covers a quarter of the route, and the ridership projection in case the entire Second Avenue Subway is built is 560,000; nobody expects the other two top bus routes in New York, the B46 on Utica and the Bx12 on Fordham, to support such ridership if they’re ever replaced with subways.

In Boston, the Green Line Extension northwest in Somerville is projected to have 52,000 weekday riders by 2030. There is no single parallel bus, but a few buses serve the same area: the 101 with 4,800 weekday riders, the 89 with 4,200, the 88 with 4,100, and the 87 with 3,800 (all bus ridership data is from the Bluebook, PDF-pp. 48-54); the busiest of these ranks 28th regionwide.

In all three cases, I think the ridership estimates are reasonable. Vancouver especially has a good track record, with Canada Line ridership meeting projections; it’s harder to tell in New York and Boston, which have not opened a rail line recently (New York’s 7 extension was just one stop, and its predicted ridership explicitly depends on future development). Since in general I do think cities should plan their rail extensions around where the busiest buses are, I want to talk about the situations that create a disjunction.

I mentioned in two past posts that rapid transit that surface transit and rapid transit alignments obey different rules, with respect to street geometry. In the more recent post, I used it to argue that tramway corridors should follow buses. In the older post, I argued that subways can take minor detours or go under narrower, slower streets to reach major destinations, for example Century City in Los Angeles, which is near the Wilshire corridor but not on it. However, the latter case isn’t quite what’s happening in any of the three examples here: Second Avenue Subway follows Second Avenue (though phases 1-2 diverge west to serve Times Square, which is important), and the Green Line Extension and Evergreen Line’s routes are both straighter than any bus in the area.

The situation in Boston and Vancouver is not that there’s an arterial bus that misses key destinations. Rather, it’s that the street network is inhospitable to buses. Boston is infamous for its cowpaths: only a few streets, such as Massachusetts Avenue, are wide and long enough to be reasonable corridors for arterial buses, and as a result, the bus network only really works as a subway feeder, with very high rail to bus ridership ratio by US standards. The corridors that do support busier buses – in the Greater Cambridge sector, those are the 77, 71, and 73 buses – are defined by the presence of continuous arterials more than by high latent travel demand.

Vancouver, of course, is nothing like Boston. Its bus grid is Jarrett Walker‘s standard example of an efficient, frequent bus grid. But this is only true in Vancouver proper, and in parts of Burnaby. In the other suburbs, either there’s an arterial street grid but not enough density for a good bus grid (Richmond, Surrey), or there’s no grid at all (Coquitlam). There’s a bus map of the Port Moody-Coquitlam area, with the 97-B line in bright orange and the 5-roundtrips-per-day West Coast Express commuter rail line in purple; the Evergreen Line will run straight from Port Moody to Coquitlam along an alignment parallel to the railroad, whereas the 97-B has to take a detour. Overall, I would class Coquitlam and Somerville together, as places where the street network is so bad for buses that rail extensions can plausibly get a large multiple of the ridership of existing buses.

Second Avenue Subway phase 1 partly belongs in this category, due to the difficulty of going from Second Avenue to Times Square by road, but high projected ridership on phase 3 suggests something else is at play as well. While First and Second Avenues are wide, straight throughfares, functioning as a consistent one-way pair, two factors serve to suppress bus ridership. First, Manhattan traffic is exceedingly slow. The MTA is proud of its select bus service treatments, which boosted speed on the M15 between 125th and Houston Streets to an average of about 10 km/h; in contrast, the Bx12 averages 13-14 km/h west of Pelham Bay Parkway. And second, the Lexington Avenue Line is 360 meters, so riders can walk a few minutes and get on the 6 train, which averages 22 km/h. The Lexington trains are overcrowded, but they’re still preferable to slow buses.

Now, the closeness to the Lexington trains can be waved away for the purposes of the principle of this post: I am interested in where preexisting transit ridership is not a good guide to future transit ridership, and in this example, we see the demand via high ridership on the 4, 5, and 6 trains. However, the issue of slow Manhattan traffic can be folded generally into the issue of circuitous street networks in Boston and Coquitlam.

It makes intuitive sense that the higher the bus-to-rail trip time ratio is, the higher the rail line’s ridership is relative to that of the bus it replaces. But what I’m saying here goes further: the two mechanisms at hand – a street network that lacks continuous arterials in the desired direction, and extensive traffic congestion – reduce the effectiveness of any surface solution. Is it possible to build tramways in the Vancouver suburbs? Yes. But in Coquitlam (and in Richmond and Surrey, for different reasons), they would be circuitous just like the buses. This also limits the ability of bus upgrades to solve transportation problems in such areas.

Now, what of New York? In theory, a bus or tram with absolute signal priority could run down the Manhattan avenues or the major outer-borough throughfares at high speed. But in practice, there is no such thing as absolute signal priority on city streets. It’s possible to speed up surface vehicles via signal priority, but they’ll still have to stop if cross-traffic blocks the intersection. In Paris, the tramways are not fast, averaging around 17-18 km/h, even though they have dedicated lanes and run on wide boulevards in the outer parts of the city and in the inner suburbs; in contrast, Metro Line 14, passing through city center, averages almost 40 km/h.

The implication here is that when a city develops its subway network, it should pay attention not just to where its busiest surface lines are, but also to which areas have intense activity but have suppressed surface ridership because the roads are slow or circuitous. These are often old city centers, built up before there were cars and even before there was heavy horse wagon traffic. Other times, they are general areas where the road network is not geared toward the desired direction of travel.

In cities without subways at all, there is a danger of overrelying on surface traffic, because such cities often have old cores with narrow streets, with intense pressure for auto-oriented urban renewal as they get richer. This is less common in the developed world, but nearly every developed-world city of note either has a rapid transit network already or is completely auto-oriented and has no areas where the road network is weak. Israel supplies several exceptions, since its transportation network is underdeveloped for how rich it is; in past posts I have already voiced my criticism of the decision to center the Tel Aviv Subway around wide roads rather than the older, often denser parts of the city.

In cities with subways, it’s rarely a systemic problem. That is, there’s rarely a specific type of neighborhood that can support higher rapid transit ridership than preexisting transit ridership would indicate. It depends on local factors – for example, in Somerville, the railroads are oriented toward Downtown Boston, but the streets are not, nor are they oriented toward good transfer points to the subway. This means transit planners need to carefully look at the road network for gaps in the web of fast arterials, and consider whether those gaps justify transit investment, as the GLX and Evergreen Line do.

# Train Weight and Safety

A recent New Jersey Transit train accident, in which one person was killed and more than a hundred was injured, has gotten people thinking about US rail safety again. New Jersey has the second lowest fuel tax in the US, and to avoid raising it, Governor Chris Christie cut the New Jersey Transit budget (see PDF-pp. 4-5 here); perhaps in reaction to the accident, Christie is announcing a long-in-the-making deal that would raise the state’s fuel tax. But while the political system has been discussing funding levels, transit advocates have been talking about regulations. The National Transportation Safety Board is investigating whether positive train control could have prevented the accident, which was caused by overspeed. And on Twitter, people are asking whether Federal Railroad Administration regulations helped protect the train from greater damage, or instead made the problem worse. It’s the last question that I want to address in this post.

FRA regulations mandate that US passenger trains be able to withstand considerable force without deformation, much more so than regulations outside North America. This has made American (and Canadian) passenger trains heavier than their counterparts in the rest of the world. This was a major topic of discussion on this blog in 2011-2: see posts here and here for an explanation of FRA regulations, and tables of comparative train weights here and here. As I discussed back then, FRA regulations do not prevent crumpling of passenger-occupied space better than European (UIC) regulations do in a collision between two trains, except at a narrow range of relative speeds, about 20-25 mph (30-40 km/h); see PDF-pp. 60-63 of a study by Caltrain, as part of its successful application for waivers from the most constraining FRA regulations. To the extent people think FRA regulations have any safety benefits, it is purely a stereotype that regulations are good, and that heavier vehicles are safer in crashes.

All of this is old discussions. I bring this up to talk about the issue of systemwide safety. Jacob Anbinder, accepting the wrong premise that FRA regulations have real safety benefits, suggested on Twitter that rail activists should perhaps accept lower levels of rail safety in order to encourage mode shift from much more dangerous cars toward transit. This is emphatically not what I mean: as I said on Twitter, the same policies and practices that lead to good train safety also lead to other good outcomes, such as punctuality. They may seem like a tradeoff locally within each country or region, but globally the correlation goes the other way.

In 2011, I compiled comparative rail safety statistics for the US (1 dead per 3.4 billion passenger-km), India (1 per 6.6 billion), China (1 per 55 billion), Japan (1 per 51 billion), South Korea (1 per 6.7 billion), and the EU (1 per 13 billion), based on Wikipedia’s lists of train accidents. The number for India is an underestimate, based on general reports of Mumbai rail passenger deaths, and I thought the same was true of China. Certainly after the Wenzhou accident, the rail activists in the developed world that I had been talking to stereotyped China as dangerous, opaque, uninterested in passengers’ welfare. Since then, China has had a multi-year track record without such accidents, at least not on its high-speed rail network. Through the end of 2015, China had 4.3 billion high-speed rail passengers, and by 2015 its ridership grew to be larger than the rest of the world combined. I do not have statistics for high-speed passenger-km, but overall, the average rail trip in China, where there’s almost no commuter rail, is about 500 km long. If this is also true of its high-speed rail network, then it’s had 2.15 trillion high-speed passenger-km, and 1 fatality per 54 billion. This is worse than the Shinkansen and TGV average of zero fatalities, but much better than the German average, which is weighed down by Eschede. (While people stereotype China as shoddy, nobody so stereotypes Germany despite the maintenance problems that led to the Eschede accident.)

I bring up China’s positive record for two reasons. First, because it is an example of how reality does not conform to popular stereotypes. Both within China and in the developed world, people believe China makes defective products, cheap in every sense of the term, and compromises safety; the reality is that, while that is true of China’s general environmental policy, it is not true of its rail network. And second, China does not have buff strength requirements for trains at all; like Japan, it focuses on collision avoidance, rather than on survivability.

The importance of the approaches used in Japan and on China’s high-speed rail network is that it provides safety on a systemwide level. By this I do not mean that it encourages a mode shift away from cars, where fatality rates are measured in 1 per hundreds of millions of passenger-km and not per tens of billions. Rather, I mean that the entire rail network is easier to run safely when the trains are lighter.

It is difficult to find exact formulas for the dependence of maintenance costs on train weight. A discussion on Skyscraper City, sourced to Bombardier, claims track wear grows as the cube of axle load. One experiment on the subject, at low speeds and low-to-moderate axle loads, finds a linear relationship in both axle load and speed. A larger study finds a relationship with exponents of 3-5 in both dynamic axle load and speed. The upshot is that at equal maintenance cost, lighter trains can be run faster, or, at equal speed, lighter trains make it easier to maintain the tracks.

The other issue is reliability. As I explained on Twitter, the same policies that promote greater safety also make the system more reliable, with fewer equipment failures, derailments, and slowdowns. On the LIRR, the heavy diesel locomotives have a mean distance between failures of 20,000-30,000 km, and the medium-weight EMUs 450,000 (see PDF-pp. 21-22 here). The EMUs that run on the LIRR (and on Metro-North), while heavier than they should be because of FRA requirements, are nonetheless pretty good rolling stock. But in Tokyo, one rolling stock manufacturer claims a mean distance between failures of 1.5 million km. While within Japan, the media responds to fatal accidents by questioning whether the railroads prioritize the timetable over safety, the reality is that the overarching focus on reliability that leads to low maintenance costs and high punctuality also provides safety.

In the US, especially outside the EMUs on the LIRR and Metro-North, the situation is the exact opposite. The mean distance between failures for the LIRR’s diesel locomotives is not unusually low: on the MBTA, the average is about 5,000 km, and even on the newest locomotives it’s only about 20,000 (State of the Commuter Rail System, PDF-pp. 8-9). The MBTA commuter rail system interacts with freight trains that hit high platforms if the boxcars’ doors are left open, which can happen if vandals or train hoppers open the doors; as far as I can tell, the oversize freight on the MBTA that prevents easy installation of high platforms systemwide is not actually oversize, but instead veers from the usual loading gauge due to such sloppiness.

Of course, given a fixed state of the infrastructure and the rolling stock, spending more money leads to more safety. This is why Christie’s budget cuts are important to publicize. Within each system, there are real tradeoffs between cost control and safety; to Christie, keeping taxes low is more important than smooth rail operations, and insofar as it is possible to attribute political blame for such low-probability events as fatal train accidents, Christie’s policies may be a contributing factor. My contention here is different: when choosing a regulatory regime and an overarching set of operating practices, any choice that centers high performance and high reliability at the expense of tradition will necessarily be safer. The US rail community has a collective choice between keeping doing what it’s doing and getting the same result, and transitioning operating practices to be closer to the positive results obtained in Japan; on safety, there is no tradeoff.

# When Through-Running Is Inappropriate

I support through-running of regional trains: as far as possible, trains should not terminate in major city centers, but instead run through to urban neighborhoods and suburbs on the other side of the CBD. My first blog posts made this point about New York, and over the years I’ve written about this in the contexts of New York, Boston, Washington, Chicago, and Tel Aviv. However, in secondary cities, through-running is not always appropriate policy. If a city is near the edge and not at the center of its metro area, then quite often it’s preferable to run a separate service, which may overlap the primary city’s regional rail system. In some cases, through-running is actively harmful; unfortunately, this is currently done in San Jose and Providence.

Theory

Consider the following example city:

The metro area lies on an east-west rail line, and consists of a central city several suburbs; higher-density areas are denoted by darker shades, with the primary CBD in the darkest shade. The city proper also has five secondary CBDs, two of which are on the rail line. On the west, one suburb, really a secondary city, is larger than the rest, and has its own CBD, as job-dense as one of the primary city’s secondary CBDs. With rough symmetry of suburban demand west and east, there is no good reason why trains should not through the primary CBD, and good reasons why they should:

• People in the eastern suburbs may work in the secondary CBD just west of the primary one, and people in the western suburbs may work in the secondary CBD just east of the primary one.
• The primary CBD may not have room to park trains at rush hour without a costly railyard expansion.
• People within the central city may use the line as a rapid transit trunk, to get to either the primary CBD or the two secondary CBDs on the line, as well as to residential neighborhoods not depicted in the diagram.

This is relatively uncontroversial – urban transit is designed along the same guidelines. Also uncontroversial is the question of how far east the commuter line should run: the diagram shows a string of medium-size suburbs, so the line should run as far as the easternmost one, potentially with short-turn runs if the trains at the end are too empty.

The real controversy is how far west to run the service. On the one hand, the secondary city provides a natural outer anchor, with some reverse-peak ridership potential, so there’s an argument for terminating service there. I have criticized the Human Transit model of anchoring as a matter of urban planning, but as a matter of transit planning with fixed urban layout, it is sound; see explanations here and here. On the other hand, there are two smaller suburbs farther west, where people might want to commute to either the primary city or the secondary one, so perhaps service should run farther, with many trains short-turning at the secondary city to avoid running too many empty trains at the western end.

Which of the two options is better – terminating services at the secondary city or continuing onward – depends on the frequency the trunk rail line can support. The reason is that continuing onward requires a very large drop in capacity to avoid empty trains. In the depicted diagram, in relative units, 10% of the western suburbs’ built-up residential area is west of the secondary city; maybe another 10% is the western areas of the secondary city, which could host a station in addition to that at the city’s center. This means that nearly all trains should short-turn; only perhaps one in three or four should continue. If the demand is so intense that a quarter of the base frequency is enough, then trains should continue. But most likely, it isn’t. An individual commuter line with a train every 10 minutes off-peak would be stepped down to every half an hour at the western end, which is borderline; a train every 10 minutes off-peak almost never happens outside Paris, Tokyo, and other enormous systems, except when multiple branches interline to a single trunk.

The alternative is to terminate commuter trains at the secondary city, but then run supplemental service, centered at the secondary city. This supplemental service is not supposed to serve demand into the primary city, handling supercommuters from the western end via a timed transfer (with possible peak through-service), so it can run shorter trains at higher frequency. Sometimes, the secondary city’s CBD must be judged too auto-oriented to be served with commuter rail, and then the correct service pattern is no trains at all west of the secondary city.

Examples

In both Providence and San Jose, a situation akin to the above diagram occurs, except without any through-service beyond the primary CBD (respectively, Boston and San Francisco). Of course, San Jose has more residents than San Francisco, 1.03 million compared with 870,000, but it has only 360,000 jobs to San Francisco’s 610,000. Moreover, San Jose’s employment is more dispersed; according to OnTheMap, its CBD’s job density is about comparable to that of Providence’s CBD. Evidently, Caltrain ridership is 13,600 per weekday at San Francisco and 4,200 at San Jose Diridon (PDF-p. 6 here), with both stations located somewhat away from their respective cities’ CBDs. A proper comparison of Providence to Boston is harder to make, since South Station has multiple line and not just the Providence Line, but Providence’s secondary role within New England is well-understood.

In both cities, service runs beyond the secondary city, at reduced frequency. Between San Francisco and San Jose, Caltrain runs 5 trains per hour at the peak, and a train every hour off-peak; but Caltrain also runs three trains per day in each direction south to Gilroy, 47 km to the south (San Francisco-San Jose is 77 km). Between Boston and Providence, a distance of 70 km, the MBTA runs 3-4 trains per hour at the peak and a train every 1.5-2 hours off-peak, but one train per hour at the peak and one train every four hours off-peak continues another 31 km south to Wickford Junction.

Both tails, to Gilroy and to Wickford Junction, are significant drags on the ability of their respective cores to modernize. Ridership is very low: Tamien, just south of San Jose Diridon, has 1,100 weekday riders, but the sum total of all the stations to its south is 559; the two stations south of Providence have between them 454 weekday riders, compared with about 2,300 at Providence and 20,000 on the Providence Line overall (see PDF-pp. 74 and 77 of the 2014 MBTA Bluebook). In both cases, low ridership is a cause of poor service rather than a consequence: Clem Tillier tallied the population and job densities near each Caltrain station and found that, except in the southern neighborhoods of San Jose, there is no real ridership potential on the Gilroy extension; a similar analysis of the Providence Line’s tail has not been carried out, but one of its two stations is in a low-density suburb without many Boston-bound commuters, while Wickford Junction is surrounded by undeveloped land. Caltrain is currently planning to electrify south to Tamien, but there is no justification for continuing electrification further, which means that maintaining Gilroy service would require mixing diesel locomotive-hauled trains with lightweight EMUs; moreover, south of Tamien, the tracks are owned by Union Pacific rather than by Caltrain, and UP has little interest in allowing modern passenger trains on its tracks. In Rhode Island, an additional complication is that the line from Providence down to Wickford Junction is prime high-speed rail territory, and commuter rail ridership is frankly too low to justify complex scheduling with multiple overtakes, unlike the situation farther north in Massachusetts.

In the Bay Area, there is little that can be done, due to the low potential ridership south of Tamien, San Jose’s suburban layout and the distance of Diridon from the CBD, and UP ownership of the tracks. Perhaps a few diesel trains could run to San Jose Diridon with timed transfers to the electrified line from Tamien to San Francisco, but quite likely service could just be canceled. In Rhode Island, Wickford Junction should probably be closed due to low ridership, but Peter Brassard proposed an alternative, a Providence-focused line running short trains at medium frequency (perhaps once every 15 minutes), with very short interstations in order to serve Providence neighborhoods and not just the CBD. Such a line, running at the same average speed as a freight train due to the frequent stops, would interfere heavily with intercity trains, which means that four-tracking the line is a necessary precondition, as discussed here, but this may be worth it given potential local ridership. The most constrained part of the right-of-way is alongside the Route 10 expressway, which requires considerable repairs and is currently being overhauled at high cost.

# Mixing Circumferential and Radial Transit in the Other Direction

Two years ago, I wrote a post criticizing subway lines that mix radial and circumferential elements. These lines, for examples Shanghai Metro Lines 3 and 6 and New York’s G train before 2001, contain long radial segments, going from an outlying neighborhood toward city center, but then switch to circumferential mode, avoiding city center and instead serving secondary nodes. Such lines do not get high ridership, because they fail at either radial or circumferential transit. Recently, I was challenged in comments about my support for a mixed line that goes in the other direction: circumferential on the outside, radial on the inside. I would like to talk more about such lines.

Consider the following diagram of a subway system:

The city is shown in light gray, with its center in dark gray. There are five subway lines: the red and blue lines are straightforward radials, the green line is a straightforward circumferential, the yellow line mixes radial and circumferential as criticized in my previous post, the pink line mixes radial and circumferential in the other manner, which I will describe in this post.

The reason the yellow line is going to underperform in this system is that it fails as a radial: it does not go to city center, which has the largest concentration of destinations for transit users. People who have equal access to the red and yellow lines, north and south of city center, are much likelier to choose the red line, which takes them where they want to go. The green line fails as a radial too, but has the positive features of a circumferential: it only serves relatively nearby neighborhoods, which are likely to be denser and produce more riders per unit length; it connects to every line in the system; it allows people to connect between two radial lines without going through the congested city center; it has no dominant direction at the peak, so trains are unlikely to be full in the peak direction and empty in the reverse-peak direction. The yellow line has none of these features, unless one wants to connect between the western legs of the blue and pink lines.

The pink line still works as a radial. Its northeastern leg is a straightforward radial, but even its southwestern leg  works as a radial for people who live west of the yellow line and wish to commute to city center. In this way, it is not truly a mixture of radial and circumferential elements the way the yellow line is, but is simply a radial with a circumferential element tacked on at the end.

Whether the pink line’s circumferential tail works must be evaluated against two alternatives: build nothing, and build a radial leg. This is because in an incrementally-built transit system, the radial parts of the line are typically built first, and the circumferential tail is tacked on as a later extension. In the no-build case, the pink line’s southwestern leg would simply be shorter than the other radial legs in this system. In the radial case, the pink line’s southwestern leg would look symmetric with the northeastern leg. This depends on the following factors:

1. The strength of the radial alternative. If the radial alternative is strong, then this discourages building the circumferential extension, and vice versa. The radial alternative can be weak in several ways: the southwestern quadrant of the city depicted above may be already replete with radial transit and not need more; the population density in the neighborhoods that would be served by the radial option may be low; and the city’s layout may not be the above-depicted perfect circle, so that there is nowhere for the line to turn except sideways.
2. The strength of the corridor that would be served by the circumferential leg. The leg can never be a complete circle, so it must be evaluated as a rapid transit line on an individual street or corridor. This far out of city center, transit demand on each route is unlikely to be high, but there may well be exceptions, for example if there is a linear secondary CBD. For example, while Seoul Metro Line 2 is fully circumferential, one of its segments follows a Tehran Avenue, a major street in Gangnam with high transit demand, which would justify a subway even if it weren’t part of a large circle.
3. The strength of the circumferential transit demand from the end of the potential circumferential extension to the radial segment. In the depicted city, there may be strong demand for east-west transit south of the CBD, and the circumferential pink line is then better at serving it than connecting between the red and yellow lines via the blue line.

The original impetus for this post, as noted at the beginning, is a comment challenging me for my support of an extension of Second Avenue Subway Phase 2, going under 125th Street from the planned terminus at Lexington Avenue to Broadway, with stations at the intersection with each preexisting subway line. I contend that in this case, all three factors above point to a very strong circumferential extension. In order:

1. The radial alternative is to extend Second Avenue Subway to the north, to the Bronx, presumably under Third Avenue, but according to some railfans also under University Avenue. This is problematic, for three reasons. First, the Bronx already has many north-south lines feeding into Manhattan trunk lines, with mediocre ridership. The Manhattan trunk lines are overloaded, but mostly with traffic coming from the Upper East and West Sides, Harlem, and Washington Heights. Second, Third Avenue is close to the Harlem Line, which could be used for local transit if fares and schedules are integrated with the subways and buses. And third, the plan for Second Avenue Subway is for the line to turn west at 125th toward Lexington, since 125th and Second is not as compelling a destination, and this makes it easier to extend the line to the west than to the north.
2. 125th Street is a very busy street, and acts as the main street of Harlem. Transit demand is high: four bus routes use the street, with a total of 32,630 boardings per weekday on 125th Street, exclusive of other segments of those routes. This count misses people who board elsewhere and get off on 125th, but conversely assigns people who board on 125th and get off elsewhere to this street and not the other segment. But with this caveat in mind, this points to about 11,000 weekday riders per route-km, ahead of New York’s busiest bus per unit length (the M86, with about 7,000), and not far behind the subway average (15,000). This is despite the fact that, in my experience going between Columbia and the Metro-North station at Park Avenue, those buses are not faster than walking.
3. East-west transit in Uptown Manhattan consists of Pokey-winning crosstown buses; the 125th Street buses are as slow on 125th. An underrated feature of Second Avenue Subway Phase 1 is that it will soon enable a two-seat subway ride from the Upper East Side to the Upper West Side, West Harlem, and Washington Heights. However, this option will require connecting at Times Square, and is useful mainly for people in the southern areas of the Upper East Side connecting to the 1/2/3 rather than to the A/B/C/D. A two-seat ride based on going up Second Avenue to 125th Street and thence connecting to the 2/3, A/B/C/D, or 1 would enable more connections, many without any backtracking. This could have a potential cascading effect on all Uptown east-west buses, and not just those using 125th Street.

Of course, a Second Avenue Subway extension on 125th Street cannot be exactly like the pink line in the diagram above, because a key feature of it is that the circumferential part is not in fact near the outer end of the city. It’s barely 5 km north of the northern edge of Midtown, not even halfway from Midtown to the northern ends of most preexisting north-south subway lines. This is how it can have such high residential and commercial density and strong transit demand. Much farther north, Fordham Road is a very strong bus corridor, with about 4,500 weekday riders per route-km on the Bx12, but this is at much higher speed than in Manhattan, about 13 km/h rather than 5 km/h. An extension of the A east toward the Bronx under Fordham would underperform, because Fordham just doesn’t have that much demand; but 125th does.

The result of this discrepancy is that in a small city, one whose subway system is only about as large as in the diagram, it’s unlikely that such circumferential extensions would work. A radial line built all the way out is going to have as its terminus either a relatively low-density area or an anchor point, such as a commercial center or big housing project, neither of which lends itself to a strong continuous circumferential corridor. A radial line built part of the way to the edge of the city could potentially find a Tehran Avenue or a 125th Street, but if the system is small, with many key outlying neighborhoods still unserved, then it is usually best to keep extending lines outward.

The factors that conspire to make a 125th Street subway extension work are in place precisely because New York already has a large, mature subway network, in which Second Avenue Subway is a relief line. Certainly the projected demand on Second Avenue is very high, but the East Side is already served by a north-south subway 500-600 meters to the west of this line; it’s being built because this subway is overcrowded, not because the East Side has no access. This means that there’s more leeway with choosing what to do with the line once it reaches Harlem – after all, the Bronx subways are not overcrowded, and do not need relief.

Whereas mixed lines like the above-depicted yellow line are always bad transit, mixed lines like the pink line, in which the circumferential part is farther out than the radial part, are potentially an option for large cities that already have many rapid transit lines. They are especially useful for providing connections between closely parallel radial lines when other crosstown transit options are slow, and should be considered as extensions for relief lines, provided the radial lines farther out do not need relief as well.

# De Blasio Versus Good Transit

In New York, the de Blasio administration has been spending considerable political capital pushing for a \$2.5 billion light rail line connecting Astoria and the Brooklyn waterfront south to Sunset Park. There has been a lot of criticism from good transit advocates about implementation – namely, it’s unclear there will be free transfers to the subway and buses, in order to avoid having to share turf with the state-owned MTA – but also of the basic concept, which is not the biggest transit priority in the region, or for matter the twentieth. In comments and on social media, I’ve seen a few wrong arguments made in support of waterfront light rail and similar bad investments over and over, and I’d like to go in some detail into where cities should and should not build such lines.

The principles below are based on various oppositions: first world versus third world, fast versus slow growth, subway versus no subway. I think a good meta-principle is that if the presence of a certain factor is an argument in favor of a specific solution, then its absence should be an argument against that solution. For instance, if high wages are an argument in favor of rail and against bus rapid transit, then low wages should be an argument in favor of bus rapid transit; this principle makes me wonder what Addis Ababa was thinking when it built light rail instead of BRT, while at the same time thinking very little of American cities that make the decision that Addis Ababa should have made. The upshot of the meta-principle is that many of the guidelines that work in New York could work in very different cities, in reverse.

1. New York is a mature first-world city with low population growth; it should build transit exclusively or almost exclusively based on current population and transportation patterns, and not attempt to engage in development-oriented transit. The upzoning the city engages in is too small compared to current population, and cannot justify anything of the magnitude of Vancouver’s Expo Line, which was built simultaneously with Metrotown and the New Westminster offices around the train stations. And even Vancouver cannot reasonably expect the growth rates of various third-world cities with annual population growth rates in the vicinity of 5% and even higher per capita income growth rates.

2. Rail bias is approximately the same on all routes. Routes with many turns and narrow roads have unusually slow buses, but they’ll also have unusually slow surface rail. Rapid transit does have the ability to avoid the extra traffic jams coming from such alignments, and this is especially important in cities where the main street is not the same as the nearby wide boulevard, but this is not what’s under discussion in New York. Yes, de Blasio’s proposed light rail line would get more riders than the buses on segments of the route in question are getting now; the same would be true of any number of light rail routes paralleling the busiest buses in the city.

3. In a city with a subway, the best light rail routes are the ones that don’t make sense as subway extensions. Of the three busiest buses in New York, two make sense as subway lines, so there’s no point building light rail and only later a subway: the M15, on First and Second Avenues, and the B46, on Utica. In contrast, the third route, the Bx12 on Fordham, is crosstown, and cannot reasonably be an extension of any subway line, so it would be a strong light rail corridor. The same can be said of Main Street in Queens, between Flushing and Jamaica; and 14th and 86th Streets in Manhattan, where the M14 and M86 are the busiest surface routes in the US in terms of riders per kilometer, well ahead of the Boston Green Line (they both have about 8,000, and the Green Line 6,000). Of note, 14th Street already hosts the L, but a branch going on Avenue D is far from the subway, and the street is so well-trafficked that despite slower-than-walking bus speeds, that arguably light rail makes sense there even with the subway.

4. As soon as a project is judged as not a top priority, it’s best to think of how useful it is once the top priorities are built. In the case of New York, let us zoom in on Brooklyn’s top two circumferential buses, the B4 B6 and B35. Triboro RX is a higher priority than turning these routes into light rail, and once it’s in place, how much demand is there really going to be for them? It would be faster to take the subway and connect to Triboro, except at very short distances, where speeding up surface traffic is less useful.

In New York, excluding the somewhat special cases of 14th and 86th Streets, I’d say there are three light rail networks that make sense: one in the Bronx, one in Brooklyn, and one in Queens. The Bronx network involves taking the borough’s most frequent buses and turning them into light rail routes: the Bx12 on Fordham as noted above, but also the Bx1/2 on Grand Concourse (like 14th Street, hosting both a subway and a very busy bus route), the Bx19 on Southern and 145th, the Bx15 on Third, and a route on Tremont combining the Bx36 and the Bx40/42. These routes roughly form a grid, each has at least 30,000 weekday riders, and none is SBS except the Bx12. In this case, light rail should really be thought of as the next step after publishing a frequent grid map based on these routes and equipping the entire city bus fleet with off-board fare collection.

In Queens, there’s less room for a grid – the borough has street grids, but it really is based on several old centers, with major roads connecting them. The strongest routes are the ones that cannot reasonably be subway extensions, because they’re too circumferential; in turn, the strongest subway extension, i.e. Northern, is not a major bus route, because it’s close enough to the Queens Boulevard subway that people instead take the subway, which is overcrowded. Of the strong surface transit routes, the corridor with the highest ridership takes in several bus routes between Flushing and Jamaica; Main Street is the most important route, but potentially there’s room both there and on the second route, Kissena-Parsons. Other potential light rail routes radiate from Flushing and Jamaica, in directions not well-served by the subway and the LIRR, or even west on Queens Boulevard to help serve the gap in subway coverage between the 7 and the Queens Boulevard Line and relieve the subway lines.

Brooklyn is the most interesting. The main missing pieces in subway coverage in Brooklyn are good subway extensions: Triboro, Utica, Nostrand. With those in place, the only real gaps are Flatbush, and some route serving Red Hook. Possibly service to the Navy Yard may be desirable, but the area is not very well-developed right now, and the buses serving it have low ridership. Those are two or three routes radiating out of the same center in Downtown Brooklyn, which makes it tempting to not only build light rail on them, but also send it over the Brooklyn Bridge to City Hall. This would be like the subway-surface lines in Boston and San Francisco, where one underground trunk splits into several at-grade branches, except that in this case the trunk would be elevated rather than underground. It’s not worth building by itself, but the possibility of leveraging Brooklyn Bridge lanes for several light rail lines may make the ridership per unit of cost pencil out.

The common factor to all of these possibilities is that they are not meant for signature development areas that the city is targeting. Maybe there’s some new development there, but the focus is on improving public transit services to existing residents, who either are riding very slow buses or have given up on public transit because of the inconvenience. It can be marketed as an improvement in transit, but cannot really be sold as part of a plan to revitalize the Brooklyn waterfront. It’s about day-to-day governing, whereas the administration is interested in urban renewal schemes, which are rarely good transit.

# Modeling Anchoring

Jarrett Walker has repeatedly called transit agencies and city zoning commissions to engage in anchoring: this means designing the city so that transit routes connect two dense centers, with less intense activity between them. For example, he gives Vancouver’s core east-west buses, which connect UBC with dense transit-oriented development on the Expo Line, with some extra activity at the Canada Line and less intense development in between; Vancouver has adopted his ideas, as seen on PDF-page 15 of a network design primer by Translink. In 2013, I criticized this in two posts, making an empirical argument comparing Vancouver’s east-west buses with its north-south buses, which are not so anchored. Jarrett considers the idea that anchoring is more efficient to be a geometric fact, and compared my empirical argument to trying to empirically compute the decimal expansion pi to be something other than 3.1415629… I promised that I would explain my criticism in more formal mathematical terms. Somewhat belatedly, I would like to explain.

First, as a general note, mathematics proves theorems about mathematics, and not about the world. My papers, and those of the other people in the field, have proven results about mathematical structures. For example, we can prove that an equation has solutions, or does not have any solutions. As soon as we try to talk about the real world, we stop doing pure math, and begin doing modeling. In some cases, the models use advanced math, and not just experiments: for example, superstring theory involves research-level math, with theorems of similar complexity to those of pure math. In other cases, the models use simpler math, and the chief difficulty is in empirical calibration: for example, transit ridership models involve relatively simple formulas (for example, the transfer penalty is a pair of numbers, as I explain here), but figuring out the numbers takes a lot of work.

With that in mind, let us model anchoring. Let us also be completely explicit about all the assumptions in our model. The city we will build will be much simpler than a real city, but it will still contain residences, jobs, and commuters. We will not deal with transfers; neither does the mental model Jarrett and TransLink use in arguing for anchoring (see PDF-p. 15 in the primer above again to see the thinking). For us, the city consists of a single line, going from west to east. The west is labeled 0, the east is labeled 1, and everything in between is labeled by numbers between 0 and 1. The city’s total population density is 1: this means that when we graph population density on the y-axis in terms of location on the x-axis, the total area under the curve is 1. Don’t worry too much about scaling – the units are all relative anyway.

Let us now graph three possible distributions of population density: uniform (A), center-dominant (B), and anchored (C).

Let us make one further assumption, for now: the distributions of residences and jobs are the same, and independent. In city (A), this means that jobs are uniformly distributed from 0 to 1, like residences, and a person who lives at any point x is equally likely to work at any point from 0 to 1, and is no more likely to work near x than anyone else. In city (B), this means that people are most likely to work at point 0.5, both if they live there and if they live near 0 or 1; in city (C), this means that people are most likely to work at 0 or 1, and that people who live at 0 are equally likely to work near 0 and near 1.

Finally, let us assume that there is no modal splitting and no induced demand: every employed person in the city rides the bus, exactly once a day in each direction, once going to work and once going back home, regardless of where they live and work. Nor do people shift their choice of when to work based on the network: everyone goes to work in the morning peak and comes back in the afternoon peak.

With these assumptions in mind, let us compute how crowded the buses will be. Because all three cities are symmetric, I am only going to show morning peak buses, and only in the eastbound direction. I will derive an exact formula in city (A), and simply state what the formulas are in the other two cities.

In city (A), at point x, the number of people who ride the eastbound morning buses equals the number of people who live to the west of x and work to the right of x. Because the population and job distributions are uniform, the proportion of people who live west of x is x, and the proportion of people who work east of x is 1-x. The population and job distributions are assumed independent, so the total crowding is x(1-x). Don’t worry too much about scaling again – it’s in relative units, where 1 means every single person in the city is riding the bus in that direction at that time. The formula y = x(1-x) has a peak when x = 0.5, and then y = 0.25. In cities (B) and (C), the formulas are:

(B): $y = \begin{cases}2x^2(1 - 2x^2) & \mbox{ if } x \leq 1/2\\ 2(1-x)^2(1 - 2(1-x)^2) & \mbox{ if } x > 1/2\end{cases}$

(C): $y = \begin{cases}(2x-2x^2)(1 - 2x + 2x^2) & \mbox{ if } x \leq 1/2\\ (2(1-x)-2(1-x)^2)(1 - 2(1-x) + 2(1-x)^2) & \mbox{ if } x > 1/2\end{cases}$

Here are their graphs:

Now, city B’s buses are almost completely empty when x < 0.25 or x > 0.75, and city C’s buses fill up faster than city A’s, so in that sense, the anchored city has more uniform bus crowding. But the point is that at equal total population and equal total transit usage, all three cities produce the exact same peak crowding: at the midpoint of the population distribution, which in our three cases is always x = 0.5, exactly a quarter of the employed population lives to the west and works to the east, and will pass through this point on public transit. Anchoring just makes the peak last longer, since people work farther from where they live and travel longer to get there. In a limiting case, in which the population density at 0 and 1 is infinite, with half the population living at 0 and half at 1, we will still get the exact same peak crowding, but it will last the entire way from 0 to 1, rather than just in the middle.

Note that there is no way to play with the population distribution to produce any different peak. As soon as we assume that jobs and residences are distributed identically, and the mode share is 100%, we will get a quarter of the population taking transit through the midpoint of the distribution.

If anything, the most efficient of the three distributions is B. This is because there’s so little ridership at the ends that it’s possible to run transit at lower frequency at the ends, overlaying a route that runs the entire way from 0 to 1 to a short-turn route from 0.25 to 0.75. Of course, cutting frequency makes service worse, but at the peak, the base frequency is sufficient. Imagine a 10-minute bus going all the way, with short-turning overlays beefing frequency to 5 minutes in the middle half. Since the same resources can more easily be distributed to providing more service in the center, city B can provide more service through the peak crowding point at the same cost, so it will actually be less crowded. This is the exact opposite of what TransLink claims, which is that city B would be overcrowded in the middle whereas city C would have full but not overcrowded buses the entire way (again, PDF-p. 15 of the primer).

In my empirical critique of anchoring, I noted that the unanchored routes actually perform better than the anchored ones in Vancouver, in the sense that they cost less per rider but also are less crowded at the peak, thanks to higher turnover. This is not an observation of the model. I will note that the differences in cost per rider are not large. The concept of turnover is not really within the model’s scope – the empirical claim is that the land use on the unanchored routes lends itself to short trips throughout the day, whereas on the anchored ones it lends itself to peak-only work trips, which produce more crowding for the same total number of riders. In my model, I’m explicitly ignoring the effect of land use on trips: there are no induced trips, just work trips at set times, with 100% mode share.

Let us now drop the assumption that jobs and residences are identically distributed. Realistically, cities have residential and commercial areas, and the model should be able to account for this. As one might expect, separation of residential and commercial uses makes the system more crowded, because travel is no longer symmetric. In fact, whereas under the assumption the peak crowding is always exactly a quarter of the population, if we drop the assumption the peak crowding is at a minimum a quarter, but can grow up to the entire population.

Consider the following cities, (D), (E), and (F). I am going to choose units so that the total residential density is 1/2 and so is the total job density, so combined they equal 1. City (D) has a CBD on one side and residences on the other, city (E) has a CBD in the center and residences on both sides, and city (F) is partially mixed-use, with a CBD in the center and residences both in the center and outside of it. Residences are in white, jobs are in dark gray, and the overlap between residences and jobs in city (F) is in light gray.

We again measure crowding on eastbound morning transit. We need to do some rescaling here, again letting 1 represent all workers in the city passing through the same point in the same direction. Without computing, we can tell that in city (D), at the point where the residential area meets the commercial area, which in this case is x = 0.75, the crowding level is 1: everyone lives to the west of this point and works to its east and must commute past it. Westbound morning traffic, in contrast, is zero. City (E) is symmetric, with peak crowding at 0.5, at the entry to the CBD from the west, in this case x = 0.375. City (F) has crowding linearly growing to 0.375 at the entry to the CBD, and then decreasing as passengers start to get off. The formula for eastbound crowding is,

(F): $y = \begin{cases}x & \mbox{ if } x < 3/8\\ x(5/2 - 4x) & \mbox{ if } 3/8 \leq x \leq 5/8\\ 0 & \mbox{ if } x > 5/8\end{cases}$

In city (F), the quarter of the population that lives in the CBD simply does not count for transit crowding. The reason is that, with the CBD occupying the central quarter of the city, at any point from x = 0.375 east, there are more people who live to the west of the CBD getting off than people living within the CBD getting on. This observation remains true down to when (for a symmetric city) a third of the population lives inside the CBD.

In city (B), it’s possible to use the fact that transit runs empty near the edges to run less service near the edges than in the center. Unfortunately, it is not possible to use the same trick in cities (E) and (F), not with conventional urban transit. The eastbound morning service is empty east of the CBD, but the westbound morning service fills up; east of the CBD, the westbound service is empty and the eastbound service fills up. If service has to be symmetric, for example if buses and trains run back and forth and make many trips during a single peak period, then it is not possible to short-turn eastbound service at the eastern edge of the CBD. In contrast, if it is possible to park service in the center, then it is possible to short-turn service and economize: examples include highway capacity for cars, since bridges can have peak-direction lanes, but also some peaky commuter buses and trains, which make a single trip into the CBD per vehicle in the morning, park there, and then make a single trip back in the afternoon. Transit cities relies on services that go back and forth rather than parking in the CBD, so such economies do not work well for them.

A corollary of the last observation is that mixed uses are better for transit than for cars. Cars can park in the CBD, so for them, it’s fine if the travel demand graph looks like that of city (E). Roads and bridges are designed to be narrower in the outskirts of the region and wider near the CBD, and peak-direction lanes can ensure efficient utilization of capacity. In contrast, buses and rapid transit trains have to circulate; to achieve comparable peak crowding, city (E) requires twice as much service as perfect mixed-use cities.

The upshot of this model is that the land use that best supports efficient use of public transit is mixed use. Since all rich cities have CBDs, they should work on encouraging more residential land uses in the center and more commercial uses outside the center, and not worry about the underlying distribution of combined residential and job density. Since CBDs are usually almost exclusively commercial, any additional people living in the center will not add to transit crowding, even as they ride transit to work and pay fares. In contrast, anchoring does not have any effect on peak crowding, and on the margins makes it worse in the sense that the maximum crowding level lasts longer. This implies that the current planning strategy in Vancouver should be changed from encouraging anchoring to fill trains and buses for longer to encouraging more residential growth Downtown and in other commercial centers and more commercial growth at suitable nodes outside the center.

# Transfer Penalties and the Community Process

In Seattle, there is an ongoing controversy over a plan to redesign the bus network along the principles proposed by Jarrett Walker: fewer one-seat rides to the CBD, more frequent lines designed around transfers to Link, the city’s light rail system. For some background about the plans, see Capitol Hill Seattle, Seattle Transit Blog, and the transit agency on a restructure specific to an upcoming Link extension to the university (U-Link), and Seattle Transit Blog on general restructure, called RapidRide+. The U-Link restructure was controversial in the affected neighborhood, with many opposing changes to their particular bus route.

Since the core of the plan, as with many restructure plans in North America, is to get people to transfer between frequent core routes more and take infrequent one-seat rides less, this has led to discussion about the concept of transfers in general, and specifically the transfer penalty. I bring this up because of a new post by Jason Shindler  on Seattle Transit Blog, which misunderstands this concept. I would like to both correct the mistake and propose why transfers lead to so much controversy.

The transfer penalty is an empirical observation that passengers prefer trips with fewer transfers, even when the travel time is the same. Usually, the transfer penalty is expressed in terms of time: how much longer the one-seat ride has to be for passengers to be indifferent between the longer one-seat trip and the shorter trip with transfers. For some literature review on the subject, see Reinhard Clever’s thesis and a study by the Institute for Transportation Studies for the California Department of Transportation.

Briefly, when passengers take a transit trip with a transfer, making the transfer takes some time, which consists of walking between platforms or stops, and waiting for the connecting service. Passengers weight this time more heavily than they do in-vehicle travel time. According to New York’s MTA’s ridership model, passengers weight transfer time 1.75 times as much as they do in-vehicle time. In other words, per the MTA, passengers are on average indifferent between a one-seat ride that takes 37 minutes, and a two-seat ride that takes 34 minutes of which 4 are spent transferring. Observe that by the MTA’s model, timed cross-platform transfers are zero-penalty. Other models disagree – for example, the MBTA finds an 11-minute penalty on top of a 2.25 factor for transfer time.

The transfer penalty can be reduced with better scheduling. Timed transfers reduce the waiting penalty, first because there is less waiting on average, and second because the (short) waiting time is predictable. When transfers cannot be timed, I believe countdown clocks reduce the waiting penalty. Walking between platforms or bus stops can be made more pleasant, and bus stops can be moved closer to train station entrances.

However, regardless of what the transit agency does, the transfer penalty is an average. Even for the same origin and destination, different people may perceive transfers differently. Any of the following situations can result in a higher transfer penalty:

1. Heavy luggage. This also leads to bias against staircases, and often against transit in general and for cars and taxis. The waiting penalty does not grow, but there may be a significant penalty even for cross-platform transfers.
2. Travel in large groups, especially with children. As an example, in comments here and on Itinerant Urbanist, Shlomo notes that ultra-Orthodox Jews, who travel with their large families, prefer one-seat bus rides over much faster and more frequent train rides. Families of 3-5 are also much likelier to drive in a family car than to take an intercity train or bus.
3. Disability, including old age. This has similar effect to heavy luggage.
4. Lack of familiarity with the system. This is common for tourists but also for people who are used to taking a particular bus route who are facing significant route restructuring. This can also create a large bias in favor of trams or trolleybuses, since their routes are marked with overhead wires and (for trams) rails, whereas bus routes are not so obvious.
5. Reading, or getting other work done in transit. For longer intercity trips, sleeping is in this category, too. This tends to bias passengers against mid-trip transfers especially, more so than against start-of-trip and end-of-trip transfers.
6. Seat availability. Passengers who get on a bus or train when it still has seats available may prefer to keep their seat even if it means a longer trip, and this shows up as a transfer penalty. This does not usually affect start-of-trip transfers (buses and trains probably still have seats), but affects mid- and end-of-trip transfers.

In contrast, people who are not in any of the above situations often have very low transfer penalties. In New York, among regular users of the subway who do not expect to get a seat, zero-penalty transferring appears to be the norm, especially when it’s cross-platform between local and express trains on the same line.

Usually, people in groups 3 and 4 are the major political forces against bus service restructuring plans. They’re also less willing to walk longer distances to better service, which makes them oppose other reforms, including straightening bus routes and increasing the average interstations in order to make bus routes run faster. This is also true of people in groups 1 and 2, but usually those are not inherent to the passenger: most disabled people are always disabled, but most passengers with luggage usually travel without luggage. The one exception is airport travel, where luggage is the norm, and there we indeed see more advocacy for one-seat rides to the CBD.

The key observation here is that even a route change that is a net benefit to most people on a particular origin-destination pair is sometimes a net liability to some riders on that pair. While it’s a commonplace that reforms have winners and losers, for the most part people think of it in terms of different travel patterns. Replacing a CBD-focused system with a grid leads to some losers among CBD-bound riders and winners among riders who travel crosstown; boosting off-peak frequency creates winners among off-peak travelers; straightening one kink in a bus route leads to losers among people served by that kink and winners among people riding through. The different transfer penalties are a different matter: even on the same origin-destination pair, among people traveling at the same time, there are winners and losers.

Solutions to this issue are bound to be political. The transit agency can estimate the net benefit of a restructure, and sell it on those grounds, but it’s not completely a win-win; thus some political process of conflict resolution is required.

In this particular case, the community process is reasonable. The main flaw of the community process is that the people who come to meetings are not representative of the body of riders and potential riders, and are especially likely to be NIMBYs. For example, on Vancouver’s West Side, the community meetings for the Broadway subway were dominated by NIMBYs who didn’t want outsiders (especially students) to have an easier commute to UBC, and not by people who could use the subway, often traveling through the West Side without living or working in it.

But the conflict when it comes to transfers is between groups of people who live in the same area. Moreover, there is no clear bias in either direction. Older people, who are usually more averse to change, are especially likely to show up to meetings; but so are transit activists, who are more informed about the system and thus more willing to transfer. People with intense familiarity with their home bus line are balanced out by people with familiarity with the system writ large. There is also no opposition of a widely shared but small benefit to most against a narrow loss to the few: instead, such reforms produce a large array of changes, ranging from major gains to major losses. Finally, frequent bus grids do not generate much transit-oriented development, unlike rail, which produces NIMBY contingents who are against transit investment on the grounds that it would lead to upzoning and new development (as in the above example from Vancouver).

The result is that here, political control can lead to positive outcomes, as the transit agency is required to consider the effect of change on many subsets of riders. Frequent grids really do generate losers, who deserve to be heard. In this case, it appears that they are outnumbered by winners, but the winners have as much of a political voice as the losers; there is no large gap between good transit and what the community thinks good transit is.