The Subway as Gears, or Scheduling for Reliability

Since the COVID-19 pandemic sent the world into lockdown, transit systems have struggled with uneven ridership recoveries. The pandemic and the rocky return to normalcy should serve as a wake-up call to New York City Transit. Despite the signs in ridership recovery, the system is still nowhere near its normal pre-pandemic ridership levels. Daily rides reached 4 million daily rides in 2023 (Bloomberg), compared to around 5.5 million daily rides in every year between 2014 and 2019 (MTA). Riders need to be tempted back to transit, but in its current state, the subway system is not very tempting. NYCT needs to rework their current operating practices in order to maximize efficiency and usability for current riders, and to attract new riders and new revenue to the system. A key area for improvement lies in how the subway is scheduled. I will lay out how the current schedule-writing practice fails at creating a reliable system, then outline what I believe should be the primary goals and methods for writing more reliable and more robust schedules. 

The current scheduling practice at MTA New York City Transit (NYCT) is oriented around the wrong metric (crowding) and fails to take into account how interlined the subway routes are. Schedule writers fine-tune each individual subway route’s frequency for each scheduling period (peak, off-peak, evening, weekend, overnight) based on observed crowding levels at the busiest point on that individual route. Then, scheduled service levels, measured in trains per hour (tph), are adjusted such that in a given hour, each train car should be carrying a certain percentage of seated capacity. These are targeted at 125% of seated capacity for off-peak service and 300% for peak times. For example, an R160 train car, used on many B-Division (letter) routes, can seat 44 people, with 202 standees, for a total capacity of 246. Under the current scheduling practice, schedule writers try to ensure that at the busiest point on each route, every R160 car will only have 132 total passengers (300% of 44), a full 114 fewer than the designed capacity. 

NYCT’s current schedule-writing method assumes that ridership levels per line are static, and that changing the number of trains per hour on a given route will only affect how crowded each train is, but not affect total ridership levels at all. This is incorrect, because it misunderstands the relationship between transit ridership and transit frequency. Rather than frequency being dependent on ridership, transit ridership is dependent on transit frequency. If NYCT observes lower ridership on a given route and thus operates fewer trains, taking transit becomes more inconvenient for riders. If transit is less convenient, fewer riders will choose transit, and thus drive down ridership numbers further, leading to further reductions in transit service, which leads to reduced ridership, and so on. This is called the transit death spiral. However, the reverse process is also true. Higher transit frequency means that waiting times are reduced, bringing the total journey time down, making transit a more attractive mode choice for potential riders and increasing the number of people who choose to take transit. Cutting service is the last thing planners should want to do in response to low observed ridership levels. Therefore, schedules should not be written based on observed ridership levels but instead based on overall system reliability and frequency.

This method of writing schedules aims to reduce crowding on each line, however it misses a key fact: crowding levels are not the primary consideration for most riders. Potential riders will take transit if it is easier, faster, or cheaper than other modes (especially driving), regardless of the crowding levels on transit vehicles. Pre-pandemic, The Lexington Avenue Line was “over-capacity” (New York Times, Politico, NY Daily News). To NYCT, “over-capacity” meant that despite running as many trains as physically possible per hour, crowding levels still exceeded the crowding guidelines of 300% seated capacity at peak hours. If crowding was the most important factor in determining transportation mode choice, and 300% seated capacity was the limit that passengers were comfortable with, it would be reasonable to assume that riders would not choose to ride the Lexington Avenue Line because it consistently exceeded this threshold. If this was the case, then the Lexington Avenue Line should have bled ridership until crowding levels fell to 300% seated capacity. This never happened, because taking the subway was a more attractive choice than driving into midtown and lower Manhattan, even when crowding was above 300% seated capacity. Therefore, since riders will choose transit even when crowding exceeds the arbitrary guidelines that NYCT lays out, subway schedules should not be written for these target crowding levels, but should instead be written to provide the kind of service which attracts potential riders to transit: high-frequency (many trains per hour), low-headway (short time between trains), and reliable (few delays).

Optimizing individual route schedules for crowding is a suboptimal solution on both the individual route level, and on the system level. On the individual route level, optimizing for crowding increases the risk of a transit death spiral, by capping capacity at an artificially low level, and forgoes the possibility of a virtuous circle for the same reason. On the system level, optimizing for crowding is suboptimal because individually optimized routes with mismatched frequencies interact poorly with each other in a heavily interlined system like New York’s. 

Interlining is the practice of running multiple routes (for example the 2 and 3 trains) on the same physical track. These sections of shared track can be just a few stations long, or nearly the entire length of a subway route. All but six routes are interlined for some part of their route, and all routes which interline with any other route fall into what I call an “interlined set”. An interlined set is the collection of all routes in which any route interlines with at least one other route in the set. For example, while the 4 only interlines with the 5, since the 5 interlines extensively with the 2 and very briefly with the 3, the 4 is in an interlined set with the 2, 3, and 5.

As the Lexington Avenue Line proved, frequency is a more important factor to riders than crowding. In order to drive up ridership, schedules should be written to make train service higher-frequency and more reliable. Because the current schedule writing practice does not incorporate the extensive interlined sections of the system in its methodology, delays at merge points are inevitable. Schedules should instead be written with these interlined sections and conflict points in mind first and foremost. By minimizing delays at merge points, train service and the riding experience will be improved for all passengers. 

Imagine two interlocking gears which are turning together. If the teeth of one gear line up perfectly with the gaps of the other gear, the two will turn in perfect harmony. If the teeth and gaps of the two gears are misaligned, the gears will grind together. Each subway route is a gear, and the individual trains which run on those routes are the teeth. When two trains on different routes arrive at their merge point at the same time, it is like the teeth of two misaligned gears trying to fit together, and the resulting grinding of the gears is the delays which stack up all throughout the system. In order to minimize these delays, frequencies on each route in an interlined set must all be equal, like making two gears which fit together perfectly. Matching the frequency of routes in this manner will improve reliability by eliminating unnecessary delays at merge points. Matching all frequencies in an interlined set will raise the frequency of all routes in the set to the frequency of the most frequent route in the set. Raising frequencies will make transit a more attractive transportation mode, and create a virtuous ridership circle. 

In addition, in the post-COVID world, office use has not rebounded to pre-pandemic levels, while non-office work and leisure travel have rebounded. The current subway schedules should reflect the current dominant travel pattern of all-day travel (and strong weekend ridership), rather than morning and evening peaks on weekdays. By creating a higher minimum all-day frequency, NYCT can achieve two goals. The primary goal is that of former New York City Comptroller Scott Stringer’s “New York City in Six” Plan (Former Comptroller Scott Stringer), which calls for every subway route to have a headway no greater than 6 minutes all day, which on shared sections means a headway of 3 minutes across both routes. Consistently high all-day transit service will better serve the increasingly diverse commuting needs of New Yorkers. This is an enormous improvement in service levels from the current schedules, in which most routes have headways of 10 minutes during non-peak hours. Higher frequency subway service will also reduce delays from people holding the doors, as missing a train will only mean a wait of 6 minutes, not 10. This higher frequency service, combined with fewer delays, will make transit a more attractive option and help bring subway ridership back towards pre-pandemic levels. 

The secondary goal of a high minimum all-day frequency is one of operational efficiency. By scheduling for similar levels of service during the peak and off-peak periods, the MTA would get far better utilization of both employees (Train Operators and Conductors) and equipment. Rather than needing high levels of both for just a few hours per day, each employee and train would be in revenue service for far longer periods. Alon Levy has calculated that NYCT gets around 550 revenue service hours per driver per year, while the Berlin U-Bahn, which has all-day frequencies, gets 900. Without changing the number of train operators, NYCT could nearly double the number of revenue service hours per driver, simply by adopting more efficient scheduling practices. Therefore, schedules should be written with all-day consistent levels of service in order to 1) better serve the riders who are returning to the system and 2) more effectively utilize the existing resources (employees and equipment).

In order to bring riders back to the system, and improve subway reliability, schedules should be rewritten with a few key rules in mind, which will allow NYCT to make the most of the current system, and improve efficient transit operations in the subway. 

1. Each route should see peak period headways of at most 5 minutes (12 tph), and daytime off-peak headways of at most 6 minutes (10 tph).
2. Interlined sections may not host more than two routes.
3. Interlined sections would see peak period headways of at most 2.5 minutes (24 tph), and daytime off-peak headways of at most 3 minutes (20 tph). 
4. All routes in an interlined set should run on matched frequencies.
5. All interlined routes should be classified into two categories, and no two routes in the same category may ever share tracks.
6. Schedule adherence should become a top priority within NYCT. All schedules should be written with precise, to-the-second times for all station stops and major junctions, with acceptable deviation from the written schedule clearly understood by dispatchers and train operators.

Category	Routes
0	1, 6, 7, L
α	2, 4, A, B, E, G, M, N, W
β	3, 5, C, D, F, J/Z, Q, R, Sf

The first category is for routes which are already operationally de-interlined, and the other two are alpha (α) and beta (β). No two α routes may share tracks and no two β routes may share tracks. Based on this categorization, it becomes clear that there are a number of places in which the current system is poorly optimized for maximum system efficiency. Luckily, the MTA will soon have roughly $1 billion/year of budget for capital projects from congestion pricing revenue. Current service on the subway could be dramatically improved with the implementation of my schedule-writing method, and a few well placed capital projects to take full advantage of the benefits of the new schedules.

Conflicting Routes	Rule Broken	Location
E/M	Categorical Conflict (α)	53rd Street Tunnel
N/W	Categorical Conflict (α)	Astoria Line
N/R/W	2 Interlined Routes	60th Street Tunnel
3/5	Categorical Conflict (β)	Rogers Junction

The E and the M are both categorized as α routes, but interline through the 53rd St Tunnel. The simplest solution is an F/M swap between the 53rd Street and 63rd Street Tunnels. E and F trains would interline through the 53rd Street Tunnel and onto the Queens Boulevard express tracks, while R trains from the 60th Street Tunnel and M trains from the 63rd Street Tunnel would use the Queens Boulevard local tracks. This preserves current service patterns along the Queens Boulevard Line, and all routes would be boosted to 12 tph during peak periods and 10 tph during non-peak daytime hours.

The W, which I have classified as α as it shares tracks with the R (β) on the Broadway Line local tracks also shares tracks with N, another α, on the Astoria Line. This is a categorical conflict, but the W furthermore shares tracks with both the N (α) and R (β) through the 60th Street Tunnel, which is a violation of the 2-routes-per-interlined-section rule. Under my proposed scheduling method the W would need to be eliminated and Astoria would see its peak service reduced from 15 tph currently, down to 12 tph, while the R would be boosted from 8 tph to 12 tph in the peak. This solution is by far the simplest as it requires no new construction, and preserves existing routing as much as possible. However, the reduction in service for the Astoria Line may make this proposal unpalatable. Supplemental bus service may be introduced to help mitigate the lost subway capacity, but as long as Broadway Line local trains continue to serve the Queens Boulevard Line, the Astoria Line will necessarily be limited to 12 tph. 

If Broadway Line local service was removed from the Queens Boulevard Line, the Astoria Line could see frequencies increased to 24 tph. This would involve 24 R tph, with Q trains interlining with the M through the 63rd Street Tunnel and onto the Queens Boulevard local tracks. The E would be rerouted onto the Queens Boulevard local tracks as well, and the F and M would use the Queens Boulevard express tracks. However in this scenario, a new storage yard would need to be constructed somewhere along the R route, as neither the Astoria Line nor the 4th Avenue Line have direct yard access.

The simplest conflict to solve is between the 3 and the 5 at Rogers Junction, just east of the Franklin Ave-Medgar Evers College station. This is where the Nostrand Avenue Line merges with the Eastern Parkway Line. There is a short section of track, in both directions, over which 2, 3, and 5 trains all operate, causing operational headaches and persistent delays. As 3 and 5 trains both fall in the same category (β), this is a problem which must be solved. There are two solutions, one of which is expensive and one of which is cheap. The expensive option is to rebuild the junction as a flying junction, eliminating the shared track section, and allowing the existing service patterns to continue. The cheaper option is building two switches east of the current interlocking, connecting the Eastern Parkway Line express tracks with the Eastern Parkway Line local tracks, east of Rogers Junction. While significantly cheaper, this would require the 3 and 5 trains to swap their southern termini, with 3 trains going to Flatbush Avenue-Brooklyn College and 5 trains going to New Lots Avenue. I have no preference for either option, only that one option must be chosen.

In order to attract riders back to transit, NYCT must rework its current practice of scheduling trains from the current crowding-based metric to a method which prioritizes system reliability and high frequencies. With these updated scheduling practices in mind, a clear roadmap for future investment in the system emerges, and forward-thinking investment of the incoming congestion pricing revenue can be implemented to bring subway service in New York City up to the level this city and its citizens require and deserve.