Benjamin Norman for The New York Times

The nation’s most crowded subway line is jammed every morning with a crush of people waiting to board trains. Angry riders often have to let a train or two pass before they can wedge themselves inside.

It turns out that the route — the Lexington Avenue line in New York City — is regularly failing to meet its train schedule, especially during rush hour, leading to dozens of trains being canceled every day and reducing the system’s capacity by tens of thousands of riders, according to an analysis by The New York Times.

Case Study: 4 5 6 Scheduled vs. Actual Trains on a Busy Subway Line Chart shows the number of 4, 5 and 6 trains passing through Grand Central-42 Street on average in June and July 2017 Source: Metropolitan Transportation Authority data | Note: Data shows trains that made a recorded stop at Grand Central-42 Street Station in the M.T.A.’s data feed from June 9 to July 31, excluding weekends, holidays and days when the M.T.A.’s data feed was interrupted.

On the Lexington Avenue line, which carries the No. 4, 5 and 6 trains, just 77 of 90 scheduled trains routinely run through the busy Grand Central Station stop from 8 to 9 a.m. The rest, 14 percent of trains, are effectively canceled, at a time when the system needs them most.

Again in the evening, from 5 to 6 p.m., only 76 of 88 scheduled trains stop at the station, on average. Each canceled train accounts for roughly 1,000 passengers who could be accommodated if the system met its published schedule.

As the subway reaches a crisis point, prompting officials to announce an ambitious rescue plan to fix the system, a critical challenge will be to increase the frequency of trains to carry riders more reliably across the city.

Many of the problems afflicting the subway have already been chronicled by The Times, including an antiquated signal system, severe overcrowding and trains that are breaking down at a much higher rate than in the past. The cancellation of trains at times of peak demand is in many ways intertwined with some of those other challenges.

Officials at the Metropolitan Transportation Authority acknowledged that the schedules were not being met, and they blamed overcrowding for the shortfall. Trains are stuck in stations as passengers struggle to get on and off, subway officials say, leading to a cascade of delays along the line.

But subway data reviewed by The Times reveal just how severe a toll overcrowding is taking on the subway. The Lexington Avenue line is the system’s most congested, but the same problem plagues other lines as well, leading to a greatly reduced number of trains during peak periods across the system.

“It’s a self-feeding problem,” said Ellyn Shannon, associate director of the Permanent Citizens Advisory Committee, a riders’ group at the transportation authority. “Crowds get bigger and slow the trains down more, and you lose capacity. But if you have fewer trains, the crowding will build and the trains slow down more.”

A System That is Consistently Behind

The shortfalls are not occasional or seasonal or exceptional. In the last two months, the number of times the Lexington Avenue line has reached its hourly weekday rush-hour scheduled train count is zero.

Case Study: 4 5 6 Scheduled vs. Actual Trains on a Busy Subway Line For days with available data in June and July, the system never sent the scheduled numbers of trains. Source: Metropolitan Transportation Authority data | Note: Data shows trains that made a recorded stop at Grand Central-42 Street Station in the M.T.A.’s data feed from June 9 to July 31, excluding weekends, holidays and days when the M.T.A.’s data feed was interrupted.

Officials say they are running as many trains as they can at peak hours, and the problem is capacity on an aging system. But the shortage stretches throughout the day, even when the system has fewer riders and runs trains less frequently.

When trains are delayed, workers continue to space trains at consistent intervals, instead of running trains more closely together, one after another, according to train data. Officials believe that is the best way to reduce the average time riders are stuck waiting on platforms. But, inevitably, that means fewer trains and reduced capacity.

Transit advocates say officials failed to adequately plan for a booming ridership and criticize the agency’s strategy of focusing on keeping trains evenly spaced rather than meeting its schedules.

Here’s how that focus leads to cancellations. On June 20, a Tuesday, at 7:55 a.m., subway officials reported delays on the No. 6 train. The data show only one southbound 6 train at Grand Central Station from 8:04 a.m. to 8:23 a.m. instead of the five scheduled. When service resumed, trains were still spaced fairly evenly at two- to four-minute intervals. The trains that were supposed to arrive during that time period were effectively canceled, and by 9 a.m., just 17 of 23 scheduled trains had made the trip.

Case Study: Southbound 6 train on June 20 from 8 to 9 a.m. Scheduled Actual 8:00 a.m. Actual 8:01 a.m. 8:04 8:04 8:06 Scheduled 8:10 8:11 8:13 8:16 8:19 8:22 8:23 Four trains behind 8:24 8:25 8:27 8:27 8:30 8:31 8:32 8:33 8:35 8:36 8:38 8:39 8:41 8:41 8:44 8:44 8:46 8:46 8:48 8:49 8:51 8:53 8:54 Five trains behind 8:55 8:57 8:57 Six trains behind 8:59 8:59 Scheduled Actual 8:00 Actual 8:01 a.m. 8:04 8:04 8:06 Scheduled 8:10 8:11 8:13 8:16 8:19 8:22 8:23 Four trains behind 8:24 8:25 8:27 8:27 8:30 8:31 8:32 8:33 8:35 8:36 8:38 8:39 8:41 8:41 8:44 8:44 8:46 8:46 8:48 8:49 Five trains behind 8:51 8:53 8:54 8:55 Six trains behind 8:57 8:57 8:59 8:59 Source: Metropolitan Transportation Authority data

The cancellations have contributed to an on-time rate for trains that has dropped steeply over the last decade to about 65 percent systemwide, from more than 90 percent. On the Lexington Avenue line — which carries about 1.6 million people each day, more than the number of daily riders on Washington’s and Chicago’s subways combined — the on-time rate is as low as 35 percent.

A Focus on Wait Time

The authority’s chairman, Joseph J. Lhota, said his priority was reducing the intervals between trains, rather than meeting the posted schedules so riders are not kept waiting too long. The current schedules are largely based on lower ridership figures from 2012, Mr. Lhota said, before overcrowding delays skyrocketed, clogging the system.

The focus on train intervals over schedules has indeed kept wait-time performance from falling sharply, even as on-time-performance has plummeted. But even that metric has been trending downward since 2013.

Even Spacing Between Trains or Maintaining a Schedule The MTA’s two measurements for systemwide subway performance 90% 80 Percent of trains meeting the standard for even spacing 70 Percent operating on schedule 60 2012 2013 2014 2015 2016 2017 90% Percent of trains meeting the standard for even spacing 80 70 Percent operating on schedule 60 2012 2013 2014 2015 2016 2017 Source: Metropolitan Transportation Authority data

In a recent interview, Mr. Lhota said the agency should adjust the published schedules to reflect current conditions, and offer the public improved performance metrics that tell riders how long they should expect to wait between trains.

“What I care about is being able to maintain a headway closer to target,” Mr. Lhota said, referring to an industry term describing the time between trains. “Obviously, to do that we’d have to put more trains through, and we could if we didn’t have the congestion problem.”

As for off-peak cancellations, subway officials blame maintenance work they must tackle during less busy periods of the day. The noticeable reduction in train speeds is because of a confluence of events, including stricter rules for slowing trains during repairs to avoid hitting workers and signal controls intended to maintain a safe distance between trains to prevent crashes.

The subway’s antiquated 1930s-era signal system is also a barrier to spacing trains closer together. Modern signals would allow trains to run more frequently, increasing the subway’s capacity, but officials say installing them systemwide could take a half-century and billions of dollars.

The growing disregard for the schedules frustrates transit advocates who view them as a promise to riders about the kind of service they should expect.

“It’s a public commitment to how much service they’re running,” Ms. Shannon said. “The amount of service they’re running is based on the loading guidelines, which say you have to put out this many trains to transport this many people.”

Benjamin Norman for The New York Times

A Cramped and Unreliable Commute

On a recent morning, express trains arrived at Grand Central with hordes of sweaty riders pressed against the glass doors. Their faces revealed a mix of misery and resignation.

Tameka Mullins likens her morning commute to being stuffed into a sardine can. If the authority keeps raising fares, then it should run a full schedule of trains, said Ms. Mullins, 47, who lives in Brooklyn.

“At times, it takes an hour and a half to get somewhere, when you should get there in 30 to 45 minutes,” she said, while riding a No. 6 train in Manhattan. “It’s because the train keeps stopping because of the train congestion. If there were more trains, and it was running more smoothly, then I think that problem would be solved.”

Another rider, Olivia French, said her commute was often “hit or miss.” Some days, the No. 6 train arrives every two minutes. But other times, Ms. French, 25, who lives on the Upper East Side, has to wait eight minutes between trains.