The math problem of the New York City subway system is no secret, its remainders spilling onto the platforms where luckless travelers watch full trains come and go.
In the last 20 years, daily ridership has increased by some two million, to roughly 5.5 million, with little change in the system’s capacity.
Amid this surge, perhaps no train has been tested like the L line, facing down the dual strains of rapidly growing Brooklyn neighborhoods and a transit map devoid of many viable options nearby.
The authority said this week that it would add 33 round trips on the L on Saturdays and 22 on Sundays beginning this fall, helping to relieve persistent overcrowding and shaving about a minute off the average wait time. Three weekday evening trips will also be added.
Transit officials had already planned to add eight weekday and eight weekend round trips next month. In 2012, the authority added 16 trips on each weekday for the L, 11 on Saturdays and seven on Sundays.
Yet as the neighborhoods have grown, gentrifying one eastbound stop at a time, even these service changes have struggled to keep pace. On Thursday morning, at the Morgan Avenue station, Marisol Santiago and her home attendant, Germania Dmeza, could not board a train around 8:30 a.m. and just watched the young faces roll by.
When a second train came, Ms. Santiago muscled in, but could not carve enough space for them both. The doors closed.
“This is normal at this hour,” said Ms. Dmeza, her charge shuttling toward Manhattan alone.
According to agency data, ridership on the L increased at every station last year. At Bedford Avenue, weekday ridership has grown by more than 50 percent since 2007. Much of the increase has come during off-peak hours.