When one train get backed up, the trains behind them become backed up as well. Trains should be able to go express and skip stations to relieve the back-up and get back on schedule.
Because each train line only operates on one track, if one train becomes late because, for example, the train doors won't close due to people cramming themselves in, the trains behind them can get jammed up. Once realizing that a train is too behind schedule, it should make an announcement to passengers on the train that it will be going express. Express meaning it will only stop at certain stops and bypass others completely. After the announcement, passengers can get off right then if the train is not going to their stop. They should hop on the next train behind them which hopefully will be stopping at all stops. Once the first train gets back on schedule, it can go from express back to its normal stops. Yes, some passengers will be upset. But it's better to have 100 upset people than 1000.