The capacity of a subway line

The factors

Image result for subway carToday, underground train systems are the fastest  way to carry people inside cities. This is mostly due to the particularity of  the underground rail, which is always a high priority line.  Despite the absolute priority of the trains, the maximal capacity of a metro line is depending on many factors, which slows it down. Some of the most important factors are:

  • train capacity
  • headway
  • marshalling
  • stop times in stations

Every one of the factors above has an impact on the capacity of the line.

Train capacity

Image result for subway car double deckThe Roadmaster double deck bus in London has been  a success because of a greater passenger capacity. Same way, trains with two decks are preferred in dense areas, as,  for the same allotted time slot, they carry more people  than a traditional train. Long trains carry more passengers than short trains for the same reason.

It is now custom to lengthen the subway trains till they cover the whole length of the platform. The number of cars is increased from 5 to 6 or from 6 to 8, depending on the size of the station. The more generous the builder has been, the more cars can be added to the train. There is a limit of about 200m for the length of a train where the driving and the control in the station is done by the same person.

Headway (or headway time)

It is the minimal time, in seconds between two consecutive trains. The number of trains per hour that can serve a given station is:

Number_trains per hour = 3600 / Headway

The formula of Headway depends on many factors, like speed, maximal deceleration of the train, length of the train, etc.

Marshaling

Image result for two  trainsSubway end stations are of two types: with a rotunda or with a dead end. For the first type, there is no time lost to turn the train in the other way.  The process occurs naturally, through the rotunda loop.

For the stations with dead ends, the train needs to change its way. This operation is called marshaling. It implies several actions:

  • the driver must walk the whole length of the train and change the driving place
  • the train itself must enter the dead end tunnel, decelerate, stop, accelerate and exit the tunnel
  • for modern trains with computer systems, the data in the black boxes of the train must be unloaded to the central IT system of the subway. The transit plan must be re-loaded in the on board computer, too.

Overall, the marshaling sequence cannot take less than 3 minutes.

Stop times in stations

Image result for subway in stationThe subway cars carry people. The passengers can board the train only when the later stops in the station. Typical stop times vary from 10 seconds to 1 full minute. If the headway is too short, the following train might need to stop just before entering the station. This adds supplementary lags to the system.

Lessons from the past

One transit company tried to increase the capacity of the line by adding more and more trains. At  some point, the stop time in station became the limiting factor. The solution was to decrease the number of trains and increase the individual capacity of each train.

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