The New York Subway’s more efficient lines follow quantum physics patterns

Train arrivals and departures on the New York Subway might not seem like they follow any kind of pattern.

However, a new study has found one of the most efficient lines on the system follows a pattern similar to those seen in quantum systems, called random matrix theory (RMT).

A pair of researchers, one at the University of Toronto, the other at the University of California, studied the arrival and departure times of two NYC subway lines, 1 line and 6 line. The less crowded 1 line runs north and serves the West Side of Manhattan, and 6 line runs south and serves the East Side, meaning it is far more popular. 

The results confirmed what many people already think about these two lines; 1 line is much more efficient than 6 line. The arrival and departure of trains on 1 line followed RMT, with the exception of the last ten stops.

But on 6 line, the times followed a Poisson distribution; in other words, the arrivals and departures were completely random.  On this line, “if you were waiting at a stop for five minutes, waiting for the next five minutes does you no good,” co-author Tom Trogdon told New Scientist.

This is not the first time transport systems have been shown to follow these random matrix patterns. In 1999 a study looking at buses in Cuernavaca, Mexico, found a similar result. When researchers analysed the bus times, they discovered that the buses were following patterns that had been observed in quantum physics experiments.

This had been because the bus drivers were working to maintain the maximum efficiency of pick up and drop off times, in order to maximise their wages. The self-employed drivers were paid depending on how many passengers they picked up, so if they were to arrive at a bus stop very soon after the bus in front, they would receive less money.

Using spies they placed along the route, the drivers would work out how long it had been since a bus had reached their next stop and adjust their speed accordingly. These buses followed RMT patterns.

The researchers in the new study, published in Physical Review E, argued that, based on the Mexican bus study, RMT could be taken as a sign of better efficiency. “If one takes RMT statistics for train arrivals to be a hallmark of efficiency, as could be argued from the Cuernavaca, Mexico case study, this type of analysis may prove fruitful as a guide to understand and improve the performance of a subway system,” they wrote.