With antiquated trains, rusty rails and straphangers who keep the doors from closing, the New York City subway could hardly be described as efficient. And yet, some trains arrive with a certain regularity, following a neat statistical model similar to that seen in quantum systems.
at the University of Toronto, Canada, and at the University of California, Irvine, used the subway system鈥檚 real-time data feeds to analyse gaps between arrival times on two lines. They found that the 6 line that runs up the east side of Manhattan is inefficient. Its trains follow the Poisson distribution, a statistical model that describes particles that arrive more or less randomly.
鈥淚f you were waiting at a stop for 5 minutes, waiting for the next 5 minutes does you no good,鈥� says Trogdon. In a more functional transit system, you鈥檇 expect that after waiting for a while, the probability of a train arriving soon would be quite high. The Poisson distribution does not guarantee this.
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In contrast, the southbound 1 line that runs down the west side of Manhattan show random matrix patterns, which are 鈥渁 sign of greater efficiency鈥�, says Jagannath, now at Harvard University. These trains run at more regular intervals.
鈥淚 think the data is confirming people鈥檚 intuition about the two lines,鈥� says Trogdon. Indeed, the 1 line is one of the three local subway lines serving the west side of Manhattan, so it鈥檚 far less crowded than the 6, which at the time of the study was the only local line on the east side.
Inspired by buses
The efficiency analysis hinges on a landmark 1990 study in Cuernavaca, Mexico. Despite operating with no central control, buses there run without much clustering, thanks to the drivers鈥� effort to maximise their profit. In that study, buses also conformed to random matrix patterns.
The parallel isn鈥檛 exact for the New York City subway system, however. The random matrix patterns break down at the last 10 stations of the southbound 1 line. Moreover, the northbound 1 line does not follow those patterns.
鈥淭he analysis of the New York system is less clear [than the Cuernavaca bus system],鈥� says at Harvard University.
Still, Amir says this kind of analysis is the first step towards optimising the subway system. For straphangers in New York, that鈥檚 always going to be a plus.
Physical Review E
