[PHYS.ORG] Part of New York's subway system found to conform to random matrix theory

(Phys.org)—A pair of researchers, one with the University of Toronto, the other with the University of California, has found that at least one line on New York city’s metro system conforms to random matrix theory. In their paper published in Physical Review E, Aukosh Jagannath and Thomas Trogdon describe their study, which included using statistical theory to analyze the arrival rates of subway cars.

Aukosh Jagannath 和 Thomas Trogdon，一个来自University of Toronto，另一个来自University of California, Irvine，他们发现纽约地铁系统至少有一条线遵从随机矩阵论。他们在发表于Physical Review E上的论文中描述了他们的研究，该研究包括使用统计理论来分析地铁的到达率。

Back in 2000, a study was conducted of bus arrivals and departures in Cuernavaca, Mexico—among other things, the researchers found that despite unpredictable traffic patterns and driver owned buses, the buses in the city ran on a predictable schedule that conformed to random matrix theory (the researchers chalked it up to the way the drivers competed for fares). In this new effort, the researchers wondered if the same might be true for the New York subway system.

回到2000年，在Cuernavaca, Mexico进行了一项关于公共汽车到达和离开的研究。研究者发现，虽然交通状况和驾驶汽车的司机都不可预测，但城市中的公共汽车仍按一个可预测的时刻表来运行，它们遵从随机矩阵论（研究者将其归结为司机竞价的方式）。在这项新的工作中，研究者想知道是否纽约地铁系统也有这样的规律。

To learn more about the timing of subway cars, the researchers picked two random routes to study. One was the 1 line, which runs north and serves the West Side of Manhattan; the other was the 6 line, which runs south and serves the East Side of Manhattan. The pair used information from the real-time data feed supplied by the subway system to track arrival times for the two lines.

为了解更多的地铁时间情况，研究者挑了两条随机线路来研究。一条是往北开服务曼哈顿西部的1号线，另一条是往南开服务曼哈顿东部的6号线。他们使用由地铁系统提供的实时数据流的信息来追踪这两条线的到达时间。

The researchers found that the 6 line ran almost randomly and therefore no predictable distribution pattern could be used to describe it. The 1 line, on the other hand, was found to follow a Poisson distribution (for all but the last 10 stations), which made it much easier for passengers to predict when the next train would arrive. The researchers suggest the difference between the lines is due to the amount of traffic on each. The 6 line is heavily used, and because of that, suffers frequent delays, such as passengers preventing doors from closing in an expedient manner. The 1 line, on the other hand, has fewer passengers, making it much easier for trains to run on time.

研究者发现6号线几乎是随机运行的，因此任何可预测的分布模式都不能用来描述它。另一方面，他们发现1号线遵从泊松分布（除了最后10站外），这使得乘客更容易预测下一趟车的到达时间。研究者认为，线路间的差别在于每条线上的交通量。6号线大量使用，如乘客阻止车门关闭等原因，会造成频繁延误。而1号线乘客相对较少，这使得列车更容易准时运行。

The researchers suggest their results might be used by city planners to optimize the system for efficiency.

研究者认为城市规划师可以使用他们的结果来优化系统。

Explore further: Driverless subway line to be extended in Paris

More information: Aukosh Jagannath et al. Random matrices and the New York City subway system, Physical Review E (2017). DOI: 10.1103/PhysRevE.96.030101 , On Arxiv: https://arxiv.org/abs/1703.02537

ABSTRACT

We analyze subway arrival times in the New York City subway system. We find regimes where the gaps between trains are well modeled by (unitarily invariant) random matrix statistics and Poisson statistics. The departure from random matrix statistics is captured by the value of the Coulomb potential along the subway route. This departure becomes more pronounced as trains make more stops.

我们分析了纽约地铁系统的地铁到达时间。我们发现（酉不变的）随机矩阵统计和泊松统计可以很好地建模列车的时间间隔。随机矩阵统计的偏离可以通过沿地铁线路的Coulomb势来刻画。这个偏离随着列车停靠站点越多而变得越明显。

Other sources:

Synopsis: Subway Stats

If NYC subways obeyed quantum maths trains wouldn’t be delayed

NYC’s subway system really IS inefficient: Statistical analysis reveals one of the busiest lines is plagued by inconsistencies - but quantum math could solve it

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

Written on September 12th, 2017 by 李军