The master equation approach is proposed to describe the evolution of passengers in a subway system. With the transition rate constructed from simple geographical consideration, the evolution equation for the distribution of subway passengers is foun
d to bear skew distributions including log-normal, Weibull, and power-law distributions. This approach is then applied to the Metropolitan Seoul Subway system: Analysis of the trip data of all passengers in a day reveals that the data in most cases fit well to the log-normal distributions. Implications of the results are also discussed.
One of Aesops (La Fontains) famous fables `The Ant and the Grasshopper is widely known to give a moral lesson through comparison between the hard working ant and the party-loving grasshopper. Here we show a slightly different version of this fable, n
amely, The Ant and the Metrohopper, which describes human mobility patterns in modern urban life. Numerous real transportation networks and the trajectory data have been studied in order to understand mobility patterns. We study trajectories of commuters on the public transportation of Metropolitan Seoul, Korea. Smart cards (Integrated Circuit Cards; ICCs) are used in the public transportation system, which allow collection of transit transaction data, including departure and arrival stations and time. This empirical analysis provides human mobility patterns, which impact traffic forecasting and transportation optimization, as well as urban planning.
The Metropolitan Seoul Subway system, consisting of 380 stations, provides the major transportation mode in the metropolitan Seoul area. Focusing on the network structure, we analyze statistical properties and topological consequences of the subway s
ystem. We further study the passenger flows on the system, and find that the flow weight distribution exhibits a power-law behavior. In addition, the degree distribution of the spanning tree of the flows also follows a power law.
