An Exploration into the Power Law Phenomenon through the Numbers of Passengers of Taipei Metro Rapid Transit System

• Main Authors: Lin, Ming-Sheng, 林明生
• Other Authors: Lai, Shih-Kung
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/71669125923300971524

碩士 === 國立臺北大學 === 都市計劃研究所 === 97 === The metropolis is regarded as organized complexity, and has the phenomenon of self-organization, such as the power law distribution of populations. This study is to explore the power law phenomenon through the numbers of passengers of the Taipei Metro Rapid Transit System by stations. The phenomenon of power law is a stable pattern derived from “self-organization” of the complex system characterized by unrepeatability and uncertainty. The power law phenomenon is described as a linear relation between the scales and the frequencies in which the objects under consideration appear. Since this law was discovered by linguist George Zipf, the law has been discussed extensively. The phenomenon of power law is also discovered in both natural and social sciences, including scales of earthquakes and fluctuations of stock market prices. Many theories are being developed to explain the cause of it, but at present no satisfactory explanation exists. In this research, the significance of the power law is examined through linear regression. The data include the numbers of passengers of the TMRTS by stations from 2002 to 2007, and the resulting regression model is y=20.49409-0.97665x , where the slope of the function is -0.97665 and the adjusted r-squared is 0.7619. If the data include only the numbers of passengers of the TMRTS of the top 65% stations, the adjusted r-squared becomes 0.9643. As for the ranking dynamics, the research analyzes the growth and concentration ratios of the numbers of passengers of the TMRTS by stations from 2002 to 2007. The numbers of passengers of TMRTS by stations is classified into top10, 20, 30, 40, and 50 groups, and sorted in terms of five forms of dynamics to analyze the probability of ranking fluctuations. With Markov chain analysis and multiple linear regressions, the research forecasts the rankings of the numbers of passengers of the TMRTS by stations.