以台北捷運系統車站進出人次規模探討冪次定律

都市被視為一複雜的有機體，具有自我組織的現象，終將呈現出一穩定的秩序結構，如冪次定律，考量研究資料的嚴謹性，是故本研究提出以台北捷運系統車站進出人次規模，來檢證冪次定律。冪次定律現象的產生，是複雜系統內「自我組織」後展現的穩定秩序結構，其主要乃是透過組織內的個體互動行為，突現出的不可測的秩序結構，模式充滿高度的「不可重複性及不確定性」，但個體之間具有自我相似性，透過系統的調適與學習，終將呈現一穩定的秩序結構。「冪次定律」乃是描述物件出現的規模與其出現的頻率，具有一直線關係，由語言學家George Zipf，發現此定律之後，引起廣泛的討論，包含自然科學及社會科學等許多領域，亦有發現此一現象，如地震規模、股市漲跌等，也有許多理論在探討其形成的背後機制，但目前為止尚未有令人滿意之解答。在冪次定律顯著性的檢證上，採用直線迴歸，並以西元2002年至西元2007年進出人次規模資料，取得迴歸式 y=20.49409-0.97665x ，冪次值為-0.97665，調整的r-squared為0.7619，本研究並發現如果資料採用前65%的車站進出人次規模資料，將會使調整的r-squared達到最高為0.9643。在排名流動性分析之部份，整理了台北捷運系統在西元2002年至西元2007年有關進出人次規模的成長率與集中率。並且透過排名分組為前十大、前二十大、前三十大、前四十大及前五十大，輔以五種排名流動狀況－新進該組、名次上升、名次不變、名次下降及退出該組，探討排名流動之機率，同時建構馬可夫鏈模式，形成移轉機率預測矩陣，再加上透過多元線性迴歸模式，針對個別車站的排名加以預測。

關鍵字

冪次定律；自我組織；排名流動；台北捷運系統

並列摘要

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.

並列關鍵字

power law ； self-organization ； ranking dynamics ； Taipei Metro Rapid Transit System

參考文獻

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2.王昱智、呂正中及賴世剛（2008），「冪次定律普遍性與恆常性－以台灣之天然災害規模為例」，2008年全國災害危機處理研討會，長榮大學，台南

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6.Zipf, George K.(1949),＂Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology＂， New York: Addison-Wesley Press.

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以台北捷運系統車站進出人次規模探討冪次定律

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