Model Analysis for Evolution of Population and Railroad

Osamu Hirayama¹, Ryuji Takaki², Takeshi Koshizuka³ and Hiroshi Yanai⁴

¹Tokyo Metropolitan Agricultural High School, Kotobuki-cho 1-11, Fuchu, Tokyo 183-0056, Japan
²Faculty of Technology, Tokyo University of Agriculture and Technology, Nakamachi 2-24-16, Koganei, Tokyo 184-8588, Japan
³Department of Social Engineering, Tsukuba University, Tsukuba, Ibaraki 305-8573, Japan
⁴Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan

(Received September 17, 2001; Accepted October 22, 2001)

Keywords: Evolution, Population Density Distribution, Railway Network, Traveling Time, Uncomfortableness, Branching

Abstract. A model analysis is made for evolution of population distribution and railroad network based upon a mathematical model where the population density distribution is determined so that a quantity standing for the uncomfortableness of residents is minimized. It is assumed that a new interval of the railroad with a constant length is added when the total population increases and the average uncomfortableness exceeds a threshold value. The position of the new interval is chosen so as to minimize the total uncomfortableness. As a result the railroad network develops straight at first and makes branching later and loops are formed in the final stage. The mirror symmetry in the network tends to appear during the evolution.