コンパクトな直方体都市の数理モデル--人口成長からみた短期と長期の移動効率 (特集都市のコンパクト化を考える)

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In this article, we consider the proportion of a rectangular city consisting of buildings which locate on dense lattice points in a square region. Each travelling route is suposed to consist of vertical route in building (s) and recti-linear route on the surface of the earth. The study is to find the shapes of the city which minimizes three values:(i) the average;(ii) the variance;(iii) the maximum value, of travelling time of office workers. For a many-to-many uniform trip pattern and many-to-one uniform trip patterns, the optimal proportions are derived.And then, we will formulate the optimal proportion model associated with population growth. This model is to explain the difference between a short-term and long-term optimizations, which has been one of the main issues in urban planning.