Size Distribution of Building Lots and Density of Buildings and Road Networks: Theoretical Derivation Based on Gibrat’s Law and Empirical Study of Downtown Districts in Tokyo

Abstract

The concept of density lacks the ability to explain the diversity of physical elements of urban form such as building lot sizes. Thus, urban planners tend to discuss the validity of density values without taking into consideration the variation of building lot sizes due to the limited data available on building lot shapes. Our objective is to discuss the potential of building density and road network density in order to estimate the size distribution of building lots at the district scale in downtown Tokyo. The study finds that (1) building lot sizes approximately follow the lognormal distribution whose parameters, mean, and variance are formulated by gross building density, the coefficient of variation of building lots, road network density, and average road width by removing large building lots and (2) the value of the coefficient of variation is approximately equal to one. As a practical problem, we discuss how to determine the maximum building density by considering the variation of building lot sizes. It was found that the maximum building density can be determined based on a stochastic approach. These findings are expected to provide urban planners with a theoretical basis for discussing the validity of density values.