Optimisation of building and road network densities in terms of variation in plot sizes and shapes

Urban form at the district scale is defined as a unique combination of the following basic spatial objects: road networks, plot patterns and building configurations. In particular, a plot represents one of the most important basic spatial objects of urban form. In recent theoretical and empirical work from downtown districts in Tokyo, it was found that (1) plot sizes and frontages approximately follow a log-normal distribution and (2) the parameters can be primarily estimated by building density (the number of buildings per unit area) and road network density (total length of road networks per unit area). High demand for housing and commerce in a district requires as many buildings and their plots as possible. However, this may generate many small and narrow plots, which makes the residential environment worse in terms of ventilation, sunlight and accessibility to a road. Hence, the ratio of the number of plots that cannot satisfy minimum criteria regarding their sizes and frontages should be as small as possible, taking into consideration the variation in plot sizes and frontages. Therefore, the rationale for the building and road network densities presented here will be discussed by considering the variation in plot sizes and frontages through a stochastic approach. Allowing for plot sizes that are smaller than the minimum plot size regulation as well as for plot frontages that are narrower than the minimum plot frontage regulation (these minimum criteria being determined by Japanese building codes), the maximum building density and optimal road network density will be obtained. These findings are expected to provide urban planners with a theoretical basis to discuss the validity of these two density values (based on the deterministic approach that assumes uniform urban form) in terms of evaluating the policy effect, such as minimum plot size and frontage regulation.