With over half of the world population living in cities, concerns about urbanization, socio-economic development, and well-being call for a better understanding of the spatial distributions of facilities and population. The information age and the online mapping revolution allow us to study and better understand the interactions of humans with their built and natural environment. Pioneering work in multi-city studies have uncovered scaling laws relating population to distribution of facilities and socioeconomic activities at macroscopic scale. It has been asserted, for example, that more populated cities are more efficient in their per capita consumption and their occupation diversity can be modeled as social networks embedded in space. Yet, a systematic understanding of the interplay of the urban form, their facilities distribution and their accessibility at multiple scales remains an elusive task.
In this work, we gain novel insights of the interplay between the distribution of facilities and the distribution of population to maximize the overall accessibility in the existing road networks. We compare the accessibility in the optimal and actual scenarios at multiple scales: At block level, we uncover the disparities and identify blocks that are affected by the actual planning. At city scale, we compare the benefits of the current distribution of diverse types of facilities and cities. Results of six cities in the U.S. and the Gulf Cooperation Countries reveal the travel costs could be reduced in half through optimally redistributing facilities. Also, in the optimal scenario, we observe that large facility densities hinder the existence of a theoretical two-thirds power law relating the density of facilities to density of population they serve. In the optimal scenario, we systematically study the average accessibility given the empirical range of facility densities, the population distribution and the road network. We find that the average travel distance to the nearest facility can be modeled as a function of the number of facilities and the urban form. As an application of this finding, it is possible to estimate the number of facilities needed for a target accessibility.