Spatial distribution of traffic in a sector-shaped city under radial–arc routing system – an analysis on the optimum assignment of road area for designing a congestion-free city

In this paper, we introduce a sector-shaped city to describe the spatial distribution of traffic over a city that contains a geographical barrier across which a journey cannot be made. Travelers are assumed to choose the shortest path on closely spaced radial roads and concentric arc roads. We seek to investigate how the radial–arc road network pattern affects the distribution of traffic within a city. To formulate the traffic distribution, we obtain the density of traffic volume passing through a segment or an arc that is perpendicular to the road network, i.e. an arc road and a radial road. As an application to planning a congestion-free city, necessary road space is assigned in each small area in accordance with the traffic volume passing through that area. By examining each small area within an entire city, optimum distribution of road area density is derived.