  Traffic congestion at urban-scale levels occurs when road network supply is
insufficient compared with demand. Therefore, the relationship between supply
and demand has been extensively investigated in the literature. Especially the
impact of a network's topology (i.e., connectivity) on traffic congestion has
been widely studied. On the other hand, only a few studies analyze the
relationship between the physical shape of the road network (i.e., morphology),
demand, and congestion. For example, angular indicators associated with links
and trips can be utilized to characterize such morphology. However, statistical
analysis of angular indicators requires a specialized methodology called
Directional Statistics, and how to apply Directional Statistics to traffic data
is not obvious. Here, this study develops a descriptive model of traffic
congestion based on Directional Statistics. It describes direction-dependent
congestion levels using angular distributions that characterize the shape of
road network and travel demand. Specifically, the shape of road network is
characterized by the distribution of angles of each road link in a specific
region. Likewise, the travel demand is characterized by the distribution of
angles of each trip in the region. Then, a statistical model that describes
travel time for a trip with arbitrary direction by these two angular
distribution is constructed by paying special attention to the fact that roads
and demands from all angles would affect congestion. A simple estimation method
for the proposed model is also presented. Finally, the model was estimated
using actual data in Tokyo, and the relationship between the characteristics of
the shape of the road network, the direction of demand, and congestion is
analyzed from the new perspective of angles.
