Analysis of the Road Traffic Based on SPCP

The transportation of people and goods has been necessary in any society for thousands of years. In modern times, transportation has become a foundation component of human activity. A great deal of problems related to traffic and transportation have been ingeniously resolved in the past and perhaps an even greater number of problems will have to be overcome in the future. Now it has been realized that more and more problems connected to traffic congestion, especially road traffic congestion in relation to the type of road networks, need to be understood and controlled. There exist many types of road networks in urban cities, and among these networks some road segments are crowded with cars while others are not. To evaluate the phenomenon quantitatively, Oyama and Taguchi [7][8] devised the SPCP (shortest path counting problem) and gave an approach that reflects the crowdedness of each road segment with respect to some special type networks. This approach has been examined to be effective by applying them to several real cities in Japan (Oyama and Taguchi [9]), and recently, some related studies such as Li [4], Oyama [6], Oyama and Morohosi [10], have also been done on the topic. However, the existing studies do not give further discussions on the fundamental properties of SPCP such as the maximum value, the expectation and the variance etc. accompanied with the shape of a road traffic network, and they do not consider the direction of a road segment, which may not be neglected in a real road traffic network. Here, in this paper, by considering two idealized typical networks — grid type networks, which are common in North American cities and radial circular type networks, which usually appear in traditional European cities, we discuss some useful properties of the above two road networks from the viewpoint of SPCP. Moreover, using the obtained results, we also compare and examine their