Gravity model in the Korean highway

We investigate the traffic flows of the Korean highway system, which contains both public and private transportation information. We find that the traffic flow Tij between city i and j forms a gravity model, the metaphor of physical gravity as described in Newton’s law of gravity, PiPj/r 2 ij , where Pi represents the population of city i and rij the distance between cities i and j. It is also shown that the highway network has a heavy tail even though the road network is a rather uniform and homogeneous one. Compared to the highway network, air and public ground transportation establish inhomogeneous systems and have power law behaviors. Copyright c © EPLA, 2008 Introduction. – Complex network science has been an active interdisciplinary research field and the methodology of physics is applied into many interdisciplinary researches [1–7]. Numerous real-world networks have been investigated, and scaling laws and patterns have been observed in nature, society, and so on [8–10]. Transportation network has attracted a lot of interests, particularly many public transportation systems. Amaral et al., Barrat et al., and Guimerà et al. [11–13] have found small-world behaviors and truncated power law cumulative degree distribution P (k)∝ kf(k/kx) with the exponent α= 1.0 from world-wide airport network. Moreover, the airport networks of India [14] and China [15] have shown small world behaviors. The Indian and Chinese airport networks are characterized by small average path lengths (〈l〉 ≈ 2) and large clustering coefficients (c > 0.6). However, the degree distribution of the Indian network follows a power law and that of the Chinese a truncated power law. Latora et al. [16] studied the Boston public transportation system including subway and bus, and Seaton et al. [17] compared the underground system of Boston to that of Vienna. The network efficiency defined as a mean value of inverse distances between nodes has been analyzed, and that of the two systems, Boston and Vienna, shows a good correspondence regarding the value of average degree, but other properties such as clustering coefficient and network size have shown differences. Sienkiewcz et al. [18] analyzed the public transport systems in Poland and observed similar features with other works. Brockmann et al. [19] studied human traveling statistics in the United States by analyzing the circulation of bank notes. They described the dispersal bank notes and human travels by a continuous-time random-walk process that incorporates scale-free jumps as well as long waiting times between displacements. At present, the studies on the traffic systems have usually been focused on the public transportation system. Collecting the data for the public system is much easier than that for private travels. In fact, it is almost impossible to keep tracking of each traveler. However, the Korean highway has a special toll system. First of all, all Korean highway are toll roads. Each and every exit has a toll plaza, and every car’s traveling information including the exit number that comes in and goes out is reported. Therefore, we can keep tracking of the travel information of a single car. We investigate the traffic flows on the Korean highway, and identify a gravity model. The traffic flow Tij between city i and j is proportional to PiPj/r 2 ij , where Pi represents the population of city i and rij the distance between two cities, i and j. We also find that the highway network including both the information of the public and private transportation has a heavy tail but not the power law behavior, even though the road network is a rather uniform and homogeneous one like random network [20], compared to air and public ground transportation networks which establish inhomogeneous systems and have power-law behaviors [12,21]. The Korean highway system. – We investigate the traffic flows between cities on the Korean highway system. The data used is the total amount of traffic during the