Lognormal distribution of daily travel time and a utility model for its emergence

Understanding the nature of human movement is important in many fields, such as transportation management, urban planning, and epidemiology. In this study, we focus on travelers who are grouped by their travel modes in the Tokyo Metropolitan Area. Notably, for each group of travelers, the distribution of daily travel time follows a lognormal distribution. For any travel mode, the distributions of normalized travel time for different years (1968–2008) and distances to the city center converge to a curve, although the average travel time and share of travel modes vary. By employing the concept of utility, we developed a disaggregate model wherein an individual maximizes utility from traveling (=benefit - cost) by modifying daily travel time. This model theoretically explained the observed distributions of travel time. The model was further used to demonstrate travel mode choices. The model parameters were estimated using the distribution of travel time, travel mode share, and manageable assumptions. These results provided interesting interpretations of the perceptual utility of the daily travel time of a population. Moreover, the obtained curves of utility versus time are similar to the shapes of the overall benefits assumed in previous studies. Overall benefit is a concept that has been developed and examined since the 1980s, and our study provides a mathematical foundation for this idea.