Exploratory analysis of Zipf’s universal power law in activity schedules

Abstract

People’s behavior is governed by extremely complex, multidimensional processes. This fact is well-established in the transportation research community, which has been working on travel behavior (travel demand) models for many years. The number of degrees of freedom in a person’s activity schedule is enormous. However, the frequency of occurrence of day-long activity schedules obeys a remarkably simple, scale-free distribution. This particular distribution has been observed in many natural and social processes and is commonly referred to as Zipf’s law, a power law distribution. This research provides evidence that activity schedules from various study areas exhibit a universal power law distribution. To this end, an elaborate analysis using 13 household travel surveys from diverse study areas discusses the efect of proportional outlier removal on the power law’s exponent value. Statistical evidence is provided for the hypothesis that activity schedules in all these datasets exhibit a power law distribution with a common exponent value. The study proposes that a Zipf power law could be used as an additional dimension within a travel demand model’s validation process. Contrary to other validation methods, no new data is required. The observation of a Zipf power law distribution in the generated schedules appears to be a necessary condition. Additionally, the universal activity schedule distribution might enable the full integration of activity schedules in models based on universal mobility patterns.