Zipf’s power law in activity schedules and the effect of aggregation

Abstract

People’s behavior depends on extremely complex, multidimensional processes. This poses challenges when trying to model their behavior. In the transportation modeling community, great effort is spent to model the activity schedules of people. Remarkably however, the frequency of occurrence of day-long activity schedules obeys a ubiquitous power law distribution, commonly referred to as Zipf’s law. Previous research established the universal nature of this distribution and proposed potential application areas. However, these application areas require additional information about the distribution’s properties. To stress-test this universal power law, this paper discusses the role of aggregation within the phenomenon of Zipf’s law in activity schedules. Aggregation is analyzed in three dimensions: activity type encoding, aggregation over time and the aggregation of individual data. Five data sets are used: the household travel survey from the USA (2009) and from GBR (2009–2014), two six-week travel surveys (DEU MobiDrive 1999 and CHE Thurgau 2003) and a donated 450-day data set from one individual. To analyze the effect of aggregation in the first dimension, five different activity encoding aggregation levels were created, each aggregating the activity types somewhat differently. In the second dimension, the distribution of schedules is compared over multiple years and over the days of the week. Finally, in the third dimension, the analysis moves from study area-wide aggregated data to subsets of the data, and finally to individual (longitudinal) data.