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

Abstract

Abstract: Modeling people's behavior in e.g. travel demand models is an extremely complex, multidimensional process. However, the frequency of occurrence of day-long activity schedules obeys a ubiquitous power law distribution, commonly referred to as Zipf's law. 1 This paper discusses the role of aggregation within the phenomenon of Zipf's law in activity schedules. Aggregation is analyzed in two dimensions: activity type encoding and the aggregation of individual data in the dataset. This research employs four datasets: the household travel survey (HTS) NHTS 2009, two six-week travel surveys (MobiDrive 1999 and Thurgau 2003) and a 24-week set of trip data which was donated by one individual. Maximum-likelihood estimation (MLE) and the Kolmogorov- Smirnov (KS) goodness-of-fit (GOF) statistic are used in the “PoweRlaw” R package to reliably fit a power law. To analyze the effect of aggregation in the first dimension, the activity type encoding, five different activity encoding aggregation levels were created in the NHTS 2009 dataset, each aggregating the activity types somewhat differently. To analyze aggregation in the second dimension, the analysis moves from study area-wide aggregated data to subsets of the data, and finally to individual (longitudinal) data.