To discover regularities in human mobility is of fundamental importance to our understanding of urban dynamics, and essential to city and transport planning, urban management and policymaking. Previous research has revealed universal regularities at mainly aggregated spatio-temporal scales but when we zoom into finer scales, considerable heterogeneity and diversity is observed instead. The fundamental question we address in this paper is at what scales are the regularities we detect stable, explicable, and sustainable. This paper thus proposes a basic measure of variability to assess the stability of such regularities focusing mainly on changes over a range of temporal scales. We demonstrate this by comparing regularities in the urban mobility patterns in three world cities, namely London, Singapore and Beijing using one-week of smart-card data. The results show that variations in regularity scale as non-linear functions of the temporal resolution, which we measure over a scale from 1 minute to 24 hours thus reflecting the diurnal cycle of human mobility. A particularly dramatic increase in variability occurs up to the temporal scale of about 15 minutes in all three cities and this implies that limits exist when we look forward or backward with respect to making short-term predictions. The degree of regularity varies in fact from city to city with Beijing and Singapore showing higher regularity in comparison to London across all temporal scales. A detailed discussion is provided, which relates the analysis to various characteristics of the three cities. In summary, this work contributes to a deeper understanding of regularities in patterns of transit use from variations in volumes of travellers entering subway stations, it establishes a generic analytical framework for comparative studies using urban mobility data, and it provides key points for the management of variability by policy-makers intent on for making the travel experience more amenable.

Due to the limitation of data collection techniques and privacy issues, the problem of missing spatial origin-destination flows frequently occurs. Data imputation provides great support for the acquisition of complete flow data, which enables us to better understand regional connections and mobility patterns. However, existing models or approaches neglect the network structure of spatial flows, thus resulting in inappropriate estimates and a low performance. The development of graph neural networks offers a powerful tool to deal with graph-structured data. In this article, we proposed a spatial interaction graph convolutional network model, which combines graph convolution and a mapping function to predict flow data from the perspective of network learning. This model utilizes geographical unit embedding in local spatial networks to improve prediction accuracy. A negative sampling technique is adopted to reduce misestimation. Experiments on Beijing taxi trip data verified the usefulness of our model in spatial flow prediction. We also demonstrated that a biased training sample had a negative impact on the model’s performance. More attributes of geographical units, a more proper negative sampling rate and a larger training set can increase the prediction accuracy of flow data.

New smart card datasets are providing new opportunities to explore travel behaviour in much greater depth than anything accomplished hitherto. Part of this quest involves measuring the great array of regular patterns within such data and explaining these relative to less regular patterns which have often been treated in the past as noise. Here we use a simple method called DBSCAN to identify clusters of travel events associated with particular individuals whose behaviour over space and time is captured by smart card data. Our dataset is a sequence of three months of data recording when and where individual travellers start and end rail and bus travel in Greater London. This dataset contains some 640 million transactions during the period of analysis we have chosen and it enables us to begin a search for regularities at the most basic level. We first define measures of regularity in terms of the proportions of events associated with temporal, modal (rail and bus), and service regularity clusters, revealing that the frequency distributions of these clusters follow skewed distributions with different means and variances. The analysis then continues to examine how regularity relative to irregular travel across space, demonstrating high regularities in the origins of trips in the suburbs contrasted with high regularities in the destinations in central London. This analysis sets the agenda for future research into how we capture and measure the differences between regular and irregular travel which we discuss by way of conclusion.