Understanding the Spatial and Temporal Activity Patterns of Subway Mobility Flows

In urban transportation systems, mobility flows in the subway system reflect the spatial and temporal dynamics of working days. To investigate the variability of mobility flows, we analyse the spatial community through a series of snapshots of subway stations over sequential periods. Using Shanghai as a case study, we find that the spatial community snapshots reveal dynamic passenger activities. Adopting a dual-perspective, we apply spatial and temporal models separately to explore where and when individuals travel for entertainment. In the two models, microblog topics and spatial facilities such as food venues and entertainment businesses are used to characterise the spatial popularity of each station and people’s travelling perceptions. In the studied case, the city centre is characterised by greater social influence, and it is better described by the spatial model. In the temporal model, shorter travel distances motivate individuals to start their trips earlier. Interestingly, as the number of food-related facilities near the starting station increases, until it exceeds 1563, the speed of people’s journeys slows down. This study provides a method for modelling the effects of social features on mobility flows and for predicting the spatial-temporal mobility flows of newly built subway stations. Introduction Urban transport plays an important role in shaping and reflecting the evolution of cities. To create the desired socialeconomic outputs, urban transport planners use human mobility flows to understand the spatial-temporal interactions of people on transportation systems. An urban public transport network (UTN) consists of the mobility flows of an urban transportation system, where the nodes represent the public transit stand locations and the directional edges denote the mobility flows from one node to another. For example, in a subway network, each node denotes a subway station and each edge denotes the mobility flow between two nodes, weighted by the volume. The mobility flows dynamically change over time as people’s reasons for travelling change activities (e.g. work or entertainment). To measure the variability of spatial-temporal mobility flows, communities in a UTN (a community is a set of densely interconnected nodes that have few connections to outside nodes) are used to show the dynamic changes in UTN over time. Furthermore, a community snapshot is a snapshot of the communities in a UTN at a single point in time (e.g. a period, day or year). Community snapshots have many applications in transport planning, e.g. in urban development analysis, experts use them to quantify the influence of urban development on transportation networks; in urban dynamics analysis, experts use them to measure the variability of human mobility patterns; and in urban area analysis, experts use them to identify functional zones. The community method is not the only means of observing dynamic mobility flows; driven spatial-temporal models with high-order structures of activity patterns are also valuable in many scenarios. For example, in public transit scheduling and pricing, ticket prices are optimised to ease traffic congestion by influencing passengers’ driven models of temporal scheduling; in urban planning, cities can be planned according to valuable factors, i.e. factors that attract individuals’ decisions to live in a or visit a particular place. To further understand the dynamic decision-making processes that shape individuals’ spatial-temporal movements, we study dynamic mobility flows by measuring the variability in a heterogeneous sample of community snapshots in a UTN and explore the models that drive these patterns. We observe the dynamic mobility flows using community snapshots of different spatial stations over time. These flows exist in many public transit systems (e.g. shared bicycle systems, public bus systems and taxi systems). Here, we use a subway system, an important part of a public transport network, to demonstrate the use of community snapshots. As current static or aggregated mobility measures are robust to perturbations and cannot clearly reveal the variability of temporal community structures, communities patterns are commonly studied retrospectively to get a deeper understanding of how people’s activities change over time. Here, we study changes in the use of a subway system by detecting and comparing community snapshots from different time periods. Retrospective studies of community snapshots improve our ability to measure the mobility flows from the perspective of the network. However, they do not provide insight into the spatial-temporal models that drive the mobility dynamics. For the current day, we cannot determine where individuals would like to go, let alone when they would like to begin any of their activities. To address this issue, we also study the patterns of passengers’ movements between places as a high-order spatialtemporal structure. The examination of the activity patterns should answer two questions: (1) where do individuals travel to for their activities; and (2) when do people start their activities? For example, in the evening, can our models infer where and when a person is likely to go for entertainment after work? These studies will raise planners’ awareness of human movements between stations over different time periods. Specifically, the likelihood of an individual participating in an activity in a particular spatial-temporal space is associated with both the station’s spatial characteristics (such as population density and number of retail venues) and temporal characteristics (such as the day of the week and time of day). Previous studies of the where (spatial) dimension of intra-urban spatial mobility in public transit have typically focused on regional populations (such as Beijing, Shenzhen, London, Chicago, Los Angeles and Abidjan) and travelling distance (e.g. in Seoul). However, the correlation between public transit and its surrounding economic and social environment is obvious (such as in Biscay), especially the subway system (e.g. in Sao Paulo). Most of the existing studies focus on universal laws of human intra-urbanmobility, but neglect the influence of a heterogeneous spatial environment on activities over periods of time, and thus ignore the dynamics of universal mobility laws. Thus, the where (spatial) dimension can be studied by analysing individuals’ spatial movements as revealed by measurements of stations’ popularity in a heterogeneous spatial environment. Static information (such as population) cannot reflect dynamic spatial popularity over periods of time. Some studies have used individual digital traces to detect the urban magnetism of different places (e.g. in New York City). For example, location-based microblogs such as Twitter have been found to correlate with individuals’ profiles, spatial-temporal behaviour and preferences. Thus, in this study, each station’s spatial popularity is measured by the volume of spatial microblogs associated with it. The study uses a location-based mobility model based on the spatial microblogs of neighbouring stations to describe the heterogeneous spatial popularity of each station, i.e. its attractiveness to individuals. Existing studies of the when (temporal) dimension of passengers’ activities focus on factors in the traffic system such as trip fares, delay cost and travel distance, and on travel discomfort or congestion). They use a variety of methods such as the equilibrium equation to measure the effect of these factors. However, it is not enough to explain the dynamic uncertainty in individuals’ scheduling decisions, especially under the influence of a particular social and economic environment. A passenger’s travelling objective is to find an equilibrium between travelling comfort and schedule delay cost. Thus, differential equations can be used to model individuals’ decision-making processes regarding temporal activities that balance travelling comfort and delay cost. More specifically, a station’s perceived travelling comfort can be measured by the number of business buildings surrounding the station (for Seoul see and for Shanghai see). In addition, the perception of delay cost correlates with the distance between two places. Thus distance can be used to infer individuals’ perception of delay cost. In this way, we study the when (temporal) dimension of flows by considering the balance between travelling discomfort and delay cost. To characterise individuals’ perceptions, features such as spatial facilities are correlated with perceptions through a generalised additive model. In this study, we take the subway system of Shanghai as a case study. This dataset provides the detailed trace information of 11 million individuals over a one-month period, including check-in and check-out times for each subway trip. The aggregated data on the subway system are collected by the Shanghai Public Transportation Card Co. Ltd, and released by the organising committee of the Shanghai Open Data Apps. To examine the stations’ environments, we collect microblog data and information about the spatial facilities around each station from Baidu APIs and Weibo APIs for the studied month. In our case study, we first measure the variability of mobility flows by investigating the dynamic spatial-temporal community snapshots of the mobility flows. The community snapshots taken at different periods (morning, morning/afternoon and evening) do not agree with each other; the evening snapshots are particularly distinct. We further investigate the high-order structure of the evening activity patterns. The findings show that most individuals return home after work. Activity patterns with more edges are less common. In addition, we use spatial and temporal models to examine the effects of social factors on activity patterns. Specifically, in our examination of the where dimension, we find that the city centre has a higher social influence. This influence is better described by the spatial model, which illustrates heterogeneous spatial popularity. Finally, in the exploration of the when dimension, we find that the individuals tend to start their trips earlier when they travel shorter distances. Interestingly, if there are more food-related facilities (but no more than 1563) near the starting station, people are more likely to slow down their trip to avoid travelling discomfort. Our results deepen the understanding of spatial-temporal mobility flows in urban public transport networks by helping to model and estimate the spatial-temporal mobility flows. Specifically, we highlight the effects of social influences as measured by microblogs and spatial facilities.