As an increasing proportion of the world’s population are migrating to urbanized areas, many metropolitan cities are facing many serious socio-economic problems, such as frequent traffic congestion, unexpected emergency events, and tragic human-made disasters, to list a few [1
]. Many of these problems are caused by huge urban crowd flows, specifically referring to the gathering process of a flock of moving objects (e.g., vehicles, pedestrians) towards specific destinations during a given time period via different travel routes [2
]. As a large-scale gathering of urban crowds involves potential threats to public safety [3
], it is crucial to inform city planners, municipal managers, and other stakeholders of the risk at an early stage. Understanding the gathering process of urban crowd flows can help mitigate the risk in case the situation evolves towards a dangerous incident.
At present, with the assistance of the growing number of Global Positioning System (GPS) trackers installed in vehicles and the widespread penetration of mobile devices (e.g., smart-phones, tablets) equipped with positioning modules, we are able to capture digital traces from individual citizens in space and time directly and easily [4
]. The use of GPS trackers and mobile positioning devices as sensor probes substantially overcomes the main drawbacks of traditional monitoring systems (e.g., fixed sensors, video cameras), namely, limited coverage of the geographical space and high costs of installation and maintenance [5
]. It therefore enables us to observe, quantify, analyze, and predict the level of crowdedness of residents in nearby urban areas by measuring dynamic population density at arbitrary locations and identifying densely populated routes in the road network [6
]. As a result, the spatio-temporal characteristics of urban crowd flows (e.g., average speed significantly lower than normal speed and space occupancy significantly higher than normal situation) have been deeply explored [7
]. Taking vehicular movements as an example, a branch of transportation studies has highlighted the formation process of road traffic congestion in urban areas as well as its social, economic, and environmental impacts on urban life [8
]. Moreover, the inherent daily rhythms of urban mobility dynamics largely lead urban crowd flows to be nonrecurrent in the short-term, recurrent in the long-term, and correlated in geographical space [11
]. These facets have already served as fundamentals for the modeling and prediction of urban crowd flows in many practical applications.
However, the existing studies typically assume or neglect morphological correlations of crowdedness, leaving the spatio-temporal evolution patterns of urban crowd flows largely untouched [12
]. Indeed, there is an urgent need for identifying, analyzing, and modeling the morphological evolutionary patterns of urban crowd flows. This will provide insights into citywide population concentration (e.g., road traffic congestion), on what factors are correlated in urban crowdedness, and how crowdedness propagates from one place (e.g., road, block) to another. Facilitated by this information, we will be able to build various applications including road planning, traffic prediction, and congestion management, just to name a few. To fill the gap of current studies on urban crowd flow analysis, we propose a novel method to model the morphological evolutionary patterns of urban crowd flows and validate it under both synthetic and real-world data scenarios.
The remainder of this article is organized as follows. In Section 2
, we review and summarize existing research works on the analysis of urban crowd flows in terms of visualization, identification, prediction, and correlation. In Section 3
, we elaborate on the methods for delineating morphological changes of urban crowd flows. In Section 4
, we validate the proposed methodology under both simulation and real-world scenarios. In Section 5
, we highlight our primary contributions, summarize the research findings, and discuss potential limitations.
2. Related Work
Analyzing the spatio-temporal distribution of urban crowd flows is a long-standing research focus. In metropolitan cities, crowd flows are influenced by the complex land uses and frequent mass gatherings, so it is more likely to form a crowded hotspot in a limited range of space and time [13
]. Several studies have investigated this phenomenon by counting instant population via camera videos [14
], telecommunications [15
], social media footprints [16
], and other ubiquitous sensing techniques. At the citywide scale, existing studies on urban crowd flow analysis can be generally categorized into four major strands concentrating on visualization, identification, prediction, and correlation.
Visualization techniques (e.g., isosurface and kernel density map) qualitatively reveal the macro-patterns of urban crowd flows as well as the micro-patterns of an individual trajectory to inform stakeholders about where and when crowded areas are formed, developed, and moved on one or several frequent routes [17
]. Yet, it is nontrivial to quantitatively perceive the level and state of crowdedness directly from point and flow density-based visualizations [19
]. Quantitatively, crowd density is the most important metric to evaluate the criticality of crowd situations by locally counting the population per unit area [20
]. Local areas where urban inhabitants are likely to congregate over the predefined density threshold can thus be detected for careful monitoring during an event to secure crowd safety [21
]. Supplemented by mobility flow mapping [23
], the visualization paradigm informatively and intuitively depicts urban dynamics such as where people are converging within the city over the course of a day and how people occupy and travel through certain urban spaces as a response to special events [24
]. Nonetheless, the local crowd density alone is insufficient for a comprehensive assessment of the criticality of a crowd situation. Many other factors related to urban crowds are adopted for a properly situational understanding, including the local speed variance, the local environment dependence, and the movement intentions [25
]. Considering that individuals typically perform with high mobility in a sparse region but, in contrast, move slowly with densely neighboring crowds, the crowdedness of a spot has also been taken as a non-density-based measurement in terms of the instant, maximum, and minimum moving speeds [26
]. This intertwined relationship between the moving speed of individuals and the crowd density [27
] eventually led to the combination of both density and speed for better identification of urban crowd flows [28
]. In particular, computer scientists have developed many efficient tools for querying densely populated regions in spatio-temporal databases [29
Beyond visualization and identification, many efforts have also been devoted to the accurate prediction of crowd density at a citywide level for the early preparation of emergent crowd situations in the real world [32
]. The basic rationale is that late arrivals in urban crowds are predictable based on the historical observations of inhabitants arriving early to attend gatherings [33
]. With longitudinal observations, the crowd population distribution can be predicted based on the diurnal dynamic changes as well as the sources and sinks of the observed population movements [34
]. Recently, deep-learning frameworks (e.g., convolutional neural networks, long short-term memory) have provided novel and promising tools for coupling periodicity, trends, residuals, and spatial locality into the prediction of urban crowd dynamics [35
]. Yet, to make previous implicit methods interpretable, the mechanisms beneath the spatio-temporal formation and propagation processes of urban crowd flows are of vital importance. Fortunately, urban crowd flows manifest significant spatial and temporal correlations [36
], as they usually have daily and weekly periodic patterns as well as instantaneous responses due to environmental and social conditions [37
]. For instance, adjacent crowded spots have strong interactions with each other, and a crowded spot remains crowded in consecutive time periods [38
]. A great deal of research has formed a macroscopic description of urban crowd flows and their propagation in time and space based on crowd simulation [40
] and traffic flow theories [41
]. Particularly, the emerging multiple sources of data enable urban crowd correlation to be captured, mined, and analyzed in very fine spatial and temporal granularities (e.g., road segments, street blocks) [42
]. However, the existing literature on urban crowd propagation in large-scale networks mainly focuses on graphical representations of crowdedness without a metric or a dynamic model [44
To support spatio-temporal modeling, there exists a rich body of research works on the evolution of spatio-temporal phenomena in the domain of Temporal GIS [46
]. Many popular models have been developed based on raster-oriented, event-oriented, and spatio-temporal object-based perspectives [48
]. Most of these models describe natural phenomena (e.g., wildfire, rainfall) without considering the human activities involved (e.g., traffic congestion, urban crowds) [50
]. For natural phenomena, thematic characteristics are represented as attributes of spatial objects and further utilized to associate objects for tracking their spatio-temporal changes [51
]. Under this scenario, an attribute denotes a single object (i.e., one-to-one mapping). Yet, to the best of our knowledge, the situation is substantially different for urban crowd modeling as there are fundamental differences between natural phenomena and human activity. For human activities (e.g., urban crowd flow), an object is a spatially cohesive region with similar attribute and a specific attribute might contain multiple objects (i.e., one-to-many mapping) [52
]. Considering that target objects (i.e., crowd regions) are not readily traceable by their attributes between consecutive time frames, additional research efforts are therefore required to intuitively represent the dynamics of urban crowds’ emerging and spreading in order to enable the real-time control of critical gathering regimes in urban environments. It is also noteworthy that existing spatio-temporal data models seldom quantify the spatio-temporal changes from the nested perspective (i.e., to support the monitoring of multiple levels of crowdedness). In summary, to fill the aforementioned research gaps, all the factors related to urban crowd visualization, identification, and correlation need to be taken into consideration integrally for the analysis of urban crowd flows.
5. Discussion and Conclusions
Understanding the spatio-temporal characteristics of urban crowd flows is of great importance to traffic management and public safety, and is very challenging because it is affected by many complex factors, including spatial dependencies, temporal dependencies, and external conditions. Our proposed method for modeling urban crowds’ morphological evolutionary patterns was validated for its ability to define urban crowd levels, derive urban crowd regions, quantify their morphological changes, and delineate the morphological evolutionary patterns with both synthetic and real-word data scenarios. In particular, we note several merits of our proposed framework in its generalization ability. As it is raster-oriented, it requires no support from spatial relation operation or spatio-temporal databases. The morphological changes can be easily traced by matrix algebra and can be clearly visualized in space and time. This will enable us to identify and understand the gathering process of urban crowd flows in an informative and intuitive manner. Moreover, the proposed framework will provide an important input for spatio-temporal phenomena modeling that heavily relies on raster-based models (e.g., the popular cellular automaton analysis). With regard to applications, the proposed framework enabled us to detect hotspots towards which potential traffic of moving objects are gathering. Supplemented with urban road networks, traffic congestion becomes traceable for transport network optimization by considering when and where the congested areas form and disappear. Beyond road traffic, the proposed framework is applicable to diverse human mobility activities (e.g., the crowdedness of pedestrians or animals), and thus could provide valuable insights into commercial facility allocation, the risk of trampling events, and many other urban and non-urban problems. Based on the proposed methodology, abnormal evolution patterns as well as emergent crowd incidents with different severity will also become detectable.
Although promising, we have also noticed several further directions and limitations in our research work. On the one hand, urban crowd flows are affected by temporal dependencies and external conditions, which results in significant short-term variations. Specificaaly, the crowd rate is parameter-dependent and might vary in different urban environments. In this sense, the sensitivity analysis of the morphological evolutionary patterns of urban crowd flows under different environmental conditions should be tested. Our proposed methodology can be easily applied to other cities, and the parameters can be determined according to the research context (e.g., spatio-temporal characteristics of the urban transportation network). From a methodological perspective, the cell size of the grid should be determined by ad hoc applications. The cell size should be chosen based on the spatial scale of the crowd phenomenon of interest and, probably, in a heuristic manner. A large cell size usually results in morphological characteristics spanning large spatial areas, whereas a small cell size enables us to zoom into crowded regions concentrated at specific spots. Urban crowd flows are also long-term recurrent in terms of morphological changes, which might be modeled and predicted by a deep-learning framework in the future. Besides, we have to admit that urban crowd flows are mainly distributed over urban road networks. For more accurate monitoring of urban crowd flows in finer spatial granularity, the urban mobility data should be map-matched onto the underlying road network under common circumstances. Consequently, crowd density should be adjusted with an appropriate mechanism by adopting an adaptive crowd rate based on the road density within cells. Meanwhile, the evolution patterns of urban crowd flows on road networks should be delineated and modeled in the constrained geographical space, which will be a nontrivial task to accomplish. Another strategy could be to adopt small grids for densely populated areas and large grids for sparsely populated areas. We believe that the quad-tree might be a good strategy for adaptive spatial partitioning and accelerating the computation process. We look forward to generalizing our calculation process for the quad-tree structure in future work.
Finally, data representativeness (e.g., sampling bias, data sparseness, and positioning accuracy) is also a critical factor for reliable urban crowd flow analysis [59
]. Considering that taxi data is a biased sample of the real population distribution, the derived congestion regions might deviate from the real urban crowd flow patterns. For instance, the crowdedness associated with taxicabs significantly underestimated the real mobility of urban inhabitants at Jianghan Road in our case study. With regard to the robustness of the proposed indices, if the input data are continuously recorded, there is no uncertainty in the calculation. However, in practice, mobility data are collected in discrete timestamps. We usually interpolate those discrete points to obtain a continuous trajectory or set the time unit to be greater than the sampling interval. However, the uncertainty cannot be eliminated. Data fusion on different types of flows (e.g., mobile phone data, social media data, transportation data) might be an efficient solution in our future works.