City-scale mass gatherings attract hundreds of thousands of pedestrians. These pedestrians need to be monitored constantly to detect critical crowd situations at an early stage and to mitigate the risk that situations evolve towards dangerous incidents. Hereby, the crowd density is an important characteristic to assess the criticality of crowd situations. In this work, we consider location-aware smartphones for monitoring crowds during mass gatherings as an alternative to established video-based solutions. We follow a participatory sensing approach in which pedestrians share their locations on a voluntary basis. As participation is voluntarily, we can assume that only a fraction of all pedestrians shares location information. This raises a challenge when concluding about the crowd density. We present a methodology to infer the crowd density even if only a limited set of pedestrians share their locations. Our methodology is based on the assumption that the walking speed of pedestrians depends on the crowd density. By modeling this behavior, we can infer a crowd density estimation. We evaluate our methodology with a real-world data set collected during the Lord Mayor's Show 2011 in London. This festival attracts around half a million spectators and we obtained the locations of 828 pedestrians. With this data set, we first verify that the walking speed of pedestrians depends on the crowd density. In particular, we identify a crowd density-dependent upper limit speed with which pedestrians move through urban spaces. We then evaluate the accuracy of our methodology by comparing our crowd density estimates to ground truth information obtained from video cameras used by the authorities. We achieve an average calibration error of 0.36 m-2 and confirm the appropriateness of our model. With a discussion of the limitations of our methodology, we identify the area of application and conclude that smartphones are a promising tool for crowd monitoring.

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Mobile on-body sensing has distinct advantages for the analysis and understanding of crowd dynamics: sensing is not geographically restricted to a specific instrumented area, mobile phones offer on-body sensing and they are already deployed on a large scale, and the rich sets of sensors they contain allows one to characterize the behavior of users through pattern recognition techniques.In this paper we present a methodological framework for the machine recognition of crowd behavior from on-body sensors, such as those in mobile phones. The recognition of crowd behaviors opens the way to the acquisition of largescale datasets for the analysis and understanding of crowd dynamics. It has also practical safety applications by providing improved crowd situational awareness in cases of emergency.The framework comprises: behavioral recognition with the user's mobile device, pairwise analyses of the activity relatedness of two users, and graph clustering in order to uncover globally, which users participate in a given crowd behavior. We illustrate this framework for the identification of groups of persons walking, using empirically collected data.We discuss the challenges and research avenues for theoretical and applied mathematics arising from the mobile sensing of crowd behaviors.2000 Mathematics Subject Classification. Primary: 68T10, 91-04, 91-02, 91D30, 62H30; Secondary: 91C20, 93A15, 93A30.

Abstract-The vast availability of mobile phones with built-in movement and location sensors enable the collection of detailed information about human movement even indoors. As mobility is a key element of many processes and activities, an interesting class of information to extract is movement patterns that quantify how humans move, interact and group. In this paper we propose methods for detecting two common pedestrian movement patterns, namely individual following relations and group leadership. The proposed methods for identifying following patterns employ machine learning on features derived using similarity analysis on time lagged sequences of WiFi measurements containing either raw signal strength values or derived locations. To detect leadership we combine the individual following relations into directed graphs and detect leadership within groups by graph link analysis. Methods for detecting these movement patterns open up new possibilities in -amongst others -computational social science, reality mining, marketing research and location-based gaming. We provide evaluation results that show error rates down to 7%, improving over state of the art methods with up to eleven percentage points for following patterns and up to twenty percentage points for leadership patterns. Our method is, contrary to state of the art, also applicable in challenging indoor environments, e.g., multi-story buildings. This implies that even quite small samples allow us to detect information such as how events and campaigns in multistory shopping malls may trigger following in small groups, or which group members typically take the lead when triggered by e.g. commercials, or how rescue or police forces act during training exercises.