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(1)AGH University of Science and Technology in Krakow Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering. PhD Thesis. Jakub Porzycki. Data-driven modeling of crowd dynamics. Supervisor: dr hab. in˙z. Jaroslaw Was, , prof AGH. Kraków 13 May 2019.

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(3) AGH Akademia G´ orniczo-Hutnicza im. Stanis¸sawa Staszica w Krakowie Wydzial Elektrotechniki, Automatyki, Informatyki i In˙zynierii Biomedycznej. Rozprawa doktorska. Jakub Porzycki. Modelowanie dynamiki tlum´ ow oparte na danych. Promotor: dr hab. in˙z. Jaroslaw Was, , prof AGH. Kraków 13 May 2019.

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(5) I would like to express my gratitude to my supervisor - Prof. Jaroslaw Was , for sharing his knowledge and for all wise advices I received. Also, I’m very grateful to my wife for her support and patience..

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(7) Streszczenie. Glównym tematem pracy doktorskiej o tytule ”Data-driven modeling of crowd dynamics” (”Modelowanie dynamiki tlum´ ow oparte na danych”) jest metodyka analizy, rozumienia i modelowania dynamiki tlum´ ow w oparciu o rzeczywiste dane opisujace olny , zachowanie pieszych. Szczeg´ nacisk polo˙zono na wykorzystanie tego podej´scia bezpo´srednio w definiowaniu modelu dynamiki tlumów. Metodyka ta zdobywa coraz wieksz a, popularno´sć w zwiazku z upowszechnieniem sie, , , róz˙ nego rodzaju czujnik´ ow i sensor´ ow oraz rozwojem metod analizy obrazów i sygnalów. W niniejszej pracy przedstawiono, przeprowadzone przez autora, badania eksperymentalne dotyczace sasiadami w tlumie oraz podejmowania decyzji o roz, przestrzennych relacji pomiedzy , , poczeciu ewakuacji. W´sr´ od najwa˙zniejszy wyników tych eksperymentów warto wymienić: wyzna, czenie typowych pozycji najbli˙zszych sasiad´ ow w tlumie wraz z ksztaltem strefy wokól pieszego , gdzie inni piesi nie moga, sie, znajdować, zdefiniowanie regul, które moga, tlumaczyć wzajemne relacje pomiedzy sasiadami w tlumie, analize, podejmowania decyzji o rozpoczeciu ewakuacji , , , w zale˙zno´sci od warunk´ ow ´srodowiskowych oraz rekomendacje, uwzglednienia gruboziarnistego , rozkladu przestrzennego czas´ ow rozpoczecia ewakuacji w symulacjach dynamiki pieszych. , Kolejnym elementem pracy jest opis metodyki modelowania dynamiki pieszych w oparciu o dane wraz z przykladami jej wykorzystania w wybranych zagadnieniach. Opisana zostala symulacja sterowana danymi, gdzie reprezentacja pieszych w symulacji jest tworzona w czasie rzeczywistym w oparciu o dane z sensorów. Opisano przykladowe metody definiowania nowych testów walidacyjnych dla modeli dynamiki pieszych w oparciu o wyniki eksperymentów. Najwa˙zniejszym elementem pracy jest nowy model dynamiki pieszych, zdefiniowany przy wykorzystaniu powy˙zszej metodyki. Zaproponowano model agentowy, oparty na siatce automatu komórkowego, wykorzystujacego koncepcje, tzw. Floor Fields– pól potencjalu wplywajacych na , , ruch pieszych. W modelu u˙zyto trzech takich pól, odpowiedzialnych za: nawigacje, do wybranego punktu (Static FF), awersje, do statycznych przeszkód (Wall FF) oraz proksemike, (Interplay FF). Trzecie pole - modelujace pieszymi jest nowym, oryginalnym , relacje przestrzenne pomiedzy , elementem. W jego definicji bezpo´srednio wykorzystano wyniki eksperymentów. Wla´sciwo´scia, wyr´ oz˙ niajac , a, zaproponowany model, jest parametryzowalna dyskretyzacja przestrzeni. W innych modelach opartych na automacie komórkowym zmiana rozmiaru kom´ orki wia˙ scia). W zaproponowanym modelu rozmiar ,ze sie, ze zmianami logiki modelu (np. funkcji przej´ komórki jest parametrem (o warto´sciach z zakresu od 1 do 50 cm). Jest to mo˙zliwe dzieki u˙zyciu , bezcielesnego” agenta, kt´ ory zawsze zajmuje jedna, komórke, automatu i modelowania faktycznej objeto´ c latwo rozszerzony. , sci pieszego poprzez pole Interplay FF. Przedstawiony model mo˙ze by´ W niniejszej pracy uwzgledniono rozszerzenia pozwalaj ace na uwzgl ednienie pieszych o róz˙ nych , , , rozmiarach i ksztaltach oraz modelowanie urazów pieszych w przypadku wysokich gesto´ sci tlumu. , W opinii autora przedstawiona praca opisuje oryginalne, warto´sciowe naukowo elementy. Do najwa˙zniejszych z nich nale˙za:, opis metodyki modelowania dynamiki pieszych opartej na danych, nowy model dynamiki pieszych ze zmienna, dyskretyzacja, przestrzeni, definicja nowego pola w automacie kom´ orkowym opisujacego relacje proksemiczne pomiedzy pieszymi oraz wnioski z eks, , peryment´ ow dotyczacych podejmowania decyzji o rozpocz eciu ewakuacji i relacji przestrzennych , , pomiedzy sasiadami w tlumie. , ,. 7.

(8) 8. J. Porzycki Data-driven modeling of crowd dynamics.

(9) Abstract. The main topic of the dissertation titled: ”Data-driven modeling of crowd dynamics” is a methodology of analysis, reasoning and modeling of crowd dynamics on the basis of real data on pedestrians behavior. Special attention is given to the application of this approach directly to crowd dynamics model definition. Popularity of data-driven methodology growths with increasing number of different kinds of sensors and development of image and signal analysis methods. This allows for easier than ever gathering data on pedestrian dynamics, both in controlled experiments and in real-life observations. The dissertation describes results of conducted experiments on the spatial relations between neighbors in crowd and the decision making process on evacuation start. Among the most important results of these experiments, it is worth mention: finding the most probable positions of nearest neighbors in crowd (including the shape of ”the forbidden zone” around a pedestrian), finding of rules explaining observed mutual spatial relations between neighbors in crowd, analysis of decision making process on evacuation start according to environmental properties and finally a recommendation of including the coarse spatial distribution of pre-movement time into crowd dynamics models. The subsequent element of this work is a description of data-driven modeling of crowd dynamics methodology. The example of data-driven simulation is presented, where pedestrian representation in simulation is created in near real-time on the basis of sensor data. Also, new validation test based on experimental results are proposed. The most important part of the dissertation is a novel crowd dynamics model, defined with the usage of above-mentioned methodology. Proposed model utilizes agents located on the lattice of Cellular Automata (CA), constructed using the concept of Floor Field (FF) – a set of gradient potential fields influencing agents movement. In the model three such fields are used, namely: Static FF - responsible for navigation to agents’ point of interest, Wall FF – a repulsive influence with obstacles and Interplay FF - which models proxemics effects. The third field, which models mutual relations between pedestrians is a new, original element. Experimental results from previous sections are used directly for its definition. The property that distinguishes the proposed model is a variable space discretization. In other models based on cellular automata, any change of cell size is related with the changes of model’s rules (e.g. its transition function). In the described model the cell size is an adjustable parameter, with available values from 1 cm to 50 cm. It is possible with the usage of unbodied agents, which always occupies only one cell of cellular automata and the modeling of actual pedestrian volume with Interplay FF. The model is easily extendable. In this work two extensions are described: agents with different sizes and shapes and the injury modeling in case of high crowd density. According to the author, this dissertation describes original and scientifically valuable elements. Among the most important of them it is worth noting: a description of data-driven modeling methodology, new model of crowd dynamics with variable space discretization, the definition of Interplay FF on the basis of experimental results and finally conclusions from experiments on decision on evacuation start and spatial relations between neighbors in crowd.. 9.


(11) Table of contents. 1. Introduction ................................................................................................................... 2. Related works ................................................................................................................ 2.1. The evolution of crowd dynamics modeling .............................................................. 2.2. Microscopic models with continuous space representation........................................ 2.3. Cellular Automata based models .............................................................................. 2.3.1. Lattice gas models ......................................................................................... 2.3.2. Basic models using Floor Field...................................................................... 2.3.3. Floor filed extensions..................................................................................... 2.3.4. Static floor field calculation........................................................................... 2.3.5. Space discretization and CA lattice............................................................... 2.3.6. Agent based modeling and CA...................................................................... 2.3.7. Applications of CA based crowd dynamics model......................................... 3. Crowd dynamics experiments .................................................................................... 3.1. Granularity of pre-movement time distribution ........................................................ 3.1.1. Pre-movement time - a crucial component of evacuation simulation ............ 3.1.2. Pre-movement time Coarse Spatial Granularity hypothesis .......................... 3.1.3. Announced fire drill of lecture hall................................................................ 3.1.4. Egress of football stadium tribune ................................................................ 3.1.5. Unannounced fire drill in academic building ................................................. 3.1.6. Unannounced evacuation of bus during fire drill in tunnel ........................... 3.1.7. Experiments conclusions................................................................................ 3.2. Pedestrians’ spatial self-organization ........................................................................ 3.2.1. Pedestrians mutual interaction - an origin of self-organization phenomena .. 3.2.2. Source of empirical data ................................................................................ 3.2.3. Concept of nth nearest neighbor.................................................................... 3.2.4. Distances to nth nearest neighbors ................................................................ 3.2.5. Spatial distribution of nth nearest neighbors................................................. 3.2.6. Angular distribution of nth nearest neighbors ............................................... 3.2.7. Result discussion and conclusions.................................................................. 4. Data-driven approach in pedestrians dynamic modeling ..................................... 4.1. Methodology overview .............................................................................................. 4.2. Observation and gathering data................................................................................ 4.3. Online data-driven simulation................................................................................... 4.3.1. Gathering pedestrian trajectories using depth map sensor ........................... 4.3.2. Pedestrians parameters calculation .............................................................. 4.3.3. Driving a simulation with real data .............................................................. 11. 13 17 17 17 18 18 18 19 19 20 21 21 23 23 23 23 24 24 26 28 29 30 30 31 31 32 33 34 36 39 39 40 41 41 42 43.

(12) TABLE OF CONTENTS. 12. 4.4. Verification and validation of models........................................................................ 4.4.1. Group coherence testing ................................................................................ 4.4.2. Influence of discretization error on flow ........................................................ 4.4.3. Grid rotation and discretization error ........................................................... 4.5. Defining crowd dynamics models based on experimental data ................................. 5. Cellular automata model of crowd dynamics with variable space and time discretization.................................................................................................................. 5.1. Motivation................................................................................................................. 5.2. Model definition ........................................................................................................ 5.2.1. Overview........................................................................................................ 5.2.2. Formal definition ........................................................................................... 5.2.3. Floor field calculation.................................................................................... 5.2.4. Static Floor Field .......................................................................................... 5.2.4.1 SFF calculation algorithm . . . . . . . . . . . . . . . . . . . . . . 5.2.4.2 SFF anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4.3 Static Floor Field and variable cell size . . . . . . . . . . . . . . 5.2.5. Wall Floor Field ............................................................................................ 5.2.5.1 Wall penetration in CA models . . . . . . . . . . . . . . . . . . . 5.2.5.2 Wall Floor Field calculation method . . . . . . . . . . . . . . . . 5.2.5.3 Influence of variable cell size on Wall Floor Field . . . . . . . . . 5.2.6. Interplay Floor Field ..................................................................................... 5.2.6.1 Physical component of Interplay Floor Field . . . . . . . . . . . 5.2.6.2 Psychological component of IFF . . . . . . . . . . . . . . . . . . 5.2.6.3 Total IFF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6.4 Interplay Floor field and variable cell size . . . . . . . . . . . . . 5.2.7. Agent representation - position ..................................................................... 5.2.8. Agent transition function and time discretization ......................................... 5.2.9. Fundamental diagram analysis ...................................................................... 5.3. Optional improvements to the model........................................................................ 5.3.1. Corrections for diagonal movement ............................................................... 5.3.2. Inertia............................................................................................................ 6. Extensions of the model .............................................................................................. 6.1. Agents with different shapes and sizes...................................................................... 6.2. Modeling pressure and injuries ................................................................................. 7. Summary.......................................................................................................................... 44 44 45 45 46 49 49 50 50 51 52 53 54 55 55 57 57 58 59 62 63 64 66 67 68 69 71 71 72 73 75 75 76 81. J. Porzycki Data-driven modeling of crowd dynamics.

(13) 1. Introduction. Crowd dynamics modeling and simulation is a constantly developing research area. The main aim of this research is to define a mathematical model that would able to reproduce a behavior of walking pedestrians in different situations. With continuous advancements in the area of crowd dynamics modeling, the number of applications of these models is quickly broadening. Currently, such models are used as a supporting tool during the building design processes, as a training tool for LEAs (Law Enforcement Agencies), in virtual experiments for dangerous situations, but also serve wide range of other purposes. The growing popularity of crowd dynamics simulations and increasing area of its applications indicates the necessity to simulate more and more complex situations and behaviors. Early approaches to crowd dynamics modeling were focused on, so called: macroscopic approach, where the crowd is modeled as a whole. Individual occupants were not differentiated. These types of models are typically based on gas-kinetics or hydrodynamics theory and focused on general parameters like flow and density. An opposite approach, a microscopic one - where each pedestrian is modeled individually, was developed at the turn of the XX and XXI centuries. Nowadays, this approach for modeling pedestrian dynamics is without any doubt the most popular method. Classic division line for microscopic models takes into consideration space representation: continuous or discretized. Among models which use continuous space representation, the most popular are models from the family of Social Force Model[43]. Similarly, majority of models that use space discretization is based on Cellular Automata and Floor Fields[11]. The transition between macroscopic and microscopic approaches was caused mostly by the increasing efficiency and performance of computers, which allows on using more computationally demanding microscopic models. Currently, a similar change in crowd dynamics methodology is beginning as a result of rapid development of devices, tools and methods that allows for easy gathering of pedestrian movement data. This new approach, where data on pedestrians dynamics are used in the whole modeling process, is called a data-driven modeling of crowd dynamics, which is main topic of this dissertation. Nowadays, data about pedestrians’ behavior can be gathered using vast number of methods. To begin well-established methods like video camera image, processed either with hands-on methods or with automatic image processing. In case of more specialized scenario a 3D camera, depth map sensors or infrared camera can be used. Alternative methods employ various kinds of tokens carried by pedestrians. Among all tokens, the most popular are mobile phones that allow on pedestrian tracking with the use of GPS, Bluetooth, Wi-Fi or infrared positioning. Substantial amount of gathered data on pedestrians’ movement allows on improving the course and the results of crowd dynamics simulations. This work describes the data-driven approach for modeling of this process. It is presented how data gathered during experiments or real time events, can be used in the different stages of the crowd modeling and simulation process. Among others, the crowd data can be used in: model calibration and validation, (both of which are most popular and well-established applications of such data), process of defining a 13.

(14) 14. new model or upgrading an existing one and finally in so called data-driven simulations 1 . This work provides examples of experimental data application in all of these areas. A simple online data-driven simulation is presented, where pedestrians’ trajectories are detected via depth map sensors and send directly for simulation. Also, new validation tests based on experimental results are described. However, a special focus is given to the model definition and improvements on the basis of experimental data. In this dissertation a new model of crowd dynamics is presented. The model is based on the results of conducted experiments. In this research experiments and observations are focused on two areas: the process of decision-making on evacuation start and its coarse granularity as well as the phenomenon of pedestrian self-organization according to the nearest neighbors position. On the basis of executed experiments and real world observations, a set of rules is proposed that can explain observed pedestrians behavior. The model definition is based on these rules. Therefore, the model is in fact a data-driven model. In the proposed model, pedestrians’ behavior is modeled by agents moving on the lattice of cellular automata. Underlying lattice of cellular automata is a main driving factor for the pedestrians and is constructed with the use of the Floor Filed concept. Floor Field used in the model consists of three sub-fields. One of them - Interplay Floor Field is a novelty defined directly on the basis of experiments2 . The unique feature of the model is a variable space discretization. It is introduced into the model in order to simulate the phenomenon of pedestrians self-organization according to the neighbors position. The size of cellular automata cell can be set to any value from the reasonable range for pedestrian dynamics, i.e. all cell size up to 50 cm are allowed. It is worth noting, that despite the variable space discretization, there are no non-local conflicts between agents, which is a unique property among CA crowd dynamics models with cell size smaller than pedestrian size. It is obtained with the usage of two factors, namely: a repulsive effect of Interplay Floor Field - that prevents agents from collisions, and a specific representation of agent as a one cell - regardless of space discretization. Definition of the model is easily extendable. Thus, a number of extensions are shortly described. Pedestrians with varying shapes and sizes can be easily simulated. The model allows for a natural way to simulate a force between agents, pressure and eventually injuries, that can occurs in case of the dense crowd. The following chapters of the dissertation are organized as follows. Chapter 2 is a review of previous works and papers related to crowd dynamics modeling. A special emphasis is given to the models based on cellular automata, since this type of model is used in further parts of dissertation. A series of experiments are presented in the Chapter 3. Described experiments focus on two aspects of pedestrians behavior, it is: on the coarse spatial granularity of premovement time and the phenomena of pedestrian self-organization according to the nearest neighbor. Chapter 4 looks into the methodology of the data driven modeling in the context of crowd dynamics modeling. It is demonstrated how the methodology can be applied to different stages of modeling process. A crowd dynamics model that reflects the experimental results is defined in details in the Chapter 5. Chapter describes the authors motivation to develop a model with variable space discretization. It also introduces a formal model definition, comprehensive explanation of how all components of Floor Field are calculated, a description of agent transition function. Finally, an analysis of simulation results using this model is provided, with a particular focus on the 1. One should distinguish between data-driven model, which is a model defined on the basis of experimental data, and data-driven simulation - a simulation that uses real-world data on pedestrian movement as an input data source 2 The field is to some extent similar to the Proxemics Floor Field, which was previously used by Ezaki et al.[21] and Leng et al.[68]. However, Interplay Floor Field proposed in this dissertation differs significantly from this approaches. Models described in that papers[21, 68] are summarized in Section 2.3, while Interplay Floor Field used in the proposed model is explained in details in Section 5.2.6.. J. Porzycki Data-driven modeling of crowd dynamics.

(15) 15. differences introduced by changes in space discretization. Proposed extensions for the model are described in Chapter 6. Finally, Chapter 7 concludes the work.. J. Porzycki Data-driven modeling of crowd dynamics.


(17) 2. Related works. 2.1. The evolution of crowd dynamics modeling A science of predicting crowd behaviors originates from the hand calculations of evacuation time for the building design process, e.g. the ASET-RSET1 analysis[52]. In these methods a set of equations is used in order to calculate basic parameters of crowd evacuation. Typically, that equations take into consideration the relation between maximal flow and the required size of evacuation routes as well as the expected evacuation time[76]. Next step in the evolution of the crowd dynamics modeling is an introduction of a computer models. At the first stage, these models are defined with the assumption that the dynamics of a crowd can be described with mathematical tools similar to the used for physical phenomenons. Crowd dynamics are usually simulated with models based on gas-kinetics[19, 48] or hydrodynamics[15, 51]. This family of methods is known as a macroscopic, since they do not differentiate the individual pedestrians, but model the crowd as a whole. Typically, a macroscopic model focuses on general relations between crowd density and velocity. The state of the crowd is described by these two parameters locally averaged over space and time. To some extent, this approach is accurate, especially in case of high crowd densities. Number of research confirms that for large densities crowd behaves very similarly to liquid[42, 45]. On the other hand, macroscopic models are limited to certain sets of applications. They do not take into account the individual behavior and decision of pedestrians. Experiment shows they are typically less accurate than microscopic models, but usually more computationally efficient[7]. Next improvement in crowd dynamics modeling is the introduction of microscopic models e.g.[11, 13, 16, 21, 43, 60, 77, 78, 84, 113, 118, 137], where behavior of each pedestrian is modeled individually. The first models of that kind use a continuous space representation, while shortly later a cellular automata models with space discretization appear2 . Finally, an introduction of autonomous agents[3, 4, 123, 127] allows on simulation of pedestrians individual properties (like desired speed, size) and behaviors (path choices or leader role). Research described in this dissertation focuses on microscopic models with space discretization. Vast majority of these models are based on cellular automata. Therefore, the special focus is given to such a models in further parts of the literature review.. 2.2. Microscopic models with continuous space representation Models with continuous space representation constitute a significant fraction of all crowd dynamics models. Their popularity is caused by their high accuracy and ability to mimic crowd behavior in both sparse and dense crowds. An important drawback of this kind of models is their high computational cost[7], thus their application for large scale or real-time simulation is limited. Among these models, the most popular are models based on Social Force Model 1. ASET - Available Safe Egress Time, RSET - Required Safe Egress Time One of the rare exeption from this rule is model propsed by H¨ anseler et al.[37], which combines macroscopic representation of crowd with space discretization. 2. 17.

(18) 18. 2.3. Cellular Automata based models. (SFM)[13, 30, 22, 43, 41, 44, 67, 137, 138], however last years a number of models based on other concepts were introduced, that also use continuous space representation. Social Force Model (SFM) was introduced in 1995, by famous paper of Helbing and Molnár[43]. In this model a pedestrian movement is driven by superposition of attraction and repulsive forces. Resultant force vector affects pedestrians direction and acceleration. With the further improvements[41] and[44] it quickly becomes one of the most established model for microscopic crowd dynamics simulation. Number of researchers develop this model and adjust it to specific situations. Influence of relative velocity between pedestrians was considered in Centrifugal SFM[13, 137]. Ability to predict further positions of other pedestrians is introduced in [30]. Optimal parameters calculations, especially time step, for SFM is discussed in [67]. Overtaking is introduced to SFM in [138], while group cohesive force and heading force are proposed in[22]. Currently, Social Force Model is recognized as one of the most reliable and well-established crowd dynamics models. It is also worth to mention other models, not related with SFM, which uses a continuous space representation. Among others, the Optimal Step Model proposed by Seitz et al. [105, 104, 102] is focused on the rules behind the individuals stepping. Köster and Zönnchen[64] proposed an interesting extension for this model where, by modification of space utility function they achieve a reliable queuing behavior. Tordeux and Chraibi[117] proposed a model focused on collision avoidance.. 2.3. Cellular Automata based models 2.3.1. Lattice gas models First crowd dynamics models based on cellular automata were proposed in the end of the last decade of the XXth century. Muramatsu et. al[78] proposed a simple lattice gas model, in order to investigate a jamming transition in a counter flow. They defined two types of agents: right and left walkers. Each walker could move with equal probability to one of its adjacent cell, except of the occupied cells and stepping back (e.g. right walkers can not move left). Maniccam [77] expanded that model, with the use of the hexagonal lattice. He showed that qualitative results are similar for both grid types - similar phase transition occurs, while quantitative results can be affected by grid type. Models of crowd dynamics, where pedestrian movement rules are defined only by local neighbors configuration can be used for simulation in simple geometries (e.g. flow in a corridor, room evacuation - see references in [77]). However, because of the lack of navigation mechanism, such models can not be adopted for real-life scenarios and more complex geometries. Currently, such models are rarely utilized, in most cases only for experimental setups, where they are applied to well-defined, simple geometry e.g. [108].. 2.3.2. Basic models using Floor Field Breakthrough in CA-based crowd dynamic modeling has came with the publication of Burstedde et. al[11], where the concept of Floor Filed is proposed. Floor field can be understood as second layer of grid cell, which drives pedestrian movement according to chosen factors. In the original paper, the authors introduce two types of Floor Fields, namely: Static Floor Field (SFF) and Dynamic Floor Field (DFF). Static Floor Filed represent a gradient potential field that leads pedestrians to the areas with the higher utility, e.g. doors. SFF is unaffected by pedestrian movement. Contrary to SFF, the Dynamic Floor Field is designed to model the long-range interaction between pedestrians. Its definition is similar to chemotaxis which occurs among ants. Each pedestrian leaves the so called boson of pheromones. These pheromones are the subject of diffusion and decay. J. Porzycki Data-driven modeling of crowd dynamics.

(19) 19. 2.3. Cellular Automata based models. Final floor field is calculated as a sum of two above-mentioned fields3 . SFF drives pedestrians to attraction points, while DFF is responsible for their mutual following behavior. It is worth mention, that in the same paper [11] authors propose the standard grid size (40 x 40 cm), on the basis of typical space occupied by a pedestrian defined by Weidmann [133].. 2.3.3. Floor filed extensions Since its publications in 2001, Floor Field Model[11] has quickly become the most popular, well-established approach in CA-based crowd modeling. New types of Floor Fields have been proposed, to take into the consideration, various factors influencing the pedestrian movement. Nishinari et. al[84] introduced the Wall Floor Field, to model the repulsive force between a pedestrian and a wall cell or an another obstacle. Each cell representing a wall is surrounded by repulsive field, which declines with distance away from this cell. Application of Wall Floor Field brings more realistic space utilization around obstacles and reduces jamming in corners. Type of repulsive field is also introduced by Ezaki et. al[21] as a method to model proxemic effect in a crowd. Proxemic Floor Field (PFF) is proposed to model pedestrian tendency to preserve a given distance to others, if it is possible. This floor field allows on reliable inflow simulation. Similarly, Anticipation Floor Field proposed by Suma et. al [113] is also dedicated to repulsive forces between pedestrians. In contrast with PFF, the AFF is used for moving pedestrians. This field models pedestrians ability to prevent collision in advance. Value of Floor Field in front of moving pedestrians is increased in order to lower the probability that someone will intrude its path. Kirik et al.[62] introduced chosen cognitive aspects into the FF model. An approach to include forces in CA crowd dynamics models in made by Henein and White [47]. They defined Force Field as a lattice of so called force bosons - directional particles, that can spread in dense crowd. Finally, pressure in the cell is described by actual number of bosons. Pressure can affect pedestrians movement, as well as cause their injuries. Similar concept of force transition between pedestrians was also presented in [34]. It is worth noting the concept of inertia in CA models. It is pedestrian preference for maintaining current movement direction. In part of the models[11, 84, 128, 108, 68], additional parameters or preference matrix is introduced. In this manner the probability that a pedestrian will continue movement in previous direction rises. This inertia parameter influences the transition probability function for the pedestrians located at Floor Filed.. 2.3.4. Static floor field calculation In recent years a lot of attention was devoted to Static Floor Field calculation methods. SFF defines pedestrians preferences in choice of next desired cell and paths to attraction points, thus its calculation method strongly influences pedestrians behavior in quantitative and even qualitative way. Multiple papers[84, 118, 65, 131, 8, 35] show that pedestrian movement can be significantly influenced by factors like: the neighborhood type (Moore/von Neumann), metric used to SFF calculation, penalty for diagonal movement and representation of attraction point on the grid. Differences in clogs shape between Manhattan and Dijkstra metrics are shown in[84]. In a similar fashion, Varas et. al[118] analyze flow through a bottleneck for various metrics and neighborhoods. That research was extended in [35], which investigates a different penalties for diagonal movement and the influence of stray - a movement to the cell with the identical value of a static field. Movement isotropy in terms of number of cells covered by a pedestrian in one simulation step, in various neighborhoods and pedestrians, was in [65]. Same issue of movement 3. In this thesis the author assumes that gradient in Static Floor Field is negative - i.e. the lowest values are assigned to points of interest. Therefore each floor field that models attractive factor, includes negative value to total floor filed, while repulsive factors include positive values.. J. Porzycki Data-driven modeling of crowd dynamics.

(20) 20. 2.3. Cellular Automata based models. isotropy is raised in [8], where an optimal penalty for a diagonal movement is calculated to maximize the movement isotropy. In [84] the issue of wide doors is mentioned. In such cases, pedestrians have a tendency to prefer one of the door sides as a desired point, instead of its center4 . The authors proposed a simple solution of a contraction mechanism, i.e. shrinking of a door width, during the SFF calculation. Same issue of wide doors, is also investigated in details by Wei et. al[131], where Virtual Reference Point is introduced. An artificial attraction point located behind the doors brings a better utilization of wide exits.. 2.3.5. Space discretization and CA lattice In the original paper by Burstedde et. al [11], authors proposed the usage of same size of pedestrians and lattice cell of 40 x 40 cm. Since that publication, substantial number of researchers has adopted this approach[84, 118, 131, 108, 35, 62]. Similar standard solution assumes the cell and pedestrian size of 50 x 50 cm [113, 9, 123]. It should be stressed that there are no differences in simulation of pedestrians behavior, introduced by the cell size difference itself. However, the differences occur in the simulation result interpretation. A cell size 40 cm allows on maximal density 6.25 persons , while for cell size 50 cm maximal density is 4 persons . Also, the m2 m2 movement speed is affected by this choice. When a pedestrian performs three steps in one second m of simulation, its speed is 1.2 m s for cell size 40 cm and 1.5 s in case of cell size 50 cm. In the paper by Kirchner et al.[60] models with typical cell size 40 x 40 cm, are compared with finer cell discretization of 20 x 20 cm. In both cases, the size of a pedestrian is 40 x 40 cm. It is shown that finer discretization leads to increased flow. Simultaneously, it causes a non-local conflicts between agents, which do not appear in case of standard grid size. In the same paper the authors analyzed influence of agent speed higher than one cell per one simulation time step on the fundamental diagram generated by the model. Over the course of last years many models adopted the concept of finer discretization of cellular automaton cell and pedestrian that could occupy more than one cell. Among others it is worth to mention a work by Was s [128, 127]. In this model the grid size is 25 x 25 , and Luba´ cm, while pedestrians are represented by ellipses (major axis = 45 cm, minor axis = 27 cm). As predicted by Kirchner such a representation leads to non-local conflicts, that have been utilized by authors to introduce proxemic effects. Forbidden and allowed states are declared according to pedestrian orientation and compressibility coefficient. Another approach to model proxemic effect is proposed in the paper by Feliciani and Nishinari [25], where sub-mesh adds new available positions for agents. An agent is allowed to move into a position on the sub-mesh only when one waits long enough without movement on regular mesh. This in turn allows increasing maximal density over 10 persons with use of standard grid size (40 x 40 cm). m2 Finer space discretization with cell size of size 13.3 x 13.3 cm is proposed in [34], however an agent was still modeled as a 40 x 40 cm square. Even finer space discretization is used by Samardy et al.[98]. Authors use cell size equals to 5 cm, while agents are represented as an ellipse projection to 5 x 5cm grid. Different projection is exploited for different agent orientation on the grid. Finally, it is worth noting the paper by Leng et al. [68], where hexagonal grid with sides equals to 20 cm is proposed. In this model pedestrians are represented as rectangles of size (60 x 34.6 cm) and they can move with different speeds depending on individual update frequency 1 s ). (multiple of basic frequency 24 4 For the majority of the grid cells, the side of doors is their closest possible desired cell with static floor value equals to 0.. J. Porzycki Data-driven modeling of crowd dynamics.

(21) 21. 2.3. Cellular Automata based models. Table 2.1: Comparison of chosen CA crowd dynamics models. Muramatsu et. al 1999 Burstedde et. al 2001 Maniccam 2003 Nishinari et. al 2004. Lattice. Vmax. square. 1. square, 40 x 40 cm. 1. square. 1. square, 40 x 40 cm. 1. Floor fields -. Neighborhood. Time step -. Inertia. von Neumann. Update procedure random. static, dynamic -. Moore. parallel. 0.3s. yes. -. random. -. -. static, wall. von Neumann. parallel. -. yes. -. 2.3.6. Agent based modeling and CA Currently, the common approach is using an Agent Based Modeling (ABM) rooted on the basis of Cellular Automata. It has been described as Situated Cellular Agents by Bandini et al.[3]. In this concept, autonomous agents are placed on the Cellular Automaton grid. Each agent has its own perception capabilities and set of possibles actions. One should notice that in most cases this models also use the Floor Field. Using ABM approach, one can diversify the agents parameters and abilities. Among them pedestrians’ speed is most often diversified parameter. Usually it is achieved by different update frequency [68, 9] or different number of step(cells) allowed during one time step [60, 128]. Ability to differentiate agents perception and possible actions gives opportunity to attach roles to agents. For example Vihas et al. [120] considers follow the leader. behavior using simple model where agents perception and actions depends on its location in the group. It should be noted, that it is hard to distinguish between heterogeneous CA and Agent Based Modeling situated on CA. Formal description of these models can be represented, both as set transition rules in CA as well as agents’ perception - action/reaction mechanism in the environment defined by CA gird and Floor Field.. 2.3.7. Applications of CA based crowd dynamics model Crowd dynamics models based on Cellular Automata can be used for various purposes, from simple crowd dynamics experiments to large-scale simulation. For example, Shimura et al.[108] used simple CA model that incorporates only a few transition rules (not using Floor Filed) to analyze a mobility of elderly pedestrians. Ezaki et al. [114] use model with static and dynamic field to investigate pedestrian behavior in a single segment of the bottleneck in case of stable inflow. On the other hand, agent based approach situated on cellular automata can be used for real life, large-scale simulation. Vizarri et al. [121] proposed a model that involves an attraction force between group members and repulsive force from other pedestrians to simulate pilgrim transportation (like queuing to the trains) during the Hajji. Version of their model dedicated to large-scale evacuation is also presented by Was , et al. in series of papers [127, 4]. Cellular automata models are known from its simplicity and efficiency. Due to the rapid development in the last years, this kind of models becomes a real alternative to other microscopic methods, even for the Social Force Models. Comparison of chosen CA models is presented in Tables 2.1 and 2.2. Additional analysis of chosen aspects of CA models is provided, with the proposed model description in the chapter 5.. J. Porzycki Data-driven modeling of crowd dynamics.

(22) 22. 2.3. Cellular Automata based models. Table 2.2: Comparison of chosen CA crowd dynamics models, continuation of Table 2.1 Lattice Kirchner et. al 2004. square, 40 x 40 cm and 20 x 20 cm. Varas et. al 2007 Henein and White 2007. square, 40 x 40 cm. Floor fields higher static, dythan namic 1 1 static. square. 1. Kirik et. al 2007 Guo and Huang 2008. square, 40 x 40 cm. 1. square, 13.3 x 13,3 cm, agent 40 x 40 cm square, 5 x 5 cm. 1. square. 1. Suma et. al 2012. square, 50 x 50cm. 1. Was , and Luba´s 2013. square, 25 x 25 cm, agents represented by ellipses square square, 40 x 40 cm. 1. square, 50 x 50 cm. Samardy et. al 2010 Ezaki et. al 2012. Vihas 2013 Wei et. al 2014 Bukáˇcek and Hrabák 2014 Shimura et. al 2014 Leng et. al 2014. Gwizdalla 2015 Vizzari et. al 2015 Feliciani and Nishinari 2016. Vmax. von Neumann. Update procedure random. Moore. parallel. Time step 0.3s and 0.15s 0.4s. static, dynamic, force static, dynamic static, dynamic, force static. von Neumann. parallel. -. -. von Neuman. parallel. 0.3s. -. von Neuman. random. 0.3s. yes. Moore. sequential. 0.025s -. Moore. sequential. -. -. von Neumann. parallel. -. -. Moore. parallel. 0.125s yes (max). von Neumann von Neumann. -. -. 1. static, dynamic, proxemic static, dynamic, anticipation static, dynamic, wall static static, dynamic static. Moore. complex[9] 0.31s. square, 40 x 40 cm. 1. -. Moore. random. hexagonal, side = 20 cm, agents are rectangles (57.9 x 33 cm) square, 40 x 40 cm. 1. static, wall, proxemic. -. parallel. 1. static. 1. static. sequential, 0.4s random random 0.33s. -. square, 50 x 50 cm. von Neumann, Moore von Neumann. square, 40 x 40 cm, with sub-mesh. 1. static, dynamic, wall, anticipation. Moore. parallel. -. 1. 1 1. Neighborhood. Inertia -. -. -. 0.25s yes (max) 1/24s yes (max). 0.29s. J. Porzycki Data-driven modeling of crowd dynamics. -.

(23) 3. Crowd dynamics experiments. 3.1. Granularity of pre-movement time distribution 3.1.1. Pre-movement time - a crucial component of evacuation simulation Pre-movement time is defined by SFPE Handbook of Fire Protection and Engineering as an interval between the time at which the alarm signal is given and the time at which the decision is made and a person starts evacuation process [18]. In microscopic crowd dynamics simulations it is usually implemented as a delay after which individuals start evacuation. Typically, the only assumption is that the distribution of these time delays for all evacuees should fall into a given pattern (uniform, normal, log-normal, exponential distribution) [94, 143]. Moreover, this is the only requirement for models, concerning pre-movement time, given by well-established documents that describes validation and verification procedures, like IMO 1238 Guideline [53], NIST Technical Note 1822[95] and RIMEA group reccomendation[33]. Although there is general agreement that pre-movement time is one of the crucial components in evacuation simulation, the issue of its spatial distribution is typically omitted1 . Next sections provide the evidences for coarse spatial granularity of pre-movement time distribution during normal condition egress and evacuation scenarios. On top of that, it is demonstrated that this phenomenon can significantly affect the process of evacuation and should be included in crowd dynamics models. This has previously been investigated in the paper [12].. 3.1.2. Pre-movement time Coarse Spatial Granularity hypothesis General idea behind the Coarse Spatial Granularity hypothesis is presented in Fig 3.1. Classical approaches consider pre-movement time, as time of pedestrians’ independent decision to begin evacuation. This omits the influence of: neighbors, pedestrians group and the leader. Such approach results in fine spatial granularity, which is presented in Fig 3.1a. Please note each individual makes decision on starting the evacuation independently. Contrary to the above-mentioned matter, Coarse Spatial Granularity hypothesis states that: pedestrians make a decision to start evacuation in groups. They are mutually influenced by their behaviors, as a neighbor or leaders. Decision to trigger movement is made in similar time by people located in neighbouring area, as shown in Fig. 3.1b. This give rise to coarse spatial granularity of pre-movement time. Moreover, since many people start moving simultaneously, one can expect higher values of instantaneous flow and density. To verify the hypotheses stated in this section, analysis of four experimental cases is conducted, namely: • announced fire drill of the lecture hall, • normal condition egress of football stadium tribune, • unannounced fire drill of academic building, 1 In this point, it is worth noting the paper of Rogsch et al. [94] where authors investigate influence of premovement time on different floors to density on a staircase.. 23.

(24) 24. 3.1. Granularity of pre-movement time distribution. (a) Fine spatial granularity.. (b) Coarse spatial granularity - pre-movement time is similar for pedestrians in nearby area.. Figure 3.1: Comparison between classical approach (A) and stated hypothesis (B). Individuals are represented as dots, the greener the dot, the shorter pre-movement time. Source: own figure [12]. • unannounced evacuation of a bus during fire drill in the tunnel. The comparison of results and observations from these four experiments allows for determining if and when hypothesis of Coarse Spatial Granularity of pre-movement time is true and what the factors that trigger such phenomena.. 3.1.3. Announced fire drill of lecture hall First experiment was conducted in the large lecture hall, with 450 participants. Also informed consent was insured - participants were aware of fire evacuation procedures. Participants were young (AGH University students), prepared for evacuation and able to see each other2 . Thus, the pre-movement time was extremely short. First person stood up after one second after the alarm went off, and the last after six seconds. Consecutive stages of evacuation are presented in Fig. 3.2, t = 0s represents the time when the alarm siren begins. The exact moment, when the alarm siren starts (t = 0s) is presented in Fig. 3.2a. All participants are sitting. 2.5s after the signal (Fig. 3.2b) one can notice that part of evacuees remain on their initial position, but there is a number of minor groups that already stood up. All participants started the evacuation until 6 seconds (Fig. 3.2c). Rapid reaction of people generates queuing and clogging in front of the exit, as presented in Fig. 3.2d. It is worth noting that in this case, due to the fast and synchronized reaction of participants, coarse spatial granularity is only weekly visible at t = 2.5 (Fig. 3.2b). It can be noticed that there are separated groups of people siting and standing. In the rest of the figures all participants remain seated (Fig. 3.2a or already stood up (Figs. 3.2c and 3.2d). Nevertheless, in this case the discussed phenomenon is barely observable and not conclusive.. 3.1.4. Egress of football stadium tribune Another observation was carried out during normal condition egress of football fans from one tribune of the stadium after the match. The tribune consists of five sectors with total capacity of 5806 persons. During the observed event it was filled with approximately 5000 persons. Consecutive stages of egress are presented in Fig. 3.3. 2. They were all in the one lecture hall.. J. Porzycki Data-driven modeling of crowd dynamics.

(25) 25. 3.1. Granularity of pre-movement time distribution. (a) t = 0s. (b) t = 2.5s. (c) t = 6s. (d) t = 25s. Figure 3.2: Four stages of announced evacuation of lecture hall. Source: own figure [12].. (a) t = 0s. (b) t = 2 min 53s. (c) t = 4 min 28s. (d) t = 9 min 34s. Figure 3.3: Four stages of egress from football stadium tribune. Source: own figure [12].. It is assumed that t = 0s is the exact moment when the match ends. At this moment one can observe differences in behavior between whole tribunes. All the people on the observed tribune stay on their places for another 46 seconds until they finish singing the club anthem (Fig. 3.3a). J. Porzycki Data-driven modeling of crowd dynamics.

(26) 3.1. Granularity of pre-movement time distribution. 26. At three other tribunes (not shown in any Figure) fans begin to move towards the exits just after the referee’s final whistle. In the second stage, the are significant differences in behavior between sectors. Majority of fans from border sectors (first and last) start moving right after the anthem. Contrary to this, vast majority of the fans from three central sectors still remain on their places to express recognition to the team. Only small groups from central sectors began leaving early (Fig. 3.3b). Note that at the same time some clogs in front of exits appears - people standing around exits already started to move. After 4 minutes, one can observe coarse spatial granularity of pre-movement time within sectors. In Fig. 3.3c there are cohesive groups of fans, close to large spots of unoccupied seats. In case of fine spatial granularity o pre-movement time, one would rather expect a uniform, sparse crowd without cohesive groups and empty spots. Finally in (Fig. 3.3d), when most of the fans already leave the tribune, one can observe isolated groups remaining on their position waiting for clogs by the exit to disappear. The last fans on the tribune remain on its seats until the tribune is practically empty, so the maximal pre-movement time is almost equal to total evacuation time - approximately 16 minutes. In this example one can observe coarse granularity at three different levels: between whole tribunes, between sectors of one tribune and between groups at one sector. At the most elementary level, each minor group of fans decide if they should already start going towards the exit. As oppose to that, at the level of tribunes and sectors the social pressure was large enough, to convince almost all fans inside particular sector/tribune to follow the behavior of majority.. 3.1.5. Unannounced fire drill in academic building The unannounced fire drill was conducted in building of AGH University of Science and Technology. The drill started at 9.20 AM, when there are approximately 350 students and employees in monitored area. At this time typical activities were performed: lectures and classes took place, number of researchers and office staff worked in their rooms. Participants were not aware that a trial evacuation would take place. Drill was raised by siren alarm. Consecutive stages of evacuation are presented in Fig. 3.4. It is extremely problematic to observe people’s behavior in separate room without making them suspicious and giving them prompts that something (in this case a trial evacuation) will happen. Therefore, an observation point at the main staircase on the first floor 3 was chosen. The first group of evacuees appears on staircase 40 s after the drill start (Fig. 3.4a). It is crucial to note a lecturer (white shirt in Fig. 3.4a). Shortly after the siren, he leaves the lecture hall, goes downstairs, checks the authenticity of alarm and then go back and instructs students to evacuate. Another leader who initialize the evacuation of many people is security guard man (a person in the right in Fig. 3.4b) who walks around the building, checks consecutive rooms and makes sure everyone will evacuate. In the same figure (Fig. 3.4b) one can see the beginning of evacuation from the lecture hall. Possible impact of coarse spatial granularity of pre-movement time can be noticed by comparison of Fig. 3.4c and Fig. 3.4d. In both situations people from another rooms/floors enters the stream of evacuees from the lecture hall (on the left side of the picture). In Fig. 3.4c joining group consist of only three persons and can smoothly merge into the flow of evacuees without any clogging. Contrary to this, when the group of 17 persons trying to enter the staircase, they form a queue waiting in the corridor(Fig. 3.4d). Coarse granularity of pre-movement time is equally visible when analyzing the evacuees flow on the staircase presented in Fig. 3.5. Flow was measured on the staircase below the corridor presented in Fig. 3.4. Above the observed corridor there were no obstacles nor bottlenecks that could significantly slow down the evacuees. 3. This building has four floors. J. Porzycki Data-driven modeling of crowd dynamics.

(27) 27. 3.1. Granularity of pre-movement time distribution. (a) t = 40s. (b) t = 1 min 12s. (c) t = 2 min 9s. Group of three persons joins the stream.. (d) t = 2 min 39s. Figure 3.4: Four stages of unannounced fire drill in academic building. Source: own figure [12].. Figure 3.5: Evacuees outflow at the staircase. Each bar represents accumulated flow from consecutive 5 seconds. Source: own figure [12].. Evacuees flow at the staircase reaches up to 1.8 person s , but also long periods of zero value (see the Fig. 3.5). Periods of high flow on the staircase are mixed with periods of very low flow 0.2 0.4 person as well as long periods where no one appears on the staircase. Break of flow last from s 30 s to even 120 s. These patterns are produced by evacuees behavior where all people located in one room/lab/lecture hall start the evacuation at the same moment. When larger groups are evacuating, there are periods of constant flow of about 0.8 - 1.2 person with peeks to 1.6 - 1.8 s person s . For example first period of high flow - from 45 to 160 s is mostly caused by students leaving lecture hall. J. Porzycki Data-driven modeling of crowd dynamics.

(28) 3.1. Granularity of pre-movement time distribution. 28. 3.1.6. Unannounced evacuation of bus during fire drill in tunnel The experiment was conducted during unannounced evacuation from the bus in road tunnel. The aim of participants in this experiment was to evacuate from the tunnel filled with artificial, noo-toxic smoke. 50 students took part in this experiment. Participants knew that they would take part in some kind of experiment, but they were not aware of any details: neither the exact moment of the start, nor the need to evacuate from the bus, nor that evacuation will took part in the tunnel, nor that artificial smoke will be used. Bus driver was instructed to remain inactive and behave passively to not influence participants decision. The only thing that he did was to stop the bus in designated place and open the door after hearing the fire drill siren. General view on experiment setup is presented in Fig. 3.6, while exact description of the experiment is presented in [2].. Figure 3.6: View on the bus from the outside, at t = 1 min 22 s. Source: own figure In the context of pre-movement time distribution, one can be interested in the first phase of this experiment, namely decision to start evacuation and leaving the bus. From the participants point of view, there are four external events that can potentially trigger participants to evacuate, namely: • bus stops in the middle of the tunnel, • smoke appears around the bus, • alarm drill siren starts and bus door opens, • voice alarm message begins4 . Interestingly, none of the first three events trigger a single participant to stand up. After the bus stop all of them remain on their seats, similarly when the smoke is noticed, participants only discuss the situation. Even starting the fire siren and opening the bus doors do not encourage anyone to evacuate. Illustrative examples of evacuees behavior are presented in Fig. 3.7. The start of fire siren is selected as a time t = 0s. This alarm last 13 seconds. After that the voice message begins. At t = 27s first four participants from the back of the bus decide to leave the bus5 (see Fig. 3.7a. Shortly after, another minor group of five people sitting nearby, also stand up. In following moments, more and more participants begin observing persons who 4. Message in Polish and English: Attention please! Attention please! Fire alarm! Leave your car and go to the nearest emergency exit 5 Interestingly, at the same moment other participant said, that such a voice message is unlikely during the real evacuation.. J. Porzycki Data-driven modeling of crowd dynamics.

(29) 29. 3.1. Granularity of pre-movement time distribution. (a) First four participants, in the back of the bus, start to evacuate (t = 27s).. (b) Begining of the evacuation of whole bus (t = 50s).. Figure 3.7: Two stages of unannounced fire drill in bus evacuation from smoked tunnel. Source: own figure [2].. left the bus. Finally, between 50 and 52 second few participants stand up simultaneously. One of them has shouted: Let’s go!, and within few seconds all participants begin the evacuation. Described experiment clearly shows that in case of finding oneself in an unfamiliar situation, even potentially dangerous, in order to take any action people need to get clear message. Message which informs them exactly what they should do. Opening the bus doors and siren alarm may appear to be unsufficient to trigger the evacuation. In case of passive behavior of the person who naturally should take the role of leader - bus driver, participants need to hear the direct and exact instruction. Crucial role is played by herding behavior. In fact, there are three moments when particular participants groups decide to begin evacuation. Firstly the group of four people, later the group of five and finally there was the decision to evacuate taken by the rest of participants. Herding behavior is distinctly visible in the last case, when participants stand up slowly, looking on each other.. 3.1.7. Experiments conclusions Experiments and observations described in sections: 3.1.4, 3.1.5 and 3.1.6 confirm the hypothesis stated in the section 3.1.2. Coarse granularity of pre-movement time spatial distribution is particularly visible during normal condition egress of football stadium (sec. 3.1.4) and during unannounced fire drill in academic building (sec. 3.1.5). Results of experiment described in section 3.1.3 are unconclusive. The case of the football stadium egress (sec. 3.1.4) reveals pre-movement time coarse granularity at different levels of crowd organization. At the highest level, there are differences between tribunes (Fig. 3.3a), between sectors inside one tribune (Fig. 3.3b) and finally between particular groups of fans within one sector (Fig. 3.3c and 3.3d). This shows the importance of custom practices in the decision of beginning of evacuation. Moreover, one should note very strong affiliation of participants to the behavior presented by the whole group. In the first two phases, there are virtually no people who decide to leave against the group. Analysis of pedestrian flow during unannounced evacuation of academic building (sec. 3.1.5) shows possible threat that can be caused by coarse granularity of pre-movement time. Large groups of evacuees starting movement at the same time, end up clogging in high densities. Clogging are shown in Fig. 3.4d and high densities on evacuation routes as shown in Fig. 3.5. This confirms simulation results of Rogsch et al. [94]. It is worth noting, that great majority of the crowd dynamics models used in evacuation simulation do not take this phenomenon into account. Such an omission could have led to overly optimistic results, when simulation do not J. Porzycki Data-driven modeling of crowd dynamics.

(30) 30. 3.2. Pedestrians’ spatial self-organization. predict dangerously high densities in escape routes, because of the assumption of fine spatial discretization of pre-movement distribution. Experiments reveal two behaviors that can lie behind coarse granularity of pre-movement time: • following the leader, • herding behavior. Leader’s decision influences all the people who has him/her in sight. Thus, evacuees located in one room can decide to start evacuation at the same time, which causes coarse spatial distribution. Following the leader behavior was clearly visible during academic building evacuation (sec. 3.1.5) when lecturer decided to begin evacuation from lecture hall. It was a decision of one person that decided on pre-movement time for all people gathered in lecture hall (Fig. 3.4a). Another example is a security staff member (Fig. 3.4b), who initializes evacuation of evacuees that ignore the siren alarm. Evacuation of the bus in smoky tunnel (sec. 3.1.6) shows how passive group can be, when their natural leader (driver) remains passive. Precise information was needed to initialize evacuation. This tendency of people to maintain their initial role [20] in case of an emergency was observed e.g.: during King Cross fire [20], Zurich metro fire [26] or Mont Blanc tunnel fire[124]. Herding behavior was clearly visible in case of bus evacuation (sec. 3.1.6) and two first phases of stadium egress (sec. 3.1.4). The whole group starts evacuation at the same time (Fig. 3.7b) or remains on their position until group decision to start evacuation is made (Figs. 3.7a, 3.3a and 3.3b). Finally, announced fire drill in lecture hall 3.1.3 gives counterexample, where coarse spatial granularity is almost invisible. This illustrates the example when spatial granularity of premovement time does not influence evacuation process significantly. It is worth noting that in this case all participants were informed what they should do and they were in one room. To sum up, coarse spatial granularity of pre-movement time distribution should be recognized as a fact. This phenomenon can significantly influence on evacuation process, causing large fluctuation of flow (see Fig. 3.5) and increasing maximal values of density. The main factors behind this phenomenon is: to follow the leader rule and herding behavior. Both of them happen when people find themselves in unexpected situations. In case of simple geometry, well informed participants and no leaders, the influence of above-mentioned phenomenon can be neglected. Its worth to note that such conditions happen in majority of crowd dynamics experiments. This can be the reason why this phenomenon is omitted by majority in research processes until now. However in case of complex geometries, unprepared participants and leaders involvement, the phenomenon of coarse spatial granularity of pre-movement time is a potential threat. It should be taken into account when creating reliable evacuation simulations.. 3.2. Pedestrians’ spatial self-organization 3.2.1. Pedestrians mutual interaction - an origin of self-organization phenomena Presence of other pedestrians, especially this located in close neighborhood, is important factor influencing individual movement behavior. In order to investigate self-organization patterns between neighbors in crowd, the unidirectional flow of pedestrians has been analyzed. Moussa¨ıd et al. [79] analyzed the pedestrian behavior in a crowd in context of interactions between slow/fast walking pedestrians. They suggested that speed differences between pedestrians in a crowd is a main factor responsible for occurrence of collective phenomena in crowd. Influence of groups on pedestrians velocity and spatial relations was investigated by Zanlungo et J. Porzycki Data-driven modeling of crowd dynamics.

(31) 31. 3.2. Pedestrians’ spatial self-organization. al. [139, 140]. Paper of Rio et al. [93] is dedicated to mechanisms of coupling between neighbors in crowd. Finally, Vizarri et al. [122] proposed crowd dynamics models that explicitly introduces influence of groups. The issue of neighbors influence on pedestrians movement and crowd spatial self-organization according to mutual interactions has also been previously described by author in [11] and [1]. Please note that this analysis is focused on unidirectional flow, typical for normal condition egress and evacuation. Thus, all conclusions refer to this kind of movement, with moderated density (approximate 2-3 persons ). m2. 3.2.2. Source of empirical data The most appropriate data to unidirectional flow analysis appear to be an experimental data from Hermes project6 [141] kindly shared by Prof. Armin Seyfried and Dr. Jun Zhang. Setup details of this experiment can be found in [141] and [142], while pedestrians trajectories have been collected using PeTrack software [6, 5]. Sample video frame from this experiment is shown in Fig. 3.8.. Figure 3.8: Sample frame from uo-300-300-300 experiment. Source: recording from Hermes experiment [141]. In order to reduce influence of walls 2 runs, with the broadest corridor and without bottleneck, out of total 28 runs from this experiment was chosen. Namely, runs with 240 and 300 cm wide corridor with 246 and 349 participants. Among shared experiment data this experiments are coded as uo-240-240-240 and uo-300-300-300.. 3.2.3. Concept of nth nearest neighbor A subject of this research are patterns formed by pedestrians as a result of influence of their neighbor position. Thus, to simplify the analysis the concept of nth nearest neighbor is introduced. Definition 1 nth nearest neighbor of given pedestrian p is such person a, that Euclidean distance dist(p, a) between mass centers of p and a is nth order statistic among the list of distances between pedestrian p and all other pedestrians. 6 http://www.asim.uni-wuppertal.de/en/database/own-experiments/corridor/2d-unidirectional.html - access: 13 April 2019.. J. Porzycki Data-driven modeling of crowd dynamics.

(32) 32. 3.2. Pedestrians’ spatial self-organization. For example a person with the shortest distance to a given pedestrian is its 1st nearest neighbor, next one is 2nd nearest neighbor, etc. This concept is illustrated in Fig. 3.9. One should remember that relation of nth nearest neighbor is not mutual. For example in the situation presented in Fig. 3.9 orange pedestrian is 1st nearest neighbor for its 2nd nearest neighbor.. Figure 3.9: Illustration of the concept of nth nearest neighbor and angle between neighbors in unidirectional flow. All pedestrians moves in right direction. Consecutive nearest neighbors for the central, orange pedestrian are shown. Θ describes the angle between orange pedestrian and its 1st nearest neighbor. Source: own figure [1]. Additionally, definition of angle Θ, between a pedestrian and its neighbor is provided. Definition 2 Angle Θ between a pedestrian and its neighbor is an angle between pedestrian direction of motion and line connecting their mass centers. For example, angle to the neighbor in front of pedestrian is 0◦ , while to the neighbor on right Θ = 90◦ . This concept is also shown in Fig. 3.9.. 3.2.4. Distances to nth nearest neighbors Experiment in 300 cm wide corridor lasts approximately 83 seconds, with frame rate 16, which resulted in 1325 frames in total. Using all frames from the experiments approximately 79800-79600 relations on nth nearest neighborhoods for each n ≤ 8 are obtained. Results for n grater than 8 are strongly disturbed by the walls limiting possible pedestrians positions. For each n ≤ 8 histogram of distances is calculated and presented in Fig. 3.10. Basic statistics (mode, median, mean, standard deviation and skewness7 ) are presented in Tab 3.1. Neighbor mode median mean σ mode skewness median skewness. 1st 54 56 58.88 12.24 0.23. 2nd 66 70 72.48 15.30 0.42. 3rd 79 84 85.89 17.44 0.39. 4th 92 94 97.88 19.76 0.30. 5th 100 105 109.44 22.42 0.42. 6th 112 116 120.58 25.29 0.34. 7th 119 126 131.20 27.40 0.46. 8th 125 136 141.29 29.60 0.55. 0.21. 0.48. 0.32. 0.55. 0.59. 0.54. 0.57. 0.54. Table 3.1: Basic statistical analysis of distance histogram for first eight nearest neighbors. 7. Pearson mode skewness is calculated as. mean−mode , σ. while Pearson median skewness as 3 ·. median−mode σ. J. Porzycki Data-driven modeling of crowd dynamics.

(33) 33. 3.2. Pedestrians’ spatial self-organization. Figure 3.10: Histogram of distances to nth nearest neighbor for n ≤ 8 Source: own figure [1]. Highest values are obtained by histogram for 1st nearest neighbor, for each consecutive n the maximum value is lower, and the distribution is sparser. Standard deviation increase linearly with n. For each n histogram is similar to log normal distribution. Positive skewness can be observed for all nth neighbors, and also increase with n. As expected mode, median and mean distance to the neighbor increase with increasing n. However quite surprisingly this values increase almost linearly with n. Pearson correlation coefficient equals to 0.9933 (mode), 0.998 (median), 0.9986 (mean). This result is interesting since available area for neighbors increase with the square of the distance.. 3.2.5. Spatial distribution of nth nearest neighbors Comprehensive analysis of positions occupied by consecutive neighbors is allowed with 2dimensional position histograms (Fig. 3.11). Neighbor distribution is condensed with circular shape for each n ≤ 6. The larger the n is, the non-zero probability of neighbors covers larger area, and condensation is lower. This corresponds with analysis of distances histogram (see section 3.2.4. Two dimensional histogram reveal substantial differences between distribution for 1st nearest neighbors (Fig. 3.11a) and other values of n. There is much stronger preference for 1st nearest neighbor at the side of a pedestrian than it is in the axis of motion. For 2nd nearest neighbor (Fig. 3.11b), there are no strong preferences for any side. Neighbors are located uniformly, in the circular area, with 50 to 100 cm distance to a pedestrian. In case of n ≥ 3 (see Figs. 3.11c- 3.11f) one can notice a growing preference for position in front and behind of a pedestrian. Analysis of accumulated positions of four nearest neighbors brings interesting results (see Fig. 3.12). Contrary to the results for particular n (except n = 2) there are no preferences to any direction. On the other hand, one can notice that shape of area with the highest probability is elliptical rather than circular. It is worth noticing the white area of zero probabilities in the center of plot. This is exclusion zone where neighbors are not allowed. Among over 159 000 mutual relations of neighborhood, that are plotted in this figure, not a single neighbor appears in this white area. Exclusion zone is elliptical with the major axis approximately 0.5 m, and the minor axis 0.25 m. The black ellipse in the center of image illustrates average size of human body [111]. One can also observe the slight asymmetry in the axis of motion. This can be explained by the influence of triads. The left-right asymmetry of pedestrian position in triads was proven in other research [139]. J. Porzycki Data-driven modeling of crowd dynamics.

(34) 34. 3.2. Pedestrians’ spatial self-organization. (a) 2D histogram of 1st nearest (b) 2D histogram of 2nd nearest neighbor position. neighbor position.. (c) 2D histogram of 3rd nearest neighbor position.. (d) 2D histogram of 4th nearest (e) 2D histogram of 5th nearest neighbor position. neighbor position.. (f) 2D histogram of 5th nearest neighbor position.. (g) Scale used in histograms above. Red color corresponds with 10 or more neighbors at particular position (size 1 x 1 cm), other colors corresponding with smaller number of cases as shown at scale.. Figure 3.11: Two dimensional histogram of nth nearest neighbor for n ≤ 6. Direction of motion corresponds with the top of figure. Space resolution of histogram is 1 cm. Source: own figure [1].. 3.2.6. Angular distribution of nth nearest neighbors Above observations can be extended by analysis of angular distribution of nth nearest neighbors. The distribution for n ≤ 6 is presented in Fig.3.13. There is clear qualitative difference between patterns for n = 1, n = 2 and n ≥ 3. The closest neighbor (n = 1) is usually located on the left/right side of a pedestrian (see Fig.3.13a). Contrary to this, for n ≥ 3 one can observe spindle-shaped distribution with distinct preference to position in front or behind the pedestrian (see Fig.3.13c-3.13f). For n = 2 one can observe an intermediate state. It is worth noting the sharp transition between allowed and avoided angle Θ for n = 1. 1st nearest neighbors is avoided in front of pedestrian for: Θ ∈ (−35◦ , 35◦ ). (3.1). Θ ∈ (−140◦ , −40◦ ) ∪ (40◦ , 140◦ ). (3.2). and allowed for:. J. Porzycki Data-driven modeling of crowd dynamics.

(35) 35. 3.2. Pedestrians’ spatial self-organization. Figure 3.12: Two dimensional histogram of accumulated positions of nth nearest neighbor for n ≤ 4. Color scale used is the same as in Fig 3.11. Black ellipse in the center corresponds with typical representation of pedestrian [111]. Source: own figure [1]. (a) Angular distribution of 1st ne- (b) Angular distribution of 2nd ne- (c) Angular distribution of 3rd nearest neighbor arest neighbor arest neighbor. (d) Angular distribution of 4th ne- (e) Angular distribution of 5th ne- (f) Angular distribution of 6th nearest neighbor arest neighbor arest neighbor. Figure 3.13: Angular distribution histogram of nth nearest neighbor for n <≤ 6. Discretization is equal to 1◦ Radius of the plot corresponds with number of neighbors at given angle. Source: own figure [1].. J. Porzycki Data-driven modeling of crowd dynamics.