Conflicting Tendencies in Pedestrian Wayfinding Decisions: a Multi-Agent Model Encompassing Proxemics and Imitation Luca Crociani, Giuseppe Vizzari and Stefania Bandini Complex Systems and Artificial Intelligence Research Centre, University of Milano-Bicocca, Viale Sarca 336/14, 20126, Milan, Italy Abstract ners1 , according to a report commissioned by the Cabinet Office [Challenger et al., 2009] there is still room for inno- Computer-based simulation of pedestrian dynamics vations in models, to improve their effectiveness in modeling is a consolidated application of agent-based models pedestrians and crowd phenomena, their expressiveness (i.e. but it still presents open challenges. The wayfind- simplifying the modeling activity or introducing the possibil- ing of pedestrians is a fundamental aspect to allow ity of representing phenomena that were still not considered the application of such models on complex envi- by existing approaches) and efficiency. ronments. Several novel approaches have recently Even if we only consider choices and actions related to been proposed in the literature, yet the lack of em- walking, modeling human decision making activities and ac- pirical knowledge still limits the reliability of the tions is a complicated task: different types of decisions are heuristics used in the models. In this paper, a novel taken at different levels of abstraction, from path planning to model for the simulation of pedestrian wayfind- the regulation of distance from other pedestrians and obsta- ing is discussed and the aim is to provide general cles present in the environment. Moreover, the measure of mechanisms that can be calibrated for the repro- success and validity of a model is definitely not the optimal- duction of empirical evidences. The model is, in ity with respect to some cost function, as (for instance) in fact, inspired by the behaviors observed in a exper- robotics, but the plausibility, the adherence of the simulation iment performed with human volunteers in Novem- results to data that can be acquired by means of observations ber 2015, which were put into a trade off sce- or experiments. nario, since different paths were available but the The present research effort is aimed at producing insights shortest one was quickly congested. We observed on this aspect: an experiment involving pedestrians has been that several pedestrians choose longer trajectories set up to investigate to which extent pedestrians facing a rel- to preserve high walking speed, and often do so atively simple choice (i.e. choose one of two available gate- following a first emerging leader. The proposed ways leading to the same target area) in which, however, they model encompasses both a proxemic tendency to can face a trade-off situation between length of the trajectory avoid congestion, as well as an imitation mecha- to be covered and estimated travel time. The closest gateway, nism: these conflicting tendencies can be calibrated in fact, is initially selected by most pedestrians but it is too according to empirical evidences. A demonstration narrow to allow a smooth passage of so many pedestrians, and of the simulated dynamics on a larger scenario will it quickly becomes congested. The other choice can therefore be illustrated in the paper. become much more reasonable, allowing a higher average walking speed and comparable (if not even lower) travel time. We observed that several pedestrians choose longer paths to preserve high walking speed, and often do so following a first 1 Introduction emerging leader. Modeling this kind of choices with current approaches can be problematic. The simulation of the movement of pedestrians and crowds The present work represents a step in the direction of pro- in spatial structures is a consolidated research and application ducing a general model fitting this kind of evidences. The context that still presents challenges for researchers in differ- proposed model encompasses both a proxemic tendency to ent fields and disciplines: both the automated analysis and avoid congestion, as well as an imitation mechanism: these the synthesis of pedestrian and crowd behaviour, as well as conflicting tendencies can be calibrated according to empiri- attempts to integrate these complementary and activities [Viz- cal evidences. After a discussion of relevant related works, an zari and Bandini, 2013], present open issues and potential analysis of different alternatives for modeling and simulating developments in a smart environment perspective [Sassi et al., 2015]. Although the currently available commercial 1 See http://www.evacmod.net/?q=node/5 for a large list of tools are used on a day-to-day basis by designers and plan- pedestrian simulation tools). this kind of scenario will be illustrated in Section 3. Results The above approach naturally leads to consider that this of the application of the proposed model in a real world sce- kind of problem has been paid considerable attention in nario, initially described in [Wagoum et al., 2012], will then the field of Artificial Intelligence, in particular by the plan- be described, with reference to their plausibility. Conclusions ning community. Hierarchical planning [Sacerdoti, 1974] and future works will end the paper. approaches, in particular, provide an elegant and effective framework in which high level abstract tasks can be decom- 2 Related Works posed into low level activities. Despite the fact that the formu- lation of the approach date to the seventies, it is still widely The inclusion in simulation models of decisions related to considered and employed in the close area of computer graph- trade off scenarios, such as the one between overall trajectory ics [Kapadia et al., 2013], in which actions of virtual pedes- length and presumed travel time (considering congestion in trians are planned with the aim of being visually plausible perceived alternative gateways), represent an issue in current and decided within real-time constraints. Within this frame- modeling approaches. work, also issues related to the reconsideration of choices and Commercial instruments, for instance, mostly provide ba- plans were analyzed, mostly within the robotics area [Levihn sic tools to the modelers, that are enabled and required to et al., 2013]. In the pedestrian simulation context, one could specify how the population of pedestrians will behave: this consider that microscopic decisions on the steps to be taken implies that the operator constructing the simulation model can follow a high-level definition of a sequence of intermedi- needs to specify how the pedestrians will generally choose ate destinations to be reached by the pedestrian. This kind of their route (generally selecting among different alternatives approach, which we experimentally investigated in [Crociani defined by means of annotation of the actual spatial struc- et al., 2015], also allows exploiting already existing models ture of the simulated environment through landmarks repre- dealing with low level aspects of pedestrian actions and per- senting intermediate or final destinations [Kretz et al., 2014]), ceptions. as well the conditions generating exceptions to the so called The main issues in transferring AI planning results within “least effort principle”, suggesting that pedestrians generally this context of application, and more generally producing try to follow the (spatially) shortest path toward their desti- generally applicable contributions to the field, are partly due nation. Space, in fact, represents just one of the relevant as- to the above suggested fundamental difference between the pects in this kind of choice: since most pedestrians will gen- measures of success between simulation and control applica- erally try to follow these “best paths” congestion can arise tions. Whereas the latter are targeted at optimal solutions, and pedestrians can be pushed to make choices that would be the former have to deal with the notions of plausibility and sub–optimal, from the perspective of traveled distance. validity. Moreover, we are specifically dealing with a com- Recent works in the area of pedestrian and crowd simu- plex system, in which different and conflicting mechanisms lation started to investigate this aspect. In particular, [Guo are active at the same time (e.g. proxemics [Hall, 1966] and and Huang, 2011] proposed the modification of the floor-field imitative behaviors [Helbing et al., 1997]). Finally, whereas Cellular Automata [Burstedde et al., 2001] approach for con- recent extensive observations and analyses (see, e.g., [Boltes sidering pedestrian choices not based on the shortest distance and Seyfried, 2013]) produced extensive data that can be used criterion but considering the impact of congestion on travel to validate simulations within relatively simple scenarios (in time. [Wagoum et al., 2012] explored the implications of four which decisions are limited to basic choices on the regulation different strategies for the management of route choice oper- of mutual distances among other pedestrian while following ations, through the combination of applying the shortest or largely common and predefined paths like corridors with uni- quickest path, with a local (i.e., minimize time to vacate the directional or bidirectional flows, corners, bottlenecks), we room) or global (i.e., minimize overall travel time) strategies. still lack comprehensive data on way-finding decisions. Iterative approaches, borrowing models and even tools from vehicular transportation simulation, propose to adopt a 3 A Model To Encompass the Pedestrian more coarse grained representation of the environment, i.e. a graph in which nodes are associated to intersections among Movement and Route Choice road sections, but the process can be also adopted in build- This Section will propose a multi-agent model designed for ings [Kretz et al., 2014]. In this kind of scenario, pedes- the simulation of pedestrian movement and route choice be- trians can start by adopting shortest paths on a first round havior. The model of agent is composed of two elements, of simulation: as suggested before, the fact that all pedes- respectively dedicated to the low level reproduction of the trians take the best path generally leads to congestion and movement towards a target (i.e. the operational level, consid- sub-optimal travel times. Some selected pedestrians, espe- ering a three level model described in [Michon, 1985]) and to cially those whose actual travel time differs significantly from the decision making activities related to the next destination the planned one, will change their planned path and a new to be pursued (i.e. the route choice at the tactical level). The simulation round will take place. The iteration of this pro- component dedicated to the operational level behavior of the cess will lead to an equilibrium or even to system optimum, agent is not extensively described since, for this purpose, the according to the adopted travel cost function [Lämmel et model described in [Bandini et al., in press] has been applied. al., 2009]. This iterative scheme has also been employed For a proper understanding of the approaches and mecha- in multi-scale modeling approaches [Lämmel et al., 2014; nisms that will be defined at the tactical level, on the other Crociani et al., 2016]. hand, a brief description on the representation of the environ- ment, with different levels of abstractions, is firstly provided This framework, on one hand, enables the agents to have in this Section. More attention will then be dedicated to the a position in the discrete environment and to perform move- introduction and discussion of the model for the management ment towards a user configured final destination. On the other of the route choice, which represents the main contribution of hand, the presence of intermediate targets allows choices at this paper. the tactical level of the agent, with the computation of a graph-like representation of the walkable space, based on the 3.1 The Representation of the Environment and concept of cognitive map [Tolman, 1948]. The method for the Knowledge of Agents the computation of this environment abstraction has been de- The adopted agent environment [Weyns et al., 2007] is dis- fined in [Crociani et al., 2014] and it uses the information of crete and modeled with a rectangular grid of 40 cm sided the scenario configuration, together with the floor fields asso- square cells. The size is chosen considering the average area ciated to openings and final destinations. In this way a data occupied by a pedestrian [Weidmann, 1993], and also re- structure for a complete knowledge of the environment is pre- specting the maximum densities usually observed in real sce- computed. Recent approaches explores also the modeling of narios. The cells have a state that informs the agents about partial knowledge of the environment by agents (e.g. [An- the possibilities for movement: each one can be vacant or oc- dresen et al., in press]), but this aspect goes beyond the scope cupied by obstacles or pedestrians (at most two, so as to be of the current work. The cognitive map identifies regions (e.g. able to manage locally high density situations). a room) as nodes of the labeled graph and openings as edges. To allow the configuration of a pedestrian simulation sce- An example of the data structure associated to the sample sce- nario, several markers are defined with different purposes. nario is illustrated in Fig. 1(c). Overall the cognitive map al- This set of objects has been introduced to allow the move- lows the agents to identify their position in the environment ment at the operational level and the reasoning at the tactical and it constitutes a basis for the generation of an additional level, identifying intermediate and final targets: knowledge base, which will enable the reasoning for the route calculation. • start areas , places were pedestrians are generated: This additional data structure has been called Paths Tree they contain information for pedestrian generation both and it contains the information about plausible paths towards related to the type of pedestrians (e.g. the distribution of a final destination, starting from each region of the environ- their destinations), and to the frequency of generation; ment. The concept of plausibility of a path is encoded in the • openings , sets of cells that divide, together with the algorithm for the computation of the tree, which is discussed obstacles, the environment into regions. These objects in [Crociani et al., 2015] and only briefly described here. The constitutes the decision elements, intermediate destina- procedure starts by defining the destination as the root of the tions, for the route choice activities; tree and it recursively adds child nodes, each of them mapped to an intermediate destination reachable in the region. Nodes • regions , markers that describe the type of the re- are added if the constraints describing the plausibility of a gion where they are located: with them it is possible to path are satisfied: in this way, paths that imply cycles or a design particular classes of regions (e.g. stairs, ramps) not reasonable usage of the space (e.g. passing inside a room and other areas that imply a particular behavior of pedes- to reach the exit of a corridor, as illustrated in Fig. 1(a)) are trians; simply avoided. • final destinations , the ultimate targets of pedestri- The results of the computation is a tree whose nodes are ans; mapped to targets in the environment and each edge refers to a particular path between two targets. The root of the tree • obstacles , non-walkable cells defining obstacles is mapped to a final destination, while the underlying nodes and non-accessible areas. are only mapped to openings. Hence, each branch from the An example of environment annotated with this set of root to an arbitrary node describes a minimal (i.e. plausible) markers is proposed in Fig. 1(b). This model uses the floor path towards the final destination associated to the tree. To fields approach [Burstedde et al., 2001], using the agents’ en- complete the information, each node n is labeled with the vironment as a container of information for the management free flow travel time2 associated to the path starting from the of the interactions between entities. In this particular model, center of the opening associated to n and passing through the discrete potentials are spread from cells of obstacles and des- center of all openings mapped by the parent nodes of n, un- tinations, informing about distances to these objects. The two til the final destination. In this way, the agents knows the types of floor fields are denoted as path field, spread from possible paths through the environment and their respective openings and final destinations (one per destination object), estimated traveling times. and obstacle field, a unique field spread from all the cells For the choice of their path, agents access the informa- marked as obstacle. In addition, a dynamic floor field that tion of a Paths Tree generated from a final destination End has been denoted as proxemic field is used to reproduce a with the function P aths(R, End). Given the region R of proxemic behavior [Hall, 1966] in a repulsive sense, letting the agent, the function returns a set of couples {(Pi , tti )}. the agents to maintain distances with other agents. This ap- Pi = {Ωk , . . . , End} is the ordered set describing paths proach generates a plausible navigation of the environment as well as an anthropologically founded means of regulating 2 The travel time that the agent can employ without encountering interpersonal distances among pedestrians. any congestion in the path, thus moving at its free flow speed. (a) (b) (c) (d) Figure 1: (a) An example of plausible (continuous line) and implausible (dashed) paths in a simple environment. (b) A simula- tion scenario with the considered annotation tools and its respective cognitive map (c) and the shortest path tree (d). which start from Ωk , belonging to Openings(R), and lead is performed and in which order. The workflow of the agent, to End. tti is the associated free flow travel time. encompassing the activities at operational and tactical level of behavior at each time-step, is illustrated in Figure 2. 3.2 The Route Choice Model of Agents First of all, the agent performs a perception of his situation This aspect of the model is inspired by the behaviors observed considering his knowledge of the environment, aimed at un- in a experiment performed with human volunteers in Novem- derstanding its position in the environment and the markers ber 2015 at the University of Tokyo, aiming at identifying perceivable from its region (e.g. intermediate targets). At the basic behavior at the wayfinding level. The participants were very beginning of its life, the agent does not have any infor- put into a trade off scenario, since different paths were avail- mation about its location, thus the first assignment to execute able but the shortest one was quickly congested. Empirical is the localization. This task analyses the values of floor fields analysis related to this experiment are not presented in this in its physical position and infers the location in the Cognitive paper for lack of space. Qualitatively, it has been observed Map. Once the agent knows the region where it is situated, it that several persons preferred to employ a longer trajectories loads the Paths Tree and evaluates the possible paths towards for achieving higher walking speed, but this kind of choice its final destination. seemed to be taken more frequently and easily after a first The evaluation has been designed with the concept of path emerging leader had performed it. utility, assigned to each path to successively compute a prob- By considering these aspects, the objective is to propose an ability to be chosen by the agent. The probabilistic choice of approach that would enable agents to choose their path con- the path outputs a new intermediate target of the agent, used sidering distances as well as the evolution of the dynamics. At to update the reference to the floor field followed at the oper- the same time, the model must provide a sufficient variability ational layer with the local movement. of the results (i.e. of the paths choices) and a calibration over The utility-based approach fits well with the needs to easily possible empirical data. calibrate the model and to achieve a sufficient variability of The discussion of the model must starts with an overview the results. of the agent life-cycle, in order to understand which activity The core functions of the wayfinding model are Evaluate The Evaluation of Traveling Times The evaluation of traveling times is a crucial element of the model. First of all, the information about the travel time tti of a path Pi is derived from the Paths Tree with P aths(R, End) (where End is the agent’s final destination, used to select the appropriate Paths Tree, and R is the region in which the agent is situated and it is used to select the relevant path Pi in the Paths Tree structure) and it is integrated with the free flow travel time to reach the first opening Ωk described by each path: P FΩk (x, y) TravelTime(Pi ) = tti + (3) Speedd where P FΩk (x, y) is the value of the path field associated to Ωk in the position (x, y) of the agent and Speedd is the Figure 2: The life-cycle of the agent, emphasizing the two desired velocity of the agent, that can be an arbitrary value components of the model. (see [Bandini et al., in press] for more details of this aspect of the model). The value of the traveling time is then evaluated by means of the following function: Paths and Choose Paths, which will be now discussed. min (TravelTime(Pi )) Pi ∈Paths(r) The Utility and Choice of Paths Eval tt (P ) = Ntt · (4) TravelTime(P ) The function that computes the probability of choosing a path is exponential with respect to the utility value associated to it. where Ntt is the normalization factor, i.e., 1 over the sum This is completely analogous to the choice of movement at of TravelTime(P ) for all paths. By using the minimum value the operational layer: of the list of possible paths leading the agent towards its own destination from the current region, the range of the func- P rob(P ) = N · eU (P ) (1) tion is set to (0,1], being 1 for the path with minimum travel The usage of the exponential function for the computation time and decreasing as the difference with the other paths in- of the probability of choosing a path P is a good solution creases. This modeling choice, makes this function describe to emphasize the differences in the perceived utility values the utility of the route in terms of travel times, instead of its of paths, limiting the choice of relatively bad solutions (that cost. in this case would lead the agent to employ relatively long This design is motivated by the stability of its values with paths). U (P ) comprises the three observed components influ- the consideration of relatively long path, which might be rep- encing the route choice decision, which are aggregated with resented in the simulation scenario. By using a cost function, a weighted sum: in fact, the presence of very high values of TravelTime(P ) in the list would flatten the differences among cost values of other choices after the normalization: in particular, in situ- U (P ) = κtt Evaltt (P ) − κq Evalq (P ) + κf Evalf (P ) (2) ations in which most relevant paths have relatively similar costs, excluding a few outliers (even just one), the normal- ized cost function would provide very similar values for most where the first element evaluates the expected travel times; sensible paths, and it would not have a sufficient discriminat- the second considers the queuing (crowding) conditions ing power among them. through the considered path and the last one introduces a pos- itive influence of perceived choices of nearby agents to pur- The Evaluation of Congestion sue the associated path P (i.e. imitation of emerging leaders). The behavior modeled in the agent in this model considers All the three functions provide values normalized within the congestion as a negative element for the evaluation of the range [0, 1], thus the value of U (P ) is included in the range path. This does not completely reflect the reality, since there [−κq , κtt + κf ]. could be people who could be attracted by congested paths as In theory, there is no best way to define these three com- well, showing a mere following behavior. On the other hand, ponents: the usage of very simple functions as well as com- by acting on the calibration of the parameter κq it is possible plicated ones might provide the same quality to the model. to define different classes of agents with customized behav- The only way to evaluate the reliability of this model, in fact, iors, also considering attraction to congested paths with the is with a validation procedure over some empirical knowl- configuration of a negative value. edge. Hence, these three mechanisms have been designed For the evaluation of this component of the route decision with the main objective to allow the calibration over empir- making activity associated to a path P , a function is first in- ical datasets, preferring the usage of simple functions where troduced for denoting agents a0 that precede the evaluating possible. agent a in the route towards the opening Ω of a path P : influence associated to each opening of the region where the 0 Forward (Ω, a) = |{a ∈ Ag\{a} : Dest(a ) = Ω ∧0 cell is situated. While multiple neighbor agents changes their (5) choices towards the opening Ω0 , the values of the diffusion PF Ω (Pos(a0 )) < PF Ω (Pos(a))}| are summed up in the respective diff Ω0 . In addition, after having changed its decision, an agent spreads the gradient in where P os and Dest indicates respectively the posi- the grid for a configurable amount of time steps represented tion and current destination of the agent; the fact that by an additional parameter τa . In this way it influences the PF Ω (Pos(a0 )) < PF Ω (Pos(a)) assures that a0 is closer choices of its neighbors for a certain amount of time. to Ω than a, due to the nature of floor fields. Each agent is The existence of values diff Ωk > 0 for some opening Ωk therefore able to perceive the main direction of the others (its implies that the agent is influenced in the evaluation phase by current destination). This kind of perception is plausible con- one of these openings, but the probability for which this in- sidering that only preceding agents are counted, but we want fluence is effective is, after all, regulated by the utility weight to restrict its application when agents are sufficiently close to κf . In case of having multiple diff Ωk > 0 in the same cell, a the next passage (i.e. they perceive as important the choice individual influence is chosen with a simple probability func- of continuing to pursue that path or change it). To introduce tion based on the normalized weights diff associated to the a way to calibrate this perception, the following function and cell. Hence, for an evaluation performed by an agent a at an additional parameter γ is introduced: time-step t, the utility component Evalf can be equal to 1 PerceiveForward (Ω, a) = only for one path P , between the paths having diff Ωk > 0 in ( the position of a. Forward (Ω, a), if PF Ω (Pos(a)) < γ (6) 0, otherwise 4 Evaluation of the Model The function Eval q is finally defined with the normaliza- The evaluation of the model is here discussed with a simula- tion of PerceiveForward values for all the openings connect- tion of a large scenario, with the aim of verifying the behav- ing the region of the agent: ior of the model in a real-world environment and to perform a qualitative comparison of the results with another wayfinding Eval q (P ) = model from the literature. PerceiveForward (FirstEl (P ), myself ) (7) All the presented results have been achieved with the cal- N· width(FirstEl (P )) ibration weights of the utility function configured as Ωtt = 100, Ωq = 27; Ωf = 5, while the parameters related to the where FirstEl returns the first opening of a path, myself ChoiceF ield are set to ρc = 1.2m, τc = 2 time-steps = denotes the evaluating agent and width scales the evaluation 0.44s and τd = 4 time-steps = 1s. The desired speed of over the width of the door (larger doors sustain higher flows). agents have been configured with a normal distribution cen- Propagation of Choices - Following Behavior tered in 1.4 m/s and with standard deviation of 0.2 m/s, in This component of the decision making model aims at repre- accordance with the pedestrians speeds usually observed in senting the effect of an additional stimulus perceived by the the real world (e.g. [Willis et al., 2004]). The distribution agents associated to sudden decision changes of other persons is discretized in classes of 0.1 m/s, and cut by configuring a that might have an influence. An additional grid has been in- minimum velocity of 1.0 m/s and a maximum one of 1.8 m/s troduced to model this kind of event, whose functioning is (see the blue boxes in Fig. 3(c)). To allow a maximum speed similar to the one of a dynamic floor field. The grid, called of 1.8 m/s —considered plausible in this outflow scenario— ChoiceField, is used to spread a gradient from the positions the time-step duration is assumed to τ = 0.22s. of agents that, at a given time-step, change their plan due to The simulation scenario describes the outflow from a por- the perception of congestion. tion of the Düsseldorf Arena, as described in [Wagoum et al., The functioning of this field is described by two parameters 2012]. The annotated environment used for the simulation ρc and τc , which defines the diffusion radius and the time with the discussed model is illustrated in Fig. 3(a): 4 start- needed by the values to decay. The diffusion of values from ing areas models the bleachers of the stadium and generates an agent a, choosing a new target Ω0 , is performed in the cells the agents in the simulation, whose aim is to reach the outside c of the grid with Dist(Pos(a), c) ≤ ρc with the following area indicated with the blue object. Cyan objects are the inter- function: mediate targets describing the wayfinding decisions of agents. 250 agents are generated at the beginning of the simulation ( from each start area, producing a total of 1000 pedestrians. 1/Dist(Pos(a), c) if Pos(a) 6= c The heat map shown in Figure 3(b) provides information Diffuse(c, a) = (8) 1 otherwise about the usage of the space during the simulation, by de- scribing the average local densities perceived by the agents The diffused values persist in the ChoiceField grid for τc (so-called cumulative mean density). The major congested ar- simulation steps, then they are simply discarded. The in- eas are located in front of the exit doors, given their relatively dex of the target Ω0 is stored together with the diffusion val- small width of 1.2 m. An interesting point that comes out ues, thus the grid contains in each cell a vector of couples from this analysis (also visible in the screen-shot in Fig. 3(a)) {(Ωm , diff Ωm ), . . . , (Ωn , diff Ωn )}, describing the values of is that the present configuration of the environment implies (a) (b) (c) Figure 3: (a) A screenshot of the simulation of the Düsseldorf Arena. Spatial markers are also displayed and the colors of the agents identifies their current target. (b) Cumulative mean density map and (c) average speed distributions configured (blue) and achieved (red). that several exits receive an incoming flow from more sources most of them experienced a significant delay during their way. (i.e. corridors), while there are 3 exits in the upper right cor- ner of the environment which are not employed at all by the 5 Conclusions agents during the simulation. In addition, the usage of the ex- The present paper has introduced a general model for deci- its is unbalanced, causing the level of density to be higher in sion making activities related to pedestrian route choices. The some of them. The evaluation of this evidence would require model encompasses three aspects influencing these choices, empirical data that could be used either to support the model- as observed in an experimental observation: expected travel ing choices or to confute these results and lead to a different time, perceived level of congestion on the chosen path, and calibration (e.g. adopting a lower weight for the considera- decisions of other preceding pedestrian to pursue a different tion of travel time, that would lead to an increased usage of path. Achieved results are both plausible and encouraging, the far exits). though a proper validation of the model would require addi- The corridors connecting each bleacher to the atrium are tional results but also the acquisition of empirical evidences affected as well by high densities (around 2.5–3 persons/m2 ) on human wayfinding decisions in congested situations. but their widths guarantee a sensibly higher flow, causing smoother congestion —and so higher speeds— inside the starting regions. References The red boxes of Fig. 3(c) shows the distribution of desired [Andresen et al., in press] Erik Andresen, David Haensel, walking speeds compared to the achieved average walking Mohcine Chraibi, and Armin Seyfried. Wayfinding and speeds of agents during the simulation. The congestion arisen cognitive maps for pedestrian models. In Proceedings of in the exit doors of the atrium sensibly affected the travel time Traffic and Granular Flow 2015 (TGF2015). Springer, (in of the agents. 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