Kwak, Jaeyoung; Jo, Hang-Hyun; Luttinen, Tapio ; Kosonen, Iisakki Modeling pedestrian switching behavior for attractions

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Powered by TCPDF (www.tcpdf.org) This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail.

1 Powered by TCPDF ( This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Kwak, Jaeyoung; Jo, Hang-Hyun; Luttinen, Tapio ; Kosonen, Iisakki Modeling pedestrian switching behavior for attractions Published in: Transportation Research Procedia DOI: 1.116/j.trpro Published: 1/1/214 Document Version Publisher's PDF, also known as Version of record Please cite the original version: Kwak, J., Jo, H. H., Luttinen, T., & Kosonen, I. (214). Modeling pedestrian switching behavior for attractions. Transportation Research Procedia, 2, DOI: 1.116/j.trpro This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user.

2 Available online at ScienceDirect Transportation Research Procedia 2 (214 ) The Conference on in Pedestrian and Evacuation Dynamics 214 (PED214) Modeling pedestrian switching behavior for attractions Jaeyoung Kwak a,, Hang-Hyun Jo b,c, Tapio Luttinen a, Iisakki Kosonen a a Department of Civil and Environmental Engineering, Aalto University, Espoo 215, Finland b Department of Biomedical Engineering and Computational Science, Aalto University, Espoo 215, Finland c BK21plus Physics Division and Department of Physics, Pohang University of Science and Technology, Pohang , Republic of Korea Abstract While walking on the streets, pedestrians can aware attractions like shopping windows. Some of them might shift their attention towards the attractions, namely switching behavior. As a first step, this study investigates collective effects of the switching behavior for an attraction by means of numerical simulations. Such switching behavior leads some pedestrians head for the attraction, or even all the pedestrians have visited the attraction if the social influence is getting stronger. These collective patterns of pedestrian behavior are summarized in a phase diagram. The findings from this study can be interpreted into pedestrian facility management particularly for retail stores. 214 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( c 214 The Authors. Published Elsevier B.V. Peer-review under responsibility of Department of PED214. of Transport & Planning Faculty of Civil Engineering and Geosciences Delft University of Technology Keywords: attraction; switching behavior; social influence; average length of stay; saturated phase; unsaturated phase 1. Introduction For the viability of pedestrian facilities including shopping centers and museums, it is important to understand the nature of pedestrians enticed by attractions such as window displays and street performances. When such attractions come into sight, individuals can make decisions between moving in their initially planned directions and stopping by the attractions. This behavior can be called switching behavior from the way that the individuals can shift their attention towards the attractions (Kwak et al. (213)). In reality, such switching behavior is likely to be influenced by what others select. In the marketing area, it is widely believed that others selection can affect one s information processing by raising awareness of merchandise displays in stores, and consequently the individual is prone to make more purchases (Bearden et al. (1989); Childers and Rao (1992)). Therefore, marketing strategies have focused on identifying influential individuals and targeting at them (Aral (211); Yim et al. (in press)). In order to incorporate the switching behavior, this study develops a simple probability model assuming that the preference for the attraction depends on the number of people who have already joined. The proposed model predicts Corresponding author. Tel.: address: jaeyoung.kwak@aalto.fi The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( Peer-review under responsibility of Department of Transport & Planning Faculty of Civil Engineering and Geosciences Delft University of Technology doi:1.116/j.trpro

3 Jaeyoung Kwak et al. / Transportation Research Procedia 2 ( 214 ) different pedestrian movement patterns with various values of the social influence and the average length of stay at the attraction. The predictions are illustrated with a phase diagram. The remainder of this paper is organized as follows. The proposed switching behavior model is described in Section 2, and its numerical simulation results are presented with a phase diagram in Section 3. Finally, Section 4 discusses the findings of this study. 2. Model 2.1. Switching behavior By the analogy with sigmoidal choice rule (Milgram et al. (1969); Gallup et al. (212); Nicolis et al. (213)), the probability of joining an attraction point P a is formulated with the number of pedestrians who have already joined N a and the number of pedestrians not stopping by the attraction N. P a = s(n a + K a ) (N + K ) + s(n a + K a ) (1) where s > is the strength of the social influence reflecting the sensitivity to the number of attendees. When s is small, individuals pay little attention to others choices. For large s, the joining probability is more likely to be influence by the number of people who have already joined to the attraction rather than the number of people not joining to the attraction. K a represents the intrinsic attractiveness of the attraction, and K for not stopping by the attraction. After joining to the attraction, the individual will then stay near the attraction for an exponentially distributed time with an average of t d, similar to previous studies (Helbing and Molnár (1995); Wu and Huberman (27); Gallup et al. (212)) Pedestrian movement According to the social force model (Helbing and Molnár (1995)), the velocity v i (t) of pedestrian i at time t is given by the following equation: d v i (t) dt = v d e i v i (t) τ + j i f ij + B f ib (2) Here the first term on the right-hand side indicates the driving force describing the tendency of pedestrian i moving toward his destination with the desired speed v d and an unit vector e i pointing to the desired direction. The relaxation time τ controls how fast pedestrian i adapts its velocity to the desired velocity. The repulsive force terms f ij and f ib reflect his tendency to keep certain distance from pedestrian j and the boundary B (e.g., wall and obstacles). A more detailed description of the pedestrian movement model can be found in previous studies (Helbing and Molnár (1995); Johansson et al. (28); Kwak et al. (213)) Numerical simulation setup Each pedestrian is modeled by a circle with radius r i =.25m. N = 1 pedestrians move in a corridor of length 3 m and width 6 m with periodic boundary condition in the horizontal direction. They move with desired speed v d = 1.2m/s and with relaxation time τ =.5s, and their speed cannot exceed v max = 2. m/s. The desired direction points from the left to the right boundary of the corridor for one half of population and the opposite direction for the other half. The joining probability (Eq. 1) is updated with the social force model (Eq. 2) for each simulation step Δt =.5s and the individual can decide whether he will join the attraction when the attraction come into his perception range R i = 1m. Once the individual decided to join the attraction, then he shifts his desired direction vector e i toward the attraction. The attraction is placed at the center of lower wall, i.e., at the distance of 15 m from the left boundary of the corridor.

4 614 Jaeyoung Kwak et al. / Transportation Research Procedia 2 ( 214 ) (a) (b) Fig. 1. Representative snapshots of numerical simulations with various values of the social influence s and the average length of stay t d. The attraction, depicted by an orange rectangle, is located at the center of the lower wall. Red and blue circles depict the pedestrians who have and have not visited the attraction, respectively. Two phases were observed: (a) Unsaturated phase in the case of s =.4 and t d = 3s, in which some pedestrians have visited the attraction while others walk in their desired directions. (b) Saturated phase in the case of s = 1 and t d = 3s, where all the pedestrians around the attraction, within a range of R a = 1m, have visited the attraction. 3. Results and discussion 3.1. Phase diagram The simulation results show different patterns of pedestrian movements depending on the social influence s and the average length of stay t d. If the social influence is weak, one can define an unsaturated phase where some pedestrians move towards the attraction while others walk in their desired directions (see Fig. 1a). For large values of s, a saturated phase can be defined. Every pedestrian near the attraction heads for the attraction, thus no more pedestrians can be enticed anymore into the attraction (see Fig. 1b). In order to quantitatively distinguish different collective patterns, this study evaluates the proportion of visitors, n v = N v /N p, reflecting the attraction influence on pedestrians. Here N v indicates the number of pedestrians who have already visited the attraction and N p is the number of passersby within a range of R a = 1m from the center of the attraction. If all pedestrians have already visited the attraction, n v becomes 1. On the other hand, n v = is observed if no pedestrians have visited the attraction. Fig. 2 shows how n v depends on the social influence s and the average length of stay t d. For a given t d, n v increases according to s, indicating that more pedestrians are distracted from their initial desired velocity due to others choice on the attraction. Furthermore, n v curves rapidly increases as t d increases, meaning that the larger t d, the smaller s is needed to attract the majority of pedestrians. According to the value of n v, the parameter space of the social influence s and the average length of stay t d is divided into two regions. n v becomes 1 above a certain value of the social influence s, indicating the transition from the unsaturated phase to the saturated phase (see Fig. 3) Marginal benefit Although the proportion of visitors n v enables us to evaluate the attraction influence on pedestrians, quantifying marginal benefits of facility improvements can also provide useful information. Here the marginal benefit represents the increase in n v with respect to the change of s, n v / s, which can be calculated as the first derivative of n v curves in Fig. 2. As indicated in Fig. 4a, each marginal benefit curve increases up to a certain level then decrease. For higher t d, the values of the marginal benefit are sensitive to a small increase of s when the social influence s is weak, meaning

5 Jaeyoung Kwak et al. / Transportation Research Procedia 2 ( 214 ) n v.6.4 t d =5s t d =1s t d =2s t d =6s t d = 3s s Fig. 2. Numerical results of the proportion of visitors n v = N v /N p.different symbols represent the different values of t d. For each given t d, n v increases according to s. Different phenomena can be characterized in terms of the behaviors of n v Saturated s.5 Unsaturated t d (s) Fig. 3. A phase diagram summarize the numerical simulation results. The parameter space of the social influence s and the average length of stay t d is divided into two regions. The saturated phase indicates that all the pedestrians have visited the attraction, while the unsaturated phase represents that not all pedestrians are enticed by the attraction. that a great improvement in n v can be observed. It is also apparent that the maximum values of marginal benefit increase as t d grows, indicating that increasing t d can amplify the impact of enhancing s (see Fig. 4b). 4. Conclusion In order to examine the collective effects of the switching behavior, this study has developed a simple behavioral model of joining an attraction. A phase diagram with different collective patterns of pedestrian behavior is presented. The phases are identified by means of the proportion of visitors n v as a function of the strength of the social influence s and the average length of stay t d. For strong social influence, the saturated phase appears where all pedestrians were

6 616 Jaeyoung Kwak et al. / Transportation Research Procedia 2 ( 214 ) nv s (a) t d =5s t d =1s t d =2s t d =6s t d = 3s ) max ( nv s (b) s t d (s) Fig. 4. Numerical results of the marginal benefit n v / s. (a) The marginal benefits increase up to a certain level then decrease for given t d.different symbols represent the different values of t d. (b) The maximum values of the marginal benefit increase as t d grows. enticed by the attraction, so all of them have visited the attraction. When the social influence is weak, the unsaturated phase is observed where the attraction is not captivating enough to entice all the pedestrians. The study results also indicate that the marginal benefit increases and then decreases as t d increases. The findings from this study might provide useful insight into pedestrian facility management. The proportion of the visitors n v can be interpreted as a store entry ratio which enables retailers to assess the attractiveness of the store and predict the number of buyers (Lam et al. (21)). For pedestrian facilities such as stores and museums, there are likely to exist costs associated with increasing the strength of social influence s and the average length of stay t d. Based on the marginal benefit and its maximum values, one can identify under what conditions facility improvements would be very effective. A very simple scenario has been considered in order to study the collective effects of switching behavior. The presented model can be extended for more realistic considerations like a shopping street having several stores. In addition, one can take into account heterogeneous properties of attractions and pedestrians such as the strength of social influence and the average length of stay. Acknowledgements This work was funded by Aalto University School of Engineering Doctoral Program and Department of Civil and Environmental Engineering (Jaeyoung Kwak), and by Aalto University Postdoctoral Program (Hang-Hyun Jo). References Aral, S., 211. Commentary-identifying social influence: A comment on opinion leadership and social contagion in new product diffusion. Marketing Science 3, Bearden, W.O., Netemeyer, R.G., Teel, J.E., Measurement of Consumer Susceptibility to Interpersonal Influence. Journal of Consumer Research 15, Childers, T.L., Rao, A.R., The Influence of Familial and Peer-Based Reference Groups on Consumer Decisions. Journal of Consumer Research 19, Gallup, A.C., Hale, J.J., Sumpter, D.J.T., Garnier, S., Kacelnik, A., Krebs, J.R., Couzin, I.D., 212. Visual attention and the acquisition of information in human crowds. Proceedings of the National Academy of Sciences 19, Helbing, D., Molnár, P., Social force model for pedestrian dynamics. Physical Review E 51, Johansson, A., Helbing, D., Shukla, P., 28. Specification of the social force pedestrian model by evolutionary adjustment to video tracking data. Advances in Complex Systems 1, Kwak, J., Jo, H.H., Luttinen, T., Kosonen, I., 213. Collective dynamics of pedestrians interacting with attractions. Physical Review E 88, Lam, S.Y., Vandenbosch, M., Hulland, J., Pearce, M., 21. Evaluating Promotions in Shopping Environments: Decomposing Sales Response into Attraction, Conversion, and Spending Effects. Marketing Science 2, Milgram, S., Bickman, L., Berkowitz, L., Note on the drawing power of crowds of different size. Journal of Personality and Social Psychology 13,

7 Jaeyoung Kwak et al. / Transportation Research Procedia 2 ( 214 ) Nicolis, S., Fernández, J., Pérez-Penichet, C., Noda, C., Tejera, F., Ramos, O., Sumpter, D.J.T., Altshuler, E., 213. Foraging at the Edge of Chaos: Internal Clock versus External Forcing. Physical review letters 11, Wu, F., Huberman, B.A., 27. Novelty and collective attention. Proceedings of the National Academy of Sciences 14, Yim, M.Y.C., Yoo, S.C., Sauer, P.L., Seo, J.H., in press. Hedonic shopping motivation and co-shopper influence on utilitarian grocery shopping in superstores. Journal of the Academy of Marketing Science.

Available online at ScienceDirect. Transportation Research Procedia 2 (2014 )

Available online at ScienceDirect. Transportation Research Procedia 2 (2014 ) Available online at www.sciencedirect.com ScienceDirect Transportation Research Procedia 2 (2014 ) 400 405 The Conference on in Pedestrian and Evacuation Dynamics 2014 (PED2014) Stochastic headway dependent