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In total, approximately 600 observed routes were used to estimate the model. The parameters of the multinomial logit model were estimated by LIMDEP (Greene,.

Paper presented to Walk21-V Cities for People, The Fifth International Conference on Walking in the 21st Century, June 9-11 2004, Copenhagen, Denmark www.citiesforpeople.dk; www.walk21.com

Simulating pedestrian route choice behavior in urban retail environments Aloys Borgers and Harry Timmermans Urban Planning Group Eindhoven University of Technology Contact details: Urban Planning Group P.O. Box 513 5600 MB Eindhoven The Netherlands [email protected]

Abstract Many European cities are preparing or realizing downtown upgrading projects. The likely effects of these plans on pedestrian behavior are commonly assessed by common sense and experience. However, research projects to get more insight into the likely effects of policy measures in inner city areas are being initiated. The purpose of this paper is to present a model to simulate individual route choice decision making of pedestrians in the Eindhoven downtown shopping area. The model assumes that 1) pedestrians enter the network at specific entry points such as parking facilities, bus stops, the railway station, or other locations, 2) pedestrians exit the downtown area where they entered the area, and 3) given a pedestrian’s current link in the downtown network, the pedestrian will choose one of the connecting links to move onwards. This way, a circuit through the downtown area is created for each pedestrian. The process of selecting the consecutive links in the downtown network is simulated in this study. A multinomial logit choice model was used to predict which link will be selected from the set of possible links. The probability a particular link will be selected from the set of connecting links depends on the physical characteristics of the link itself (e.g. supply of shops), distance walked so far and minimum distance to the exit location, the side of entering the link, and the number of times the link was passed before. The parameters of the choice model were estimated from observed routes. These routes were observed in the Eindhoven downtown area. Data were collected in March 2002. Approximately 850 pedestrians participated in the on-site interviews. For these analyses however, only those respondents were selected who returned to their entry point and did not leave the downtown area in between. Approximately six hundred respondents satisfied this criterion.

The performance of the model will be discussed at the level of individual link choices as well as at the level of link intensities.

Biographies Aloys Borgers and Harry Timmermans are respectively associate and full professor at the Urban Planning Group of the Eindhoven University of Technology. Their main interest is in modeling behavior of (groups of) individuals in urban contexts in order to support spatial decision-making. Specific application domains include transportation, retailing, housing, and recreation and tourism.

Simulating pedestrian route choice behavior in urban retail environments Aloys Borgers and Harry Timmermans Urban Planning Group Eindhoven University of Technology

Introduction Recent models of pedestrian behavior focus on pedestrian movement at the microscopic level. These models can be used to assess the effects of detailed design decisions, like the positioning of street furniture or the shape of a building. These models require a detailed description of the spatial environment. Not all decisions related to designing pedestrian environments need that kind of detail. For example, one might be interested in assessing the likely effects of policy measures related to the urban traffic infrastructure, parking facilities, upgrading or extending urban retail environments, and so in terms of pedestrian flows in shopping areas. Changing pedestrian flows in shopping areas may result in changing turnover figures and changing real estate values. Therefore, the aim of this contribution is to develop a model that is able to predict the likely effects of urban planning on pedestrian flows in downtown retail environments at the level of shopping streets. This contribution is organized as follows. In the next paragraph, we will discuss some of the relevant literature on modeling pedestrian behavior. Then, we will present the theory and assumptions underlying our model, describe the data we collected to estimate the parameters of the model, report the estimation results and test the validity of the model. A discussion and some directions for further extensions of the model will conclude the paper.

Literature Models for predicting pedestrian behavior or numbers of pedestrians in public urban areas have been developed since the 1970’s. One of the first models was developed by Sandahl & Percivall (1972) to assess the effects of larger retailing and parking facilities on pedestrian traffic in a Swedish town. They regressed observed numbers of pedestrians in the links of the central area network against characteristics of the links, like retailing floor space, parking facilities, accessibility by bus, centrality of the link in the network, number of street stalls and seating places. Likewise, Pushkarev & Zupan (1975) analyzed pedestrian presence in avenues and streets in Manhattan. They related pedestrian counts on block sectors to building floor space, walkway area, and proximity to transit facilities. In contrast to using characteristics related to objects along the links as explanatory variables, Hillier and his coworkers (Hillier et al; 1993; see also Teklenburg et al; 1994) used characteristics of the network itself. Based on topological distances between the lines in a network, their space syntax model determines some measure of centrality, ‘integration’, which is used to relate observed numbers of pedestrians to. Obviously, this space syntax approach is not able to account for the effects of, for example, changing retailing floor space. Therefore, Saarloos (2000) combined both types of explanatory

variables – characteristics of links as well as a measure of centrality - to predict the number of pedestrians in links of downtown shopping network of three Dutch cities. The models discussed above might be able to predict pedestrian volumes, but they are not able to predict pedestrian movement. Borgers & Timmermans (1986a, 1986b) proposed a model to predict pedestrian movement at the level of links in a downtown shopping area. Their model consists of three modules. Assuming a list of types of shops to be visited and an entry point for each pedestrian, the destination module selects a destination-link from the set of links providing a particular type of shops. This link will be the next destination. The route choice module then predicts the route from the current position to the selected destination. Having reached this location, the destination module selects a next destination and so on, until all types of shops on the list have been visited. The last destination will be the exit-link, which is assumed to be the entry-link. The third module predicts possible impulse stops along the route through the shopping area. This model can be used to simulate individual pedestrian behavior (Borgers & Timmermans, 1986b). In contrast to these models, models of much more detailed, microscopic, pedestrian behavior have come into fashion during the 1990’s (Batty, 2001). These models offer very detailed description of pedestrian behavior, e.g. avoidance of obstacles, movement of crowds, at the scale of grid-cells in links. Examples of such models are the Cellular Automata based models by Blue & Adler (2001), the social force model for pedestrian dynamics by Helbing and Molnar (1995), and the agent-based models proposed by Kerridge et al (2001) or Dijkstra et al (2002). Haklay et al (2001) presented with their STREETS-model a system of modeling pedestrian movement at different spatial levels. Their model consists of two sub-models. The first model operates at the level of subregional, urban districts; it populates the gate-ways (like parking garages, train stations, bus stops) of the downtown area with populations of agents (pedestrians), having predetermined activity schedules/route plans. In the second phase, an agent-based model simulates the movement of the agents in the downtown area under influence of spatial configuration, predetermined activity schedules, and the distribution of land uses. The agents are ‘operated’ by five behavioral modules. The mover module determines the very local moving to the next grid square. Medium range (maintaining a proper direction) and longer range (to the next destination) movement is taken care of by the helmsman and navigator module. The chooser module enables an agent to search a nearby area and to recognize buildings near its route. A building, which an agent has seen, might distract an agent from its predefined activity schedule. Changes in the agent’s plan are managed by the planner module. The first three modules deal with tactical movement, while the latter two deal with strategic movement and planning. Hoogendoorn (2003) described a model for activity scheduling and trajectory choice, based on the assumption that pedestrians are subjective utility maximizers who schedule their activities, the areas where activities will be performed, and the trajectories between the activity areas. The trajectories are assumed to be continuous in space and time.

Model description Most recent models of pedestrian behavior assume a grid based space or even continuous public space to move around. According to Hoogendoorn (2003), facilities like airports and

large shopping malls offer pedestrians freedom of movement by providing an infinite number of route alternatives through the facility. However, the aim of this paper is not predicting microscopic pedestrian behavior rather than predicting pedestrian behavior at the level of links in downtown retail areas. Most models of pedestrian behavior assume that pedestrians have a predefined set of destinations to visit, activities to perform or a route to follow through the public space. In contrast, we assume in this paper that we do not know the aims of pedestrians visiting the downtown area. We assume people go downtown for shopping, stroll around, or other reasons. They enter the downtown area at entry points near car parks, bus stops, bike sheds, railway station, or other locations. An entry point is just a link at the edge of the downtown area network. After having entered a link of the downtown area, a pedestrian has to choose one adjacent link to proceed. This process of choosing links continues until the pedestrian reaches the entry point where he leaves the downtown area. In fact, it is assumed that a pedestrian walks some circuit through the downtown network. The pedestrian’s decision on the next link in his trip is likely to depend on a set of variables. First of all, the distance will be an important variable. In the beginning of the trip, we expect the pedestrian prefers to move away from the entry point into the downtown area. This desire to move away from the entry point is likely to diminish when the pedestrian moves further away from the entry point. At some moment, the desire to move back to the entry point will become apparent. Ultimately, the pedestrian just wants to return to the entry point. So, in the beginning of the trip the pedestrian prefers to choose a link in the network that gives the opportunity to increase the distance from the entry point, while in the end, the pedestrians prefers to decrease the distance to the entry point. This implicates that at any decision moment in the route choice process, we need to take into consideration the distances walked so far and the distance back to the entry point. Another important variable is the attractiveness of the links to be chosen from. We expect pedestrians prefer more attractive links over less attractive links. In a shopping environment, the attractiveness is likely to be related to the supply of shops and the type of shopping street: indoor or outdoor. However, other aspects like street furniture, pavement, architectural design, etc. might be relevant as well. From previous research, e.g. Hillier et al (1993) and Teklenburg et al (1994), we know that measures of accessibility or centrality are important. We assume that links giving good access to the attractive parts of the downtown area are preferred over other links. Again, in a shopping environment, links giving good access to attractive shopping streets will have a higher probability to be chosen. Another variable we expect to be important is whether a link has been passed before during the trip. Maybe, pedestrians don’t like twice passing the same link. On the other hand, it is possible that people prefer to walk back to the entry point the same way they walked away from the entry point. If a pedestrian enters a link at one side, it might be expected he will leave the link at the other side. However, pedestrians can make a turn and leave the link at the side of entrance. We will include a variable for each adjacent link indicating whether the adjacent link implies a turn in the current link. We expect this variable to have a negative effect.

If the pedestrian’s current location is close to his entry point, he might end his trip. In this case, the set of alternatives consists of the set of adjacent links plus the opportunity to stop. We assume that the attractivity of the ‘stop’-alternative increases with the distance the pedestrian has been walking through the downtown area. Most recent Cellular Automata en Multi-Agent based models of microscopic pedestrian movement use rules to decide which of the adjacent grid cells will be selected for the next step of movement (e.g. Blue & Adler, 2001; Kerridge et al, 2001). We could use the above-discussed assumptions to formulate a set of rules to determine which link from the set of adjacent links will be chosen. However, a main drawback of using rules is that it is difficult to calibrate the model against observed movement (see also Batty, 2001). For this reason, we decided to use the conventional, and in the field of marketing and transportation still popular, multinomial logit model. According to this model, the probability that an alternative (link) will be chosen from a set of alternatives (the adjacent links) depends on the utility of the alternatives. The utility of an alternative consists of a structural part and a random part. The structural utility is directly related to the characteristics of the alternative. In general, the structural utility is a weighted summation of the scores of the alternative on the selected variables. These weights can be estimated from observed choices. So, based on choices made at each link and the scores of the adjacent links on the above-discussed variables, we can statistically estimate the weights of the variables. These weights can be used to predict the probability each of the adjacent links will be chosen.

Data Data were collected in March 2002 during two consecutive days, a Friday and a Saturday in Eindhoven downtown area. Eindhoven is a medium sized city of approximately 200 thousand inhabitants in the southern part of the Netherlands. In Eindhoven, shops close at 21.00 hrs on Fridays and at 17.00 hrs on Saturdays. On both days, data collection started at 11.00 hrs. Data were collected by means of personal interviews. Interviewers were positioned at the exit points of the downtown shopping area. They were instructed to invite only pedestrians who left the shopping area to participate. Each interview consisted of the following items (see also Lorch and Smith, 1993): mode of transport to city center, destinations (shops) visited, time spent, and personal characteristics. The respondent was asked to reproduce his route on a map of the Eindhoven downtown area. Main buildings and all streets were identified on this map. First, the respondent had to indicate where he left his mode of transportation (car, bike, bus, train). Starting from this point, the respondent had to draw (assisted by the interviewer) his route through the downtown area on the map, also indicating all outlets he visited. The route of each individual respondent was stored in a geographical information system. In total, 490 and 358 respondents were interviewed on Friday and Saturday respectively. Response rates were approximately 30% for both days. On Friday, the percentage of female respondents was 55, and on Saturday 56. On Friday, 7% of the respondents were younger than 18 years of age, 78% were between 18 and 55 years, and 15% were over 55 years of age. For Saturday, these figures were 4%, 84%, and 12% respectively. For this paper only data regarding routing is of interest.

In addition to the interviews, the numbers of pedestrians leaving the downtown area were counted at each exit point. This was done during five time intervals (of 5 minutes) on Friday and during three time intervals on Saturday. These counts were used to estimate the total number of respondents leaving the downtown area at each exit point during periods of the day. These estimated numbers were used to weight the interviews. Data about shopping supply in each link of the downtown area were also collected. In fact, the local Chamber of Commerce provided the number of shop assistants working in each individual shop. The municipality of Eindhoven provided a digital map of the downtown area. Model estimation To estimate the weight of the variables in the model, data discussed in the previous section were used. As it was assumed that pedestrians walk a circuit through the shopping area, all observed routes not ending within close distance from the entry point were excluded from the estimation set. Also, routes exceeding the edge of the shopping area were excluded. In total, approximately 600 observed routes were used to estimate the model. The parameters of the multinomial logit model were estimated by LIMDEP (Greene, 2003). Parameters were estimated for the following variables: - distance to entry point (positive effect in the beginning, negative if walked distance increases), - type of shopping street (indoor or outdoor), - shopping supply per link per branch (Food products; Personal care & fashion; Household articles; Appliances; Books & reading material; CD’s & DVD’s; Department stores; Other shops; Restaurants & café’s; Services & entertainment), - access to shopping supply in all other links (same branches), for each link defined as the summation of the ratios between the shopping supply in each other link and the distance to that link, - ‘passed before once’ and ‘passed before twice or more’, - ‘turn in current link’, - walked distance (for stop-alternative only). The results of the estimation are very encouraging as the goodness of fit of the multinomial logit model is rather high (ρ2=0.56) and most variables have anticipated directions. However, some parameters need further discussion. For example, both parameters for the branch of Food products (supply in link and access to supply in other links) are negative, indicating that pedestrians do not prefer to visit links (giving access to links) with large supply of food products. The reason might be that pedestrians don’t like to visit this kind of utilitarian shops during more or less hedonic trips to the downtown shopping area. Links giving good access to other links with Restaurants & café’s or Services & entertainment are not preferred by the pedestrians. Apparently, pedestrians are not looking for good access to these kinds of outlets. If a link has been passed before only once, this link is likely to be chosen again, possibly to proceed the same way back. However, a link that has been visited two or more times becomes less likely to be chosen again. Indoor links are preferred over outdoor links.

According to the parameter for the ‘turn in current link’-variable, pedestrians strongly prefer to leave the link at the side opposite to entering the link. So, pedestrians don’t like to turn back within a link.

Model validation The parameters of the multinomial logit model have been estimated given the observed choice from the set of adjacent links for each pedestrian at each link. This model will now be used to predict complete routes. We assume that for each pedestrian, the entry point is known. Starting at this link, the pedestrian will walk a circuit through the downtown area. To leave the starting link, the pedestrian has to choose one link from the adjacent links. The multinomial logit model is used to predict the probabilities for each alternative. Monte Carlo Simulation is used to decide which alternative will be chosen. The probabilities for the alternatives are cumulated and a random number is drawn from a uniform distribution. The alternative having a lower value in the cumulative distribution less than the random number and an upper value greater than the random number will be selected as the chosen alternative. The pedestrian moves into the selected link and the process is repeated. This way, a set of consecutive links will constitute a route. If the current link is close to the entry point, the ‘stop’-alternative is an alternative in addition to the adjacent links. If the ‘stop’-alternative is chosen, the pedestrian has finished his trip. For all respondents used to estimate the multinomial logit model, a route was predicted. This was repeated 25 times to cancel out effects of coincidence and get more stable results. To compare the simulated route choice behavior with observed route choice behavior, two indices were calculated. First, the correlation between observed number of pedestrians per link and simulated number of pedestrians per link was calculated (see also Figures 1 and 2). The correlation coefficient is equal to 0.70. This is reasonable, however, Figures 1 and 2 show that the links in the southern part of the downtown area especially are seriously under predicted. When assessing the predictive power of the model, one should take into consideration that the model does not use any information about plans of pedestrians to visit particular destinations. The second index to compare observed and simulated pedestrian behavior is the mean length of the routes. The mean length of simulated routes (1183 m) is quite close to the mean length of observed routes (1135 m).

Figure 1: Number of observed pedestrians per link

Figure 2: Number of simulated pedestrians per link Conclusions and future research In this contribution, we presented a model to predict the number of pedestrians in downtown shopping streets. The main assumption of the model is that an individual enters a shopping area, walks around in the streets of the shopping area and eventually returns to

the location of entrance. In each link of the retail area network, the pedestrian chooses one of the connecting links to proceed. The preferences for links are related to shopping supply in the link and the accessibility from each link to shopping supply in other links. Further, distance from and to the entry point, type of shopping street (indoor/outdoor), whether the link has been passed before and an inclination of pedestrians not to return in a link affect the choice of a link. The model performs reasonably well. However, it can be extended in several ways. One important extension would be to include shopping behavior into the model. By assuming that pedestrians may have a list of products to buy during the shopping trip, the effect of shopping supply per link could be differentiated into an overall effect of shopping supply on route choice behavior and specific effects for goods still to be bought. By passing a link supplying a required product, the specific effect for that product will decrease after leaving this link as the pedestrian has had the opportunity to buy the product. So far, apart from shopping supply, physical characteristics of the links in the retail network are not included in the model. Examples of such characteristics are the width of a street related to the height of facades, the type of pavement, the presence of trees, etc. These kind of characteristics can easily be incorporated into the model by estimating a weight for each additional characteristic. Such extensions would be very interesting for town planners as they can use the results for increasing the number of pedestrians in particular streets. The model presented in this paper was estimated for the downtown area of Eindhoven. The spatial structure of this area is relatively simple compared to downtown areas of some other cities. Furthermore, as a large part of the inner city area of Eindhoven was destroyed during the World War II, the buildings in downtown Eindhoven lack a historical atmosphere. Therefore, the model has to be tested in other cities as well. Different types of pedestrians visiting a shopping center exist. For example, Bellenger and Korgaonkar (1980) found empirically that recreational shoppers behave different from economic shoppers in that the first do more non-planned purchases and spend more time on a shopping trip. Therefore, it would be interesting to investigate whether the weights estimated in this paper differ for these groups of shoppers.

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