Distribution of shoppers in multi-layered shopping complex · Distribution of shoppers in...

SSS10 Proceedings of the 10th International Space Syntax Symposium

035

Distribution of shoppers in multi-layered shopping complex: Estimation of shopper density considering escalators, elevators, stairs

Natsumi Saruyama Graduate School of Science and Technology, Keio University, Yokohama, Japan [email protected] Tatsuya Kishimoto Graduate School of Science and Technology, Keio University, Yokohama, Japan [email protected]

Abstract

Today, complex commercial facilities are being developed that have many elevators, escalators, and stairs and comprises multilayered floors; the number of such facilities is increasing in large cities due to the compactification and densification of cities. These commercial facilities are similar to those in a three-dimensional space such as a town. We investigated the relationship between the space configuration of a facility that is complex, similar to a three-dimensional town, and the distribution of shoppers in this space. The target facility is Bay-Quarter, which is adjacent to Yokohama Station in Kanagawa pref. Japan. In Bay-Quarter, circulation paths are outdoor space. Moreover, many vertical paths such as elevators, escalators, and stairs constitute a complicated space that connects those circulation paths up and down. We considered how complicated and multilayered space configuration influences shopper dispersal by investigating the distribution of shoppers in Bay-Quarter and formulating equations for those distributions. First, we investigated 1.) the distribution of walkers in all circulation paths and 2.) the number of visitors in all stores to understand the distribution of shoppers in the target facility. The researcher walked through the facility and recorded the distribution of walkers by taking snapshots, and counted the number of visitors in each shop. We divided the target facility into 335 convex spaces and totalled the number of shoppers in each convex space, as well as calculated the population densities in each circulation path and in each shop. Next, we analysed the spatial configuration of the target facility using Convex Analysis, Axial Analysis, and Visibility Graph Analysis from space syntax theory to understand the spatial character, and calculated the indices of the spatial configuration by space syntax. In the analysis, we distinguished non-vertical movement from vertical movement and adjusted each step number based on the accessibility and visibility of the escalator, elevator, and stairs. We treated convex spaces as units of analysis and analysed the relationship between ten types of space syntax indices, including Isovist and walker density and visitor density in each shop. Through multiple regression analysis that assumed walker density as a dependent variable, we revealed that the integration value of space and the “closeness to the nearest escalator” influence the distribution of walkers in circulation paths. Using a multiple regression analysis with visitor density in shops spaces as a dependent variable, we revealed that the visitor density in some stores is significantly estimated. The “area of the field of vision range from the shop window” and the “length of the shop window” affect the number of visitors in retail stores, whereas no indices of spatial configuration influence the number of visitors in the restaurants and service shops.

Keywords

Visual analysis, shopping complex, distribution of shoppers, escalator, elevator.

N Saruyama & T Kishimoto, Distribution of shoppers in multi-layered shopping complex: Estimation of shopper density considering escalators, elevators, stairs

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1. Introduction

Nowadays multi-layered commercial facilities have increased in large cities because they can be developed in limited land effectively. In these facilities, it is difficult to predict shoppers’ distribution, because spatial configuration is very complex and every shopper performs a complicated shopping action including not only horizontal movements but also vertical movements. This study aims to reveal the influence of the spatial structure on shoppers’ distribution in the complex multi-layered commercial facilities that have many and various vertical paths such as elevators, escalators and stairs. Firstly, we investigated the walkers’ distribution in circulation paths and the number of visitors in tenants. Secondly, we analysed the properties of space by Visibility Graph Analysis (VGA) based on the space syntax theory. Finally, we showed the relation between the spatial properties and the density of shoppers in circulation paths or in tenants. We suggested a model which estimates the walkers’ density in circulation paths and the visitors’ density in every tenant, by the multiple regression analysis.

We review some studies using the space syntax theory on the prediction of shoppers’ activity distribution in commercial facilities. Zhang et al. (2012) performed a multiple regression analysis with the number of the walker as an dependent variable, and with independent variables including Integration value of axial analysis, floors, and connection to vertical paths and entrances. They revealed that the number of the walker can be predicted from depth, connection with the vertical paths, connection with entrance and floor in multi-layer space.

Min et al. (2012) analysed the relations of number of walkers with Integration value of axial analysis in a large-scale and single-layered commercial facility in Seoul. They classified stores into four types (convenience store, entertainment shop, restaurant, and retail store), and indicated that the number of walkers in front of the retail store could be explained by Integration value. Kong et al. (2013) showed that there were correlation between the sales of stores and the mean Integration value in the visible area from shopwindow of tenants, in a large-scale and single-layered commercial facility in Seoul. Moreover, they made multiple regression analysis predicting the amount of sales of tenants (restaurant, retail store, and entertainment) with the independent variables such as distances from the entrance, total floor area, number of walkers and Integration value. They revealed that the floor area of tenant space and Integration value influenced the sales of retail stores.

2. Distribution of walkers in circulation and shoppers in shops

This study targeted the Yokohama Bay Quarter, six storied shopping center situated at Yokohama-bay near Yokohama station. Yokohama Bay Quarter is constructed as part of the redevelopment of bay area. Elevated pedestrian walk are constructed and it connects Yokohama station and large buildings including Yokohama Bay Quarter and other department stores. On the ground floor, there are parking entrance and sea port where tourists can get on sea bus connecting to other ports in Yokohama bay. Main entrance of Yokohama Bay Quarter is at the third floor with the access from elevated pedestrian walk. The circulation space of Yokohama Bay Quarter are very attractive spaces where visitors feel the atmosphere of sea, wind, and sun light and sky light because they are almost half-outdoor spaces.

Moreover, Yokohama Bay Quarter has many atriums on different floors in it and they are connecting different spaces visually. Plaza and terrace seat are arranged along the sea line, from which we can have a nice panoramic view of Yokohama bay. It has the fun of wandering. In a general commercial facility, we cannot experience these rich spaces and funs. It has three-dimensional structure like a town, and we can observe many shopping visitors to various directions. The second floor has four entrances and is connected to the parking lot, but there are few stores. The third floor has eight entrances, and some entrances are connected to pedestrian walk. Moreover, this floor has the many retail stores and the restaurant. The greater part of stores is retail stores on fourth floor, and the restaurant occupies about half area of fifth floor. Main part of sixth floor is a roof garden. We investigated the number of shoppers in all stores and pedestrians on all circulation floor spaces. Investigation area includes second floor to seventh floor of the building. The first floor of the parking lot and the floors above seventh were excluded because there weren’t any stores. There were 84


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stores in investigation area. The investigation was conducted by ten surveyors from 12:00 to 15:30 ( weekend holidays in November of 2013). Two surveyors were located on each floor. The pedestrian distributions of the circulation space were counted by the snap shot method. Surveyors snapshot the pedestrian distribution in intervals by cameras on each investigation day and counted the number later. Shoppers in stores or visitors in restaurants were counted on site. As a result, the distributions of the shoppers at the same time were recorded. Distribution was counted six times in each day.

Figure 1: Yokohama Bay Quarter, View from Sea Boat On the other hand, we divided the circulation space of Yokohama Bay Quarter into 251 polygons. We made the polygon around the node which is in front of vertical paths, benches, stores, and turning point. We calculated walker’s density in each polygon. And, shoppers’ density in each store was calculated by the floor space of the store and the number of shoppers in the store. Figure 2 shows shoppers’ density in the store and walkers’ density in the circulation space. The bigger the density, the deeper colour is.


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Figure 2: Unit population density in the circulation paths and the store

3. Space form analysis by space syntax

We analyze the spatial configuration of Yokohama Bay Quarter by using space syntax, and calculate the indices of SS.

Firstly, we put the ground plan of each floor into depthmap (Turner, 2004), which is space analysis software based on space syntax, and build data for Visibility Graph Analysis. We divided space into cells of square with side length of 0.6m for analysis.

Depthmap cannot analyze three-dimensional space. Therefore, we regard vertical paths such as an escalator, an elevator and stairs as two-dimensional models artificially. Specifically, when we analyze multi-layered space which has such equipment, we connect ground plan of each floor via the two-dimensional models of equipment by using Link function of depthmap. Figure 3 shows instances of two-dimensional models.

3F

4F

2F

5F

6F


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Figure 3: The Models of Vertical Paths

The model of an escalator is set so that it has step increase of one step per movements between floors. The step means the number of spaces which is needed to move from certain space to another space. The model of an elevator is set so that it has step increase of two steps per movements between floors without considering floor difference which we move from certain floor to another.

The model of stairs has different steps by shape of stairs. When the floors are connected by a turn-around stairs, we count three steps. Figure 4 shows the connection between every floor via these models of vertical paths. We analyse this model shown in Figure 4, and calculate spatial indices of Yokohama Bay Quarter.

In this study, we calculate 10 indices: Connectivity, Integration value, three types of Metric Shortest Path Length which means distance from three types of vertical paths (an escalator, an elevator or stairs), four types of Visual Step Depth from the entrance and each vertical paths, and shopwindow Length. We consider that these indices enable analysis considering effects of vertical paths. The cell which has high connectivity means that it can see broad area and it is seen from many sides. Thus, when we are in high connectivity space, it becomes easy to understand our present location and the relation between surroundings and us. Integration value means the centrality of space. We can calculate Integration value by the global analysis or the local analysis. In the former method, we analyse entire space, and find global characteristics. On the other hand, in the latter method, analysed area is restricted, and we find local characteristics. We calculate Integration value by the global analysis and the local analysis (Radius=3). Global integration means Integration value calculated by the global analysis, and Local integration means Integration value calculated by the local analysis. Metric Shortest Path Length shows the shortest distance from a certain cell, such as the cell which means the entrance or three types of vertical paths, to other cell in metric units. Visual Step Depth shows the number of steps which is needed to connect visually a certain cell, such as the cell which means the entrance or three types of vertical paths, to other cell. When this value is small, it means that we can see the cell in some steps from the entrance or vertical paths. We write an escalator, an elevator, stairs and the entrance as “ESC”, “EV”, “Stair” and “Entrance”. For example, Visual Step Depth from the entrance is written as “Visual Step Depth from Entrance”, and Metric Shortest Path Length from the escalator is written as “Metric Shortest Path Length from ESC”.


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Figure 4: Connection Relations of Vertical Paths

4. Relation between space syntax indices and distribution of shoppers

At first we consider the result of VGA. We show Connectivity, Global integration, Visual Step Depth from ESC in Figure 5, Figure 6 and Figure 7. Figure 5 shows the result of Connectivity. A main passage to tie entrances of 3F is the highest value and shows that the range of vision from this place is wide. Figure 6 shows the result of Global integration. The place whose index value is high concentrates on 3F and 4F. An open space of the neighbourhood of main entrance in 3F shows a particularly high value. Figure 7 is a result of Visual Step Depth from ESC. Visual Step Depth from ESC shows "The turn number of times from the nearest escalator ". In brief, this means that the place is easy to go visually from the entrance of the escalator. On the contrary, the place that has a large value of Visual Step Depth from ESC is difficult to go visually from the nearest escalator. The difference of the index level is small in all floors because the escalators in Yokohama Bay Quarter are located in a good balance. The value of a narrow passage in 6F is high because the sixth floor has only one escalator.


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Figure 5: A Result of Connectivity

Figure 6: A Result of Global integration


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Figure 7: A Result of Visual Step Depth from ESC

Then, we evaluated the mean value of space syntax indices. We calculated the mean value of each index in the polygon to find the indices of circulation paths. We calculated the mean value of each index at the shopwindow part to find the indices of shops. We added “Length of the shopwindow” to the index of the shop. We show these analysis in Table1. Moreover, we divided the stops into retail stores, restaurants, service shops because we expected that the shopper density greatly varied according to a type of industry of the stores. In addition, we divide the walkers’ density into 69 groups every 0.01 (person /m2) and the shoppers’ density into 44 groups every 0.01 (person /m2). And, We calculate the mean value of each group to decrease the influence of the outlier. And, we analysed a correlation between index of the circulation space and the walker’s density and analysed a correlation between index of shops and the shopper’s density.

Table 1 shows that the walker’s density in the circulation space is associated with almost all space syntax indices. In particular it has a strong association with Global integration and Visual Step Depth from ESC. The plus coefficient of correlation of Global integration is shows that the walker’s density is high in the place where it is easy to access. The walker’s density is high as a place with a little turn number of times from escalators because the coefficient of correlation of Visual Step Depth from ESC is minus. The shopper’s density of retail stores has a strong association with Connectivity, Local integration, the shopwindow of the length. This means that the store where a visible range is wide and the store where it is easy to access have high shopper’s density and the store having a long shopwindow. In addition, we analysed the correlation between shopper’s density and space syntax indices of restaurants and service shops. From table 1, there is not the correlation of visitor density and space syntax indices in these shops. The shopper’s density of restaurants and service shops has nothing to do with the placement of the shop and can suppose that these shops are connected with a type of industry or the popularity.


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Spatial Configuration Circulation path Retail store Restaurant Service

Connectivity .511** .828** .041 .231

Global integration .681** .672** -.211 -.077

Local integration -.120 .759** .073 -.015

Visual Step Depth fromEntrance_ -.287* -.536* -.122 -.059

Metric Shortest Path Length fromESC -.155 -.290 -.196 -.299

Visual Step Depth fromESC_ -.612** -.075 .-014 -.193

Metric Shortest Path Length fromEV -.259* -.159 -.019 -.606*

Visual Step Depth fromEV -.283* -.493 -.214 -.352

Metric Shortest Path Length fromStair -.274* -.377 -.061 .020

Visual Step Depth fromStair -.359** -.601* -135 -.326

Length of shopwindow .804** .316 .000

(**p<.001, *p<.005)

Table 1: Correlation analysis between population densities and spatial configuration

5. Estimated equation of distribution of shoppers

We made the estimated equation of walkers' density in the circulation space, and that of shoppers' density in the retail stores, restaurants and service stores. First, we performed the multiple regression analysis using 10 indices calculated in VGA and we estimated walkers’ density in every convex polygon which we divided the circulation space into. Second, using 10 indices, Length of shopwindow and the floor level differences from the entrance floor as independent variables, we performed the multiple regression analysis to estimate respectively shoppers' density in three types of stores. In this case, the floor level differences were used as dummy variable. We used stepwise method in SPSS (ver.21) for analysis. As a result, we obtained the estimated equation shown in equations (1) and (2). The following equation (1) is the estimated equations of the walkers’ density in the circulation space, and equation (2) is the estimated equations of shoppers’ density of retail store. However, we could not obtain the estimated equations in the restaurant and the service store. In other words, the spatial indices in restaurants and service shops don’t affect the shoppers’ density. It seems difficult to estimate shoppers’ density in restaurants and service shops. The multiple correlation coefficient and coefficients of determination are shown in Table 2 and the results of analysis are shown in Table 3 and Table 4.

Walker’s density= 0.414Global integration-0.189Visual Step Depth fromESC0.451 … (1)

Shopper’s density of retail store=

0.0002Connectivity+0.001Length of shopwindow-0.078 … (2)


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R R2

In circulation path .718 .516

In retail store .912 .832

Table 3: Model summary

Table 4: Results of analysis in retail stores.

The R2 of 0.516 from Table 2 shows that the estimated equation of the walker’s density in the circulation space has high degree of explanatory power. Moreover, the R2 of 0.832 shows that the estimated equation of the shopper’s density in the shops has high interpretability. The Standardized Coefficients of Global integration and of Visual Step Depth from ESC from Table 3 shows that the index to affect the walker’s density in circulation paths most is Integration value and the second is Visual Step Depth from ESC. The Standardized Coefficients of Connectivity and of Length of shopwindow from Table 4 shows that the index to affect the shopper’s density in shops most is Connectivity and the second is the Length of shopwindow.

6. Conclusions

This study analysed the relationship between the shopper’s distribution and the spatial configuration. As a result, we revealed that the walker’s density in the circulation space has a strong correlation with Global integration and Visual Step Depth from ESC. This result shows that the walker’s density in the circulation space receives major influence from "accessibility" and "the number of the turns from escalators." We revealed that shoppers’ density of the retail store has a strong correlation with Connectivity, Local integration, and Length of shopwindow. This result shows that the shopper’s density in the retail stores receives major influence from "flat area within the range in which it sees it from the shopwindow". "accessibility" and “length of the shopwindow”. On the other hand, the restaurant and the service shop did not have an index to be significantly associated with shoppers’ density. Moreover, we made the equation to estimate walker’s density in the circulation space and shoppers’ density in the retail stores from the multiple regression analysis. Both of the equations have high degree of explanatory power, we can explain the walker’s density in the circulation space from two elements of Global integration and Visual Step Depth from ESC, and can explain shoppers’ density in retail stores by two element of Connectivity and the length of the shopwindow. Future study is to consider the spaces such as voids and escalators that can be seen from the other side, but can’t go. When this problem is solved, the models can predict shopper’s distribution more correctly. And we think that this model is utilized for future facilities planning such as the decision of the optimum placement of the store.

Unstandardized Coefficients

Standardized Coefficients t VIF

Int.V .414 .489 4.394 1.691

fromESC_Visual Step Depth -.189 -.299 -2.688 1.691


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References

Kong, E.M., Kim, Y.O. (2013), ‘Examination of spatial characteristics influencing sales by tenant types in shopping malls’. In: Kim, Y. O., Park, H. T. and Seo, K. W. (eds.), Proceedings of the ninth International Space Syntax Symposium, Seoul: Sejong University, p.18.1-18.18

Min, S.Y., Kim, C.J. and Kim, Y.O. (2012), ‘The impacts of spatial configuration and merchandising on the shopping behavior in the complex commercial facilities’. In: Greene, M., Reyes, J. and Castro, A. (eds.), Proceedings of the eighth International Space Syntax Symposium, Santiago de Chile: PUC, p.8066.1-8066.15

Turner, A. (2004), Depthmap 4 – A Researcher’s Handbook, [online] London: UCL. Available from: http://eprints.ucl.ac.uk/2651/. [Accessed: 22th Jan 2014].

Varoudis T. (2012), 'depthmapX Multi-Platform Spatial Network Analysis Software’, Version 0.30 OpenSource. Available at: http://varoudis.github.io/depthmapX/

Zhang, L., Zhuang, Y. and Dai, X. (2012), ‘A configurational study of pedestrian flows in multi-level commercial space. Case study Shanghai’. In: Greene, M., Reyes, J. and Castro, A. (eds.), Proceedings of the Eighth International Space Syntax Symposium, Santiago de Chile: PUC, p.8044.1-8044.16


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http://varoudis.github.io/depthmapX/

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