Combined impacts of configurational and compositional properties of street network on vehicular flow

Combined impacts of configurational and compositional properties of street network on vehicular flow Yu Zhuang Tongji University, Shanghai, China arch-urban@163.com Xiaoyu Song Tongji University, Shanghai, China xiaoyusong25@gmail.com Abstract Space Syntax, which was developed based on Graph Theory, has been proved as one of important research methods regarding urban movement. The conversion from spatial network to J-Graph and the independent analysis of spatial configuration in space syntax makes it possible to quantitatively analyze the spatial network. However, it is undeniable that compositional properties of spatial network are partly discarded in configurational analysis of space syntax. By a study of vehicular movement in five cases of Shanghai, this article re-examined the predicting model of vehicular flow associated with configurational analysis in the irregular street patterns of Shanghai; explored if and how the compositional properties of urban network street width and direction influence on the vehicular flow; and then further established an integrated and optimized predicting model of vehicular flow. Keywords Configuration, compositional properties, street width, street direction, vehicular movement. 1. Introduction and summary Background A metro station area is a spatial and functional node of transferring among multiple modes of transportation. Due to a growing interest in travelling by public transit in the recent years, building and developing metro station areas with great accessibility has drawn public attention. In the studies on promoting public transit, many researchers usually focused on the mobility options by walking or metros, but ignored the impact of vehicles. Actually, as one of the essential modes of transport in the modern cities, vehicle is one of the simultaneous movement systems in the city (Bacon E.N., 1976). For a research regarding synergy among multiple movement systems, it is of great significance to involve the vehicular movement in it and then to consider the network of multiple transit modes as a whole. Moreover, the research on vehicular flow has important implications for effective distribution of limited resources coordinated with movement systems. 89:1

Spatial configuration and vehicular movement Space Syntax, which was developed based on Graph Theory, has been proved as one of important research methods regarding urban movement. A lot of research findings indicate that the configuration of the urban street network is in itself a major determinant of urban movement, for either vehicular or pedestrian flow (Hillier et al, 1987; Hillier et al, 1993; Penn et al, 1998; Hillier et al, 2005). This is mainly because that in the urban daily life, vehicular and pedestrian movement is mostly likely to intended to choose shorter-distance paths, which could be effectively described by distance calculation of spatial configuration. Therefore, to some extent, the vehicular and pedestrian distribution could be predicted by the configurational analysis of network. Specifically, one very important aspect in it is how to quantitatively analyze the configuration of spatial network, which is achieved by converting spatial network to J-Graph, a kind of mathematical model: the movement space of vehicle and pedestrian is considered as nodes of J-Graph, while the configuration describing the arrangement of nodes and links is the core in the analysis. Configuration and composition of street network In fact, street network is presented its spatial properties from both configuration and composition sides. The configuration is regarded as an abstraction from composition (Marshall, 2005). The conversion process from composition to configuration discards some things like metric length, width and angle of orientation. Although with the increasing improvement of space syntax software, some compositional properties of spatial network like length and angle could be involved in the configurational analysis of space syntax, it is undeniable that the missing compositional properties like width and direction do limit the accuracy of movement. For example, the potential influence of street width exerted on the vehicular flow, which could be significant from our daily experience, was obviously not considered in the configurational analysis of space syntax (Penn et al, 1998). On the other hand, the lack of direction attributes means that the one-way streets and two-way streets cannot be processed in the configurational analysis. The existence of one-way streets limits vehicles to make certain turns at the crossing, which means lower accessibility in the graph between certain nodes, thus it becomes harder to get to these nodes representing certain movement paths in the network. This decreasing accessibility caused by the lack of direction attribute is not reflected in regular spatial expression and configurational analysis in the space syntax. Based on the questions and thoughts above, the objectives of the article are three folds: i) to conduct the configurational analysis of street networks and to correlate the results with real vehicle flow, in order to re-examine the predicting models of vehicular flow associated with configurational analysis; ii) to explore if and how the compositional properties of street network street width and direction influence on the vehicular flow; iii) and then to further establish the integrated and optimized predicting model of vehicular flow. 2. Data collection Five metro station areas in shanghai were chosen as the study cases, including metro station area in Wujiaochang, metro station area in Shangchenglu, metro station area in Xujiahui, metro station area in Jingansi, metro station area in Xintiandi. The five cases presented different street patterns. The metro station area defined in this article was exactly the study area in this research, which was a collection of all the reachable areas within 500m walking distance from the entrances/exits of the metro stations on a basis of street network. All the vehicular flow surveys in the five cases were conducted in good environmental conditions, e.g., sunny and warm days. The data of vehicular flow on weekday and weekend were respectively collected in the six different observing periods of one surveying day, including 8:00 am 10:00 am, 10:00 am 12:00 am, 12:00 am 2:00 pm, 3:00 pm 5:00 pm, 5:00 pm 7:00 pm, and 7:00 pm 9:00 pm. There were 57 gates observed in the Wujiaochang station area, 51 gates observed in Shangchenglu station area, 67 gates observed in Xujiahui station area, 58 gates observed in Jingansi 89:2

station area and 135 gates observed in Xintiandi station area, which included almost all the vehicular paths within the five study areas. It took three minutes for investigating each gate during each observing period, totaling eighteen minutes for all the six observing periods. Average values of vehicular flow were used here based on the data gathered on both weekday and weekend. Figure 1 showed actual vehicular flow distributions in all the five case-study areas. (a) (c) (b) (e) (a) Wujiaochang station area (b) Shangchenglu station area (c) Xujiahui station area (d) (d) Jingansi station area Figure 1 Daily vehicular distribution within five case-study areas 89:3

On the other hand, the data regarding street width as well as one-way /two-way streets within five case-study areas were collected. The number of lanes (Num_Lane) was used as a proxy of street width in order to easily process the investigation. Here what the Num_Lane variable considered was just the number of lanes for passing vehicles, excluding the curb-side parking part. From this perspective, the number of lanes might be more correlated with the vehicular movement when comparing with the variable of physical width. The results showed that the number of lanes within the five case-study areas ranged from 1 to 10. During the surveying process, investigators were also required to record the data regarding one-way /two-way streets, which was represented as the variable of Direc_Street in the following analysis. The statistical results about percentage amount of streets were showed in Figure 2. As seen from the chart, the number of one-way streets accounted for more than a quarter of the total vehicular streets within all the case-study areas, except for Shangchenglu case, where the amount of one-way streets was just 8%. Specifically, Xujiahui case had the most one-way streets, sharing 43% of the total vehicular streets. This illustrated that the direction of streets was a spatial attributes which could not be ignored in the actual vehicular street network. Figure 2 Percentage amounts of streets within five study-case areas 3. Configurational analysis of street networks In order to eliminate the influence caused by analysis range on the analysis results as much as possible and acquire more accurate data, this research chose the vehicular network which was bounded by outer ring streets in shanghai as the analysis range. Then the segment map of vehicular paths was established, in which the elevated highways and the underground freeways from multiple layers combined with the ground streetways were effectively linked or unlinked. The choice and integration values (radius at 500m, 1000m, 2000m and n) were calculated by the angular analysis in depthmapx. Choice (commonly called betweenness outside space syntax) and integration (commonly called closeness) are two important measures used to describe structural centrality in the network. The choice indexes how often each line is used on closest paths from all lines to all other lines within the calculated radius; while the integration describes how far each line is from other lines within the calculated radius. Translating the numerical analysis results of spatial configuration into visual images, in which the red was for the most accessible segments and the dark blue for the least accessible segments. The analysis results of choice value and integration value were showed in the following Figure 3, 4. 89:4

Figure 3 Radius n choice map of Shanghai within the outer ring streets 89:5

Figure 4 Radius n integration map of Shanghai within the outer ring streets By correlating the calculated choice value and integration value with actual vehicular flow, it could be found that there were significant positive correlations between the configurational variables and observed vehicular flow (Figure 5). In all five study cases, the most powerful configurational correlations of flow were found to be with the global configurational variables, which were Integration_n (Radius n integration) and Choice_n (Radius n choice), when comparing with other choice and integration values (radius at 500m, 1000m, 2000m), shown in Table 1. Specifically, the correlation coefficients of Integration_n in the wujiaochang and shangchenglu cases, which were 0.811 and 0.719 respectively, are higher than correlation coefficient of Choice_n. While in the xujiahui, jingansi and xintiandi cases, the strongest configurational coefficients are Choice_n, which is at r=0.796 in xujiahui case, r= 0.747 in jingansi case, r=0.655 in xintiandi case. 89:6

Wujiaochang Shangchenglu Xujiahui Jingansi Xintiandi Figure 5 Scattergrams with vehicular flow and configurational measures 89:7

Table 1 Correlations between vehicular flow and choice value, integration value (Raidus at 500m, 1000m, 2000m, n). Best correlations are marked with bold font. Vehicular_Flow Wujiaochang Shangchenglu Xujiahui Jingansi Xintiandi Choice_n 0.735 *** 0.707 *** 0.796 *** 0.747 *** 0.655 *** Choice_500m 0.314 * -0.099 0.310 * 0.102 0.291 ** Choice_1000m 0.452 *** 0.167 0.461 *** 0.442 ** 0.580 *** Choice_2000m 0.536 *** 0.287 * 0.586 *** 0.727 *** 0.352 *** Integration_n 0.811 *** 0.719 *** 0.709 *** 0.695 *** 0.629 *** Integratio_500m 0.640 *** 0.435 ** 0.568 *** 0.658 *** 0.567 *** Integratio_1000m 0.610 *** 0.523 *** 0.635 *** 0.351 ** 0.377 *** Integratio_2000m 0.592 *** 0.611 *** 0.694 *** 0.498 *** 0.427 *** *p <.05. **p <.01. ***p <.001. 4. Analysis on compositional properties of street networks The following analyses mainly focused on the two issues: i) if the street width or direction describing the compositional attributes of street network has a significant influence on the vehicular flow? ii) how much influence they have on the vehicular flow? The vehicular paths within five case-study areas were divided into 5 groups according to the number of lanes. The statistical analyses showed an obvious correlation existing between the averaged passing-vehicular flow per path and the number of lanes. The averaged vehicular flows gradually went up with increasing number of lanes (as shown in Figure 6). This illustrated that the street width, which cannot be reflected in the configurational analysis of network, should be considered as an important influencing factor in the analysis of vehicular movement. On the other hand, by grouped the vehicular paths into one-way streets and two-way streets based on the direction of streets, it was found that the averaged vehicular flow on one-way streets was much less than averaged vehicular flow on two-way streets. Considering the impact on accessibility caused by unidirectional streets, the one-way streets were assigned value 0, which meant the limit of direction added the difficulty of their own accessibility; while two-way streets were assigned value 1, which meant greater accessibility than one-way streets. Figure 8 and Table 2 showed the correlations between vehicular flow and lane number, street direction. Besides lower correlations between street direction and vehicular flow in Shangchanglu, which is due to the small percentage amount of one-way streets, there are strong correlations between vehicular flow and lane number, street direction presented in other four case-study network. Moreover, for all five study cases, the number of lanes is a more important factor in accounting for flows, comparing with the variable of Direc_Street. 89:8

Figure 6 Relationship of vehicular flow and number of lanes Figure 7 Relationship of vehicular flow and direction of streets Table 2 Correlations between vehicular flow and Num_Lane, Direc_Street. Best correlations are marked with bold font. Vehicular_Flow Wujiaochang Shangchenglu Xujiahui Jingansi Xintiandi Num_Lane 0.766 *** 0.646 *** 0.831 *** 0.832 *** 0.766 *** Direc_Street 0.492 *** 0.170 0.591 *** 0.715 *** 0.502 *** *p <.05. **p <.01. ***p <.001. Table 3 Multiple regression analyses of vehicular flow with best configurational measures, Num_Lane and Direc_Street wujiaochan g Shangcheng lu Xujiahui jingansi Xintiandi Model R 2 F p Variable Standardized Coefficients t p Model A 0.680 114.753 0.000 Integration_n 0.825 10.712 0.000 Model B 0.568 71.013 0.000 Num_Lane 0.754 8.427 0.000 Model C 0.740 75.319 0.000 Integration_n 0.598 6.253 0.000 Num_Lane 0.333 3.488 0.001 Model A 0.521 53.379 0.000 Integration_n 0.722 7.309 0.000 Model B 0.417 35.118 0.000 Num_Lane 0.646 5.926 0.000 Model C 0.597 31.419 0.000 Integration_n 0.526 4.070 0.000 Num_Lane 0.290 2.247 0.029 Model A 0.633 112.102 0.000 Choice_n 0.796 10.588 0.000 Model B 0.710 159.324 0.000 Num_Lane 0.843 12.622 0.000 Model C 0.763 102.833 0.000 Choice_n 0.360 3.760 0.000 Num_Lane 0.566 5.914 0.000 Model A 0.558 69.552 0.000 Choice_n 0.747 8.340 0.000 Model B 0.739 155.933 0.000 Num_Lane 0.860 12.487 0.000 Model C 0.746 79.158 0.000 Choice_n 0.220 2.036 0.047 Num_Lane 0.682 6.305 0.000 Model A 0.426 95.821 0.000 Choice_n 0.653 9.789 0.000 Model B 0.590 185.256 0.000 Num_Lane 0.768 13.611 0.000 Model C 0.661 125.032 0.000 Choice_n 0.324 5.215 0.000 Num_Lane 0.586 9.430 0.000 89:9

Wujiaochang Shangchenglu Xujiahui Jingansi Xintiandi Figure 8 Scattergrams with vehicular flow and Num_Lane, Direc_Street 89:10

5. The integrated model Three regression models were established: Model A, which just considered the impact of configurational measures on vehicular flows; Model B, which just considered the influence of compositional elements including street width and direction on flows; Model C, which was an integrated model considering both configuration and compositional elements of network as independent variables. By comparing the analysis results of Model A and Model B (as showed in Table 3), it could be found that the configurational measures were better related to vehicular flows in Wujiaochang and Shangchenglu cases, which had small percentage number of one-way streets within the networks; while in Xujiahui, Jingansi and Xintiandi study networks, where the number of one-way streets accounted for a relatively large proportion, the Num_Lane that described compositional attributes shows greater correlations with vehicular flows than configurational measures. In fact, a large proportion of one-way streets within the network could lead to a relatively great inconsistency between calculated network and actual operating network, which was speculated as an important reason of explaining the weaker correlations of configurational analysis. The measures of configuration, number of lanes and unidirectional roads were all integrated in Model C, and then the integrated models of predicting vehicular flow were established. By the stepwise regression analyses, the unnecessary variables were excluded from the original models, and the optimization models were shown in Table 3. It can be found that the variables of Num_Lane and configurational measures (choice or integration) had been included in the final optimization models for all five study cases, while the variable Direc_Street describing one-way streets were excluded. On the one hand, this was because that there was a degree of self-correlation between the variables of Direc_Street and Num_Lane. The relatively weaker correlation of Direc_Street with flows made itself removed from the models. On the other hand, the current simple weighting method of one-way streets just reflected the influence caused by unidirectional properties of oneway streets on their own accessibility, but cannot effectively express the extended influence of oneway streets on their neighboring roads. The analysis results of Model C for five cases, r2=0.740 in Wujiaochang, 0.597 in Shangchenglu, 0.763 in Xujiahui, 0.746 in Jingansi, 0.661 in Xintiandi, showed that introducing number of lanes together with configurational measures into the models can improve the predictive ability of vehicular flow approximately 60%-75% of the vehicular movement can be predicted by the integrated analysis. 6. Conclusions Spatial network shows its structural properties in both configurational and compositional sides. However, the conversion process from urban street network to configurational model J-Graph discards its own compositional properties. By conducting the five-case studies in the irregular street patterns of Shanghai, it did not illustrate that which one of configurational measures, Choice and Integration, is more related to vehicular movement, but all the five-case studies indicated that both Choice and Integration are very important determinants of vehicular distribution within the network. Moreover, by compared to configurational values with different calculated radius, the global Choice and global Integration values with calculated radius n showed most significant correlations with vehicular movement. Such compositional elements as street width (number of lanes) and direction (one-way streets), which were fully ignored in configurational analysis of street network, have been proved to have strong correlations with vehicular movement. There are usually more vehicular flows on the streets with more lanes or both directions. In which, street width (number of lanes) showed more significant correlation with the vehicular flow than street direction. However, the direction of the streets is still an important factor that cannot be ignored in the analysis of vehicular flow. The findings in this research showed that the configurational measures usually had greater correlations with flows than street width in Wujiaochang and Shangchenglu cases, which are network with smaller percentage amount of one-way streets; but in Xujiahui, Jingansi, Xintiandi, the cases with relatively larger 89:11

percentage amount of one-way streets, the configurational measures showed less correlations than street width. Based on a consideration of the comprehensive impacts of configuration and compositional properties (number of lanes) on vehicular flow, the integrated models of vehicular movement we created achieved better results approximately 60%-70% of the vehicular flow can be predicted by the integrated models in all the five study cases. Limitations in this article and future research In this article, the configurational measures were only calculated by angular analysis, which based on the angular distance. In fact, the configuration calculation in a graph is affected by how distance is conceptualized. It could be further discussed which one of three different distance analysis, including Euclidean distance, topological distance and angular distance, will have a more correlation with the vehicular flow. It could be found from the analysis above that the direction attribute, as one of the compositional properties of network, is still an important factor of vehicular movement. However, the current simple weighting method of one-way streets in this article was not able to effectively describe their extended influence on the neighboring roads. How to effectively express the street direction in the configurational analysis? Whether it is required a high-precision diagram to replace the current single-line map to express the vehicular paths? They will be further explored in the future related research. References Bacon E.N. (1976), Design of Cities, New York: Penguin Books. Hillier B., Burdett R., Peponis J., and Penn A. (1987), Creating life: or, does architecture determine anything?. In Architecture and Behaviour, Vol. 3 (3), p.233-250. Hiller, B., Iida, S. (2005), Network and psychological effects in urban movement. In: Cohn, A.G., Mark, D. M. (eds), Spatial Information Theory: COSIT, Lecture Notes in Computer Science number 3693, p.475-490, Berlin: Springer-Verlag. Hillier B., Penn A., Hanson J., Grajewski T., and Xu J. (1993), Natural movement: or configuration and attraction in urban pedestrian movement. In Environment and Planning B: Planning and Design, Vol. 20, p.29-66. Marshall S. (2005), Streets and patterns: the structure of urban geometry, New York: Taylor & Francis Group. Penn A., Hillier B., Banister D., Xu J. (1998), Configurational modelling of urban movement networks. In Environment and Planning B: Planning and Design, Vol. 25, p.59-84. 89:12