Investigating the safety impact of roadway network features of suburban arterials in Shanghai

Accident Analysis and Prevention 113 (2018) 137–148

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Investigating the safety impact of roadway network features of suburban arterials in Shanghai

T

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Xuesong Wanga,b,c, , Jinghui Yuand, Grant G. Schultze, Shouen Fanga,b a

School of Transportation Engineering, Tongji University, Shanghai 201804, China Road and Traffic Key Laboratory, Ministry of Education, Shanghai 201804, China c National Engineering Laboratory for Integrated Optimization of Road Traffic and Safety Analysis Technologies, China d Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL, 32816, USA e Department of Civil & Environmental Engineering, Brigham Young University, Provo, UT, 84602, USA b

A R T I C L E I N F O

A B S T R A C T

Keywords: Suburban arterials Road network patterns Signal density Access density Macro level safety modeling Conditional Autoregressive (CAR) model

With rapid changes in land use development along suburban arterials in Shanghai, there is a corresponding increase in traffic demand on these arterials. To accommodate the local traffic needs of high accessibility and efficiency, an increased number of signalized intersections and accesses have been installed. However, the absence of a defined hierarchical road network, together with irregular signal spacing and access density, tends to deteriorate arterial safety. Previous studies on arterial safety were generally based on a single type of road entity, either intersection or roadway segment, and they analyzed the safety contributing factors (e.g. signal density and access density) on only that type of road entity, while these suburban arterial characteristics could significantly influence the safety performance of both intersections and roadway segments. Macro-level safety modeling was usually applied to investigate the relationships between zonal crash frequencies and demographics, road network features, and traffic characteristics, but the previous researchers did not consider the specific arterial characteristics of signal density and access density. In this study, a new modeling strategy was proposed to analyze the safety impacts of zonal roadway network features (i.e., road network patterns and road network density) along with the suburban arterial characteristics of signal density and access density. Bayesian Conditional Autoregressive Poisson Log-normal models were developed for suburban arterials in 173 traffic analysis zones in the suburban area of Shanghai. Results identified that the grid pattern road network with collector roads parallel to arterials was associated with fewer crashes than networks without parallel collectors. On the other hand, lower road network density, higher signal density and higher access density tended to increase the crash occurrence on suburban arterials.

1. Introduction With the rapid growth of the suburban area in Shanghai, the percentage of the population who lives in its suburbs increased by 142% from 2009 to 2014, and the vehicle kilometers travelled in the suburban area has also increased by 64% within the same period (Shanghai Construction and Traffic Development Research Institute, 2015). Suburban arterials, act as the primary traffic corridors in suburban areas, usually have the highest efficiency among the neighboring road networks. However, the increasing traffic demand on suburban arterials, including the frequent accessing by local traffic, has uncovered several issues related to road network structure, signal spacing and access density. In the rapidly developing suburban areas in China, construction of

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the road network usually lags behind land use development. Many local streets provide direct access to arterials with no collector roads between them. Without a properly designed hierarchical road network to distribute local traffic, more and more signals and accesses are installed on suburban arterials, which tends to decrease the arterials’ efficiency and safety. However, there is no current authoritative guidelines for the establishment of signal spacing standards along suburban arterials in China, the addition of increasing numbers of close and irregularly spaced signals tends to reduce arterial travel speeds, resulting in an excessive number of stops, which may, in turn, increase crash occurrence. In addition, high access density is common on suburban arterials, which leads to further traffic conflicts. Together, these problems are contributing to the deterioration of the safety performance of suburban arterials.

Corresponding author at: School of Transportation Engineering, Tongji University, Shanghai 201804, China. E-mail address: [email protected] (X. Wang).

https://doi.org/10.1016/j.aap.2018.01.029 Received 23 January 2016; Received in revised form 18 January 2018; Accepted 19 January 2018 0001-4575/ © 2018 Elsevier Ltd. All rights reserved.

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data from Calgary, Canada, classifying street patterns into four categories: gridiron, warped parallel, loops and lollipops, and mixed patterns. They came to similar conclusions, finding that limited access designs, such as warped parallel, loops and lollipops, and mixed patterns, are safer than the traditional gridiron (grid) pattern. Other studies have investigated the effects of street pattern on crash severity. In two-vehicle crashes, loops and lollipops is a safer pattern, from an injury risk perspective, than the traditional gridiron (Rifaat and Tay, 2009). Yet for crashes involving vulnerable road users (pedestrians or cyclists), the loops and lollipops design was found to be associated with an increase in the severity of crashes (Rifaat et al., 2011, 2012). This discrepancy indicates that a road network with less connectivity, which means a greater presence of cul-de-sacs and loop streets, were not safer for pedestrians than roads with the traditional gridiron pattern. It has been argued that the presence of frequent curves and loops might restrict drivers’ sight distance, resulting in lower perception, longer reaction times, and lower ability to reduce vehicle speed, all of which might increase the possibility of a pedestrian incurring an injury in the event of a crash (Rifaat et al., 2012). The research outlined above, however, has the disadvantage of relying on the subjective and time-consuming method of classifying networks into various patterns by visual observation, a procedure which must usually be repeated by professional-level students or researchers (Rifaat et al., 2009; Rifaat and Tay, 2009; Rifaat et al., 2011, 2012). To overcome these difficulties, several studies have attempted to describe network structure quantitatively based on topological measurements to investigate their impacts on traffic safety (Wang et al., 2012, 2013, 2017; Zhang et al., 2011, 2015). One of these measurements, the centrality index, can capture the “skeleton’’ of an urban structure to reflect the degree to which a network is centralized along a core road. Among all the centrality indexes, network betweenness centrality has been found to be the best measure to distinguish and describe various traffic analysis zone (TAZ) road network patterns (Zhang et al., 2011). As for safety, Zhang et al. (2015) found that a higher network betweenness centrality, that is, a network more highly centered on major roads, was related to fewer non-motorist-involved crashes. In any case, previous research was mainly concentrated on the safety impacts of road network pattern on zonal safety. Attention has not yet been given to the safety impacts of road network patterns on suburban arterials.

Although signal spacing and access density may influence the crash occurrence on both intersections and roadway segments simultaneously, previous studies on arterial safety have generally been conducted by modeling a single type of road entity, either intersection or roadway segment. Moreover, the safety impact of road network structure on suburban arterials has rarely been investigated. Road network structure plays an important role in trip route determination. A road network that includes proper functional hierarchy could reduce local traffic access along arterials, which may improve the safety performance of arterials by reducing the traffic conflicts. Macro-level safety modeling is commonly conducted to investigate the relationship between zonal crash frequency and socio-economic, demographic, road network, and traffic characteristics. In this study, a new modeling strategy is proposed to apply the macro-level safety modeling method to investigate the combined impacts of access density, signal density, and road network patterns on full (segment and intersection) arterial safety.

2. Literature review 2.1. Road network patterns Several studies have analyzed the safety impact of road network patterns at the zonal level. Researchers have found that the grid pattern (high street connectivity) experienced a substantially higher crash frequency than the limited-access pattern (e.g., loops and lollipops) (Lovegrove and Sayed, 2006; Marshall and Garrick, 2011; Rifaat et al., 2009; Rifaat and Tay, 2009; Rifaat et al., 2011, 2012). Marshall and Garrick (2011) found that increased intersection density was correlated with fewer crashes and that increased street connectivity (link to node ratio) was significantly associated with more crashes. However, Dumbaugh and Rae (2009) found that the safety impact of different intersection types varied as to severity level. For example, the higher density of three-leg intersections was associated with fewer injury crashes but an increasing number of total crashes, while the density of four-leg intersections had a positive association with both injury and total crashes. Lovegrove and Sayed (2006) found that the modified Dutch sustainable road safety (SRS) road network (first introduced in the Dutch national SRS guidelines) and the three-way offset network were safer than the conventional grid and cul-de-sac neighborhood street patterns, due to their greater number of three-way intersections. Rifaat et al. (2009) explored the effect of street pattern on crash frequency using Table 1 Literature of the safety effects of road network density related metrics. Study

Dependent variable

Location

Road network density related metrics

Impact on crash frequency

Dumbaugh and Rae (2009)

Total crash

San Antonio/Bexar County metropolitan region

+

Hillsborough County, Florida 24 California Cities

Number of three-leg intersections Number of four-or-more-leg intersections Density of lower-speed streets Number of intersections Road density Intersection density Road density Intersection density Intersection density Intersection density

24 California Cities

Intersection density

−

Alameda County, California 20 cities around the world

Street density Length of road per million inhabitants

− −

Dumbaugh and Zhang (2013) Rifaat et al. (2009)

Crashes involving older motorists, pedestrians, and cyclists Total crash

San Antonio/Bexar County metropolitan region City of Calgary

Rifaat et al. (2010)

Equivalent PDO (9.5*fatal+3.5*injury +PDO) Total crash 12 safer cities and 12 less safe cities (grouped by fatality rate) Total crashes Severe injury crashes Fatal crashes Non-motorist accidents Accident-related fatalities

City of Calgary

Wang and Huang (2016) Marshall and Garrick (2010) Marshall and Garrick (2011)

Zhang et al. (2015) Moeinaddini et al. (2014)

138

+ − + + + + + + −

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the intersections. However, because signal spacing and access density influence the crash frequency of both segments and intersections, limiting the study area to a single road entity type could not reveal the full relationship between such factors and arterial safety. To address this problem, Zeng and Huang (2014) proposed a Bayesian spatial joint model of crash prediction that included both road segments and intersections in an urban road network, through which the spatial correlations between the two heterogeneous types of road entities could be considered. However, they separated the crash data by the two types of entities (segment and intersection) and then employed two different sets of independent variables, one for segments and one for intersections. Their results regarding the full safety impact of specific factors on the arterial level (including segments and intersections) were inconclusive. More recently, Wang and Huang (2016) proposed a hierarchical joint model that included both segments and intersections. Their goal was to establish relationships between road network risk and micro-level variables related to road entities and traffic volume, as well as socioeconomic, trip generation, and network density variables at the macro level. Even though the macro level variables were included in the joint model, the researchers still developed two separate models for segments and intersections, and encountered a problem similar to that confronted by Zeng and Huang (2014). However, Wang and Huang (2016) found that several TAZ-level variables (e.g., signal density) showed significant positive impact on both intersection and segment crash frequency. The model results also confirmed that applying the macro level safety modeling method to investigate the full safety impact (both segment and intersection) of roadway network features on arterials is very important and necessary. Many macro-level safety analyses have been conducted at the TAZ level to investigate the relationship between TAZ-level crash frequency and demographics, roadway network features, and traffic characteristics (Cai et al., 2016, 2017a, 2017b; Huang et al., 2010; Lovegrove and Sun, 2010; Siddiqui et al., 2012a; Wang et al., 2012). A conventional Generalized Linear Model (GLM) was developed under the assumption that all samples are independent. Such assumptions, however, are sometimes violated because TAZs in close proximity to each other are similar in nature (e.g. roadway network features, demographics, etc.) as well as in safety performance. To address this spatial correlation problem, several studies have been conducted over the years using a Conditional Autoregressive (CAR) model (Aguero-Valverde and Jovanis, 2006, 2008; Guo et al., 2010; Li et al., 2007; Quddus, 2008; Wang et al., 2012; Xu and Huang, 2015).

2.2. Road network density With respect to the safety effects of road network density, inconsistent results have been reported by the previous research (as shown in Table 1). One set of studies found that higher road density (or intersection density) was associated with more crash occurrence (Dumbaugh and Rae, 2009; Dumbaugh and Zhang, 2013; Rifaat et al., 2009, 2010; Wang and Huang, 2016). However, another set of studies showed that higher road density was associated with less crash occurrence (Moeinaddini et al., 2014; Marshall and Garrick, 2010, 2011; Zhang et al., 2015). 2.3. Signal spacing Signal spacing refers to the distance between two consecutive signalized intersections. Two main features are derived from the signal spacing: signal density and uniformity of signal spacing. The safety impact of signal density is consistent in the literature, which shows that higher signal density leads to a higher number of crashes (Abdel-Aty and Wang, 2006; Gluck et al., 1999; Schultz et al., 2010; Wang et al., 2014; Wang and Yuan, 2017; Yuan and Wang, 2015). Abdel-Aty and Wang (2006) analyzed the safety impact of signal spacing on intersections and found that longer signal spacing was associated with fewer crashes. Wang et al. (2014) developed several hierarchical Bayesian models to investigate the safety impact of signal spacing based on segment-level data collected from eight suburban arterials in Shanghai. They found that with other variables held constant, one additional signalized intersection installed per kilometer was associated with an increase in crash frequency of 172%. Non-uniform signal spacing disrupts traffic operation and forces drivers to frequently accelerate and decelerate. Gluck et al. (1999) reported that long and uniform signal spacing could achieve more efficient traffic operation and improve safety. At the arterial level, Wang et al. (2014) investigated the safety impact of signal uniformity and found that a larger standard deviation of signal spacing tended to increase minor injury crash frequency. 2.4. Access density Many studies have shown that access density is one of the key factors that influence crash frequency. Gluck et al. (1999) reported that arterial roadways that doubled the number of access points on an arterial roadway from 6.25 to 12.5 per km would increase crash rates by 30–40%. To investigate the safety impacts of various access-related factors on two-lane undivided rural highways in India, Dinu and Veeraragavan (2011) classified the accesses into private access points (houses or shops) and public access points (driveways). They found that an increase in the number of both private and public access points resulted in increased crash frequency. Several before and after analyses on the safety impact of access density can also be found in the literature. For example, based on a before and after case study on arterial segments in Utah, Schultz et al. (2007) found that crash frequency could generally be expected to increase along with an increase of access density.

3. Data preparation 3.1. TAZ delineation and macro features extraction This study was conducted based on the suburban area of Jiading and Baoshan Districts in Shanghai. There are 62 original TAZs in the study area, with an average area of 10.62 sq. km which is too large to capture the heterogeneity of microscopic characteristics (e.g. access density and signal density). Since this study focuses on arterial-level safety analysis with the consideration of macro-level variables, the optimal zonal system should be able to capture both microscopic and macroscopic traffic crash characteristics. Therefore, new TAZs were delineated based on the original TAZs for the specific purpose of arterial safety analysis. Generally, the TAZ system is not specifically delineated for traffic safety analysis but for long-range transportation plans. Several previous studies also tried to delineate different aggregate-level zonal systems for macro-level traffic safety analysis, which are called traffic safety analysis zones (TSAZs) (Lee et al., 2014; Xu et al., 2014). In terms of the delineation method, there are two kinds of methods: objective delineation and manual delineation. The objective delineation methods (e.g., grid delineation) usually cut the road network in a more rigid manner and they can hardly capture the full picture of the road network pattern in the context of a highly complicated and irregular

2.5. Modeling methodology The majority of previous studies on arterial safety have modeled single types of road entity, that is, either intersection (Abdel-Aty and Wang, 2006; Guo et al., 2010; Lee et al., 2017; Wang et al., 2016) or road segment (Wang et al., 2014). Abdel-Aty and Wang (2006) investigated the significant safety influencing factors for intersections along corridors, based on the intersections’ functional areas (i.e., within 250 ft (76.25 m) of the center of the intersection). Wang et al. (2014) conducted a safety analysis for arterials based on the road segments between signalized intersections, but excluding the functional areas of 139

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nodes. The relative betweenness centrality of node i is defined as outlined in Eq. (1) (Freeman, 1977):

shaped road network. Because the safety effect of road network pattern is one of the major objectives in this study, the manual delineation is more preferred. The original 62 TAZs were disaggregated by combining river boundaries, town boundaries, district boundaries, highway, and railway map, and then modified by several rules suggested by Cambridge Systematics, Inc. (2007). For the TAZs with irregular shape or where the land use type was not consistent within a single TAZ, the modification rules are: (1) employing the main roads to act as the TAZ boundary (arterials take precedence over collector roads); (2) the TAZ area must exclude rivers; (3) the TAZ should maintain a regular shape; and (4) each TAZ should keep the same land use type. Finally, a total of 202 TAZs were delineated in the study area and the average area of the new delineated TAZs is 3.26 Km2. Twenty-nine TAZs were excluded from the dataset since there is no any suburban arterial in it. Therefore, all of the modeling data were collected from the remaining 173 TAZs. The land use properties distribution of Jiading and Baoshan Districts were acquired from the Bureau of Planning and Land Administration, and each TAZ in this study was classified into 1 of 7 types: industrial (18.3% of TAZs), commercial (22.3%), educational (7.4%), research and development (R&D) (8.4%), residential (20.8%), greenspace (8.4%), and agricultural (14.4%). The number of trip productions and attractions per day within each TAZ were provided by the Shanghai Urban Planning and Design Research Institute. The traffic information for the suburbs is usually limited and the traffic count data are not available for all of the arterials. In addition, trip generation has been widely treated as a proxy for traffic exposure in TAZ-level traffic safety analysis (Abdel-Aty et al., 2011; Naderan and Shahi, 2010; Siddiqui et al., 2012b; Wang and Huang, 2016). Therefore, the trip productions and attractions were chosen as the traffic exposure variables in this study. As stated in previous research (Pitombo et al., 2011), trip generation of each TAZ is highly influenced by the socioeconomic characteristics, therefore, trip generation could also be treated as a proxy of socioeconomic characteristics. Because the trip generation data were included as an exposure variable, the socioeconomic characteristics were not considered in this study. The road network density within each TAZ was calculated based on the total mileage for all roadways divided by the area.

CiB =

1 × (N −1)(N −2)

∑ j≠k≠i

njk (i) njk

(1)

where N is the total number of nodes, njk is the number of shortest paths between node j and k, and njk (i) is the number of shortest paths between j and k that contain node i. For the zonal road network (each TAZ), the betweenness centrality is defined in Eq. (2) as the average difference between the relative centrality of the most central point (C B* ) and that of all other points i (Freeman, 1977). N

CB =

∑i = 1 (C B* −CiB )

where C B* i

i

(2)

N −1 of CiB ,

is the maximum value and the other parameters are the same as the above function. The betweenness centrality of the road network within each TAZ was collected by extracting the road network for each TAZ and calculating the adjacent road network matrix for that TAZ using a customized procedure based on ArcMap®. The adjacent matrix for each TAZ was imported into UCINET, a social network analytical program that quantifies the network’s structural features (Borgatti et al., 2002) and calculates betweenness centrality. The scatter-plot shown in Fig. 2 illustrates the relationship between the number of suburban arterial crashes per kilometer and the value of betweenness centrality for the studied TAZs. The trend line indicates that TAZs with higher betweenness centrality tended to have higher crash rates. 3.3.2. Betweenness centrality and road network patterns To confirm the relationship between the betweenness centrality values and road network patterns, a visual inspection was conducted on each TAZ. Based on the inspection, graphics were generated; significant differences in the road network patterns for various values of betweenness centrality were evidenced. A comparison of patterns was conducted on 10 TAZs with substantial value differences. As shown in Fig. 3, these TAZs were grouped into two categories, one representing some of the lowest betweenness centrality values and the other representing some of the highest values. As can be seen in Fig. 3(a), the TAZs in Group 1 all have one or more collector roads parallel and within a short distance to the arterials, and the entire road networks show spreading trends perpendicular to the arterials. As a result of these patterns, local traffic would be distributed among the collector roads and local streets, and may not be as dependent on the arterials as the traffic within the Group 2 TAZs (Fig. 3(b)). Group 2 TAZs generally have a greater number of accesses along arterials than Group 1, and its collector roads are rarely parallel to arterials or are discontinuous. Unlike Group 1, Group 2’s road networks are spread along arterials in tree-like structures, suggesting a high dependency of local traffic on the arterials. To illustrate the ability of betweenness centrality values to represent the characteristics of collector roads parallel to arterials, two simplified road network samples were drawn, as shown in Table 2. The betweenness centrality value decreases significantly with the additional four parallel links, analogous to the addition of collector roads parallel to arterials.

3.2. Extraction of road features The road features used in this study included the arterial length, and the signal and access density along the arterials. Arterials included both arterial highways and secondary highways, which were selected by roadway functional class using ArcMap®. All arterials in Jiading and Baoshan Districts are shown as Fig. 1. The arterial length in each TAZ was calculated using the spatial join toolbox in ArcMap®, based on the total mileage of arterials in the TAZ. The roadways on the boundaries of TAZs were evenly distributed to the adjacent TAZs (Sun and Lovegrove, 2013). The numbers of signalized intersections and access points along the arterials within each TAZ were calculated and then divided by the arterial length to generate the corresponding signal density and access density. Intersections that lay on the boundaries of TAZs were allocated evenly to the adjacent TAZs. 3.3. Classification of road network patterns 3.3.1. Calculation of betweenness centrality Previous research has shown that betweenness centrality is the best measure to distinguish and describe various TAZ road network patterns (Zhang et al., 2011). Betweenness centrality is used to examine the shortest distance between any two nodes as a way to measure their importance in terms of traversing the network. The index is based on the idea that a node is central if it lies among many other nodes, and therefore is traversed by many of the shortest paths connecting pairs of

3.3.3. Road network patterns studied Although the betweenness centrality index has been used to describe topological features of road network structural patterns, and the index as well as the patterns have demonstrated relationships to safety, the index is an abstract continuous variable that may be difficult to visualize. The preceding subsection (3.3.2) begins to identify which kinds of road network patterns can be referenced by specific 140

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Fig. 1. Suburban arterials in Jiading and Baoshan districts (outside the Outer Ring).

Table 2 Comparison of two categories of road network samples.

100 Categories

Betweenness centrality

Description

Low value

0.27

Grid pattern: 9 nodes and 12 links

High value

0.67

Tree-like pattern: 9 nodes and 8 links

80

Road network samples

60 40 20 0 0

0.1

0.2

0.3

0.4

0.5

0.6

Fig. 2. Relationship of total arterial crashes per kilometer and betweenness centrality for each TAZ.

Fig. 3. Comparison of road networks with high and low betweenness centrality. Note: Bold lines represent suburban arterials.

141

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Table 3 Summary of road network patterns and the corresponding sample size. Road Network Patterns

Grid

Irregular Grid

Mixed

Tree-like

Grid structure with collector roads parallel to arterials 13 (7.5%)

Grid structure with discontinuous collector roads parallel to arterials 97 (56.1%)

Mixed structure of grid pattern and tree-like pattern 32 (18.5%)

Tree structure without continuous collector roads parallel to arterials 31 (17.9%)

Roadway network figures

Description Sample size

3. Assigning all boundary crashes to the adjacent TAZ by a specific weight (1/number of TAZs adjacent to the crash location) (Lovegrove and Sun, 2010). 4. Based on the travel direction information in the crash location description, assign the crash to the exact travel direction (e.g., east vs. westbound) of the boundary road, and consequently to the corresponding TAZ (Hadayeghi et al., 2010). 5. If the crash location and the travel direction can be confirmed, then allocate the crash to the corresponding TAZ; if the crash location or the travel direction could not be confirmed, then share the crash with adjacent TAZs by pro-rating the crash with a weight equal to the reciprocal of the number of adjacent TAZs (Wang et al., 2012, 2013). In this study, only 26 TAZs have boundary crashes. Therefore, methods 3–5 are more feasible for this study. Among these three methods, method 3 is the most straightforward and method 5 combines methods 3 and 4. Starting in 2012, five location elements have been required in the recording of all crashes that occurred in Shanghai: name of the road where the crash occurred, reference point, geographic orientation, distance from the reference point, and travel direction information. The data quality is good enough to extract the exact travel direction for the majority of the crashes. Therefore, method 5 is more preferable and was used in this research. All the boundary crashes were able to be assigned to the exact TAZ according to the travel direction. For most arterials (non-boundary), the geocoding procedure in ArcMap® was used to locate the crashes on the GIS base map according to the location description. The TAZ shape was overlaid on the base map and the crash count that occurred on the arterials of each TAZ were calculated using the spatial join toolbox in ArcMap®. The trip productions and attractions, arterial length, signal density, and access density were calculated. The descriptive statistics of these continuous independent variables are listed in Table 4.

Fig. 4. Relationship between 4 road network patterns and betweenness centrality.

betweenness centrality values. In order to better visualize the safety impacts, four categories of road network patterns were defined in this study based on their relationships with betweenness centrality. Each of the 173 TAZs was visually inspected and assigned the graphical road network pattern to which it best conformed. A summary of the four categories of TAZ road network patterns and the corresponding sample sizes is shown in Table 3. The box-plot shown in Fig. 4 illustrates the relationship between road network patterns and betweenness centrality for the studied TAZs. The betweenness centrality value not only differentiated between road network patterns, but also did it in a systematic way. The value changes from low (grid pattern) to high (tree-like pattern). This indicates that the above classification of road network patterns could properly join the graphical road network patterns and betweenness centrality values for describing TAZs. 3.4. Descriptive statistics of continuous variables

Table 4 Descriptive statistics of continuous independent variables.

Once the TAZs’ road network patterns were defined along with their other arterial safety-impacting features (e.g., access and signal density), crash data were prepared. Total crashes on the suburban arterials of Jiading and Baoshan Districts for the year 2012 were collected for analysis. In terms of the boundary crashes in zonal-level safety analysis, the allocation issue is a common problem. Generally, there are five methods that have been employed in previous research to address this issue:

Variables TAZ area Ln_Production Ln_Attraction Arterial length Access density

1. Ignore the boundary crashes and only consider crashes that occurred within the TAZ (Khondakar et al., 2010; Lovegrove and Sayed, 2006). 2. Separating the boundary crashes and interior crashes for each TAZ, and then modeling these two kinds of crashes separately in two models. (Siddiqui and Abdel-Aty, 2012).

Signal density

Road network density

142

Description, per TAZ 2

Area (km ) Natural log of trip productions per day Natural log of trip attractions per day Total length of arterials (km) Number of accesses per kilometer along arterials Number of signalized intersections per kilometer along arterials Total length of road network per square kilometer (km/ km2)

Mean

Min

Max

SD

3.26 9.89

0.75 7.13

13.42 12.10

2.40 0.88

9.84

6.82

12.02

0.96

4.70 2.08

0.84 0.47

14.96 7.73

2.18 1.31

1.74

0.54

4.05

0.75

3.52

0.28

8.31

1.54

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Table 5 Modeling strategy illustration. Modeling strategy

Models

Traditional approach

New strategy

Figure illustration

Dependent variables

Independent variables

Road segment model

Crash occurrence on road segments

Traffic characteristics, Roadway features

Intersection model

Crash occurrence in the functional area of intersections

Traffic characteristics, Roadway features

Model for arterials at TAZlevel

Total crash occurrence on the full arterial within the TAZ

Trip generation, Road network structures, Roadway features,

Note: In figure illustration, areas of modeling are designated with bold lines.

4. Modeling methods

results showed that the Poisson-lognormal model outperformed the negative binomial model. Therefore, both the spatial and non-spatial models were developed based on the Poisson-lognormal model. The Poisson-lognormal CAR model was used in the Bayesian framework to account for the spatial correlation between the crash occurrences on arterials in neighboring zones. Letting yi represent crash frequency on the arterials within TAZi , it is assumed that the dependent variable yi follows the Poisson distribution as outlined in Eq. (4):

4.1. Modeling strategies With the traditional macro-level safety modeling strategy, researchers can only estimate the safety impact of roadway features on intersections or road segments separately, even though signal density and access density may influence crash occurrence for both intersections and roadway segments simultaneously. In this study, a new strategy is proposed to meet this need, analyzing the safety factors impacting the full suburban arterial (segments and intersections) at the TAZ level. The crash frequency on the arterials within each TAZ were analyzed as the dependent variable. Roadway network features (i.e., road network patterns, signal density, and access density) and traffic characteristics were analyzed as independent variables. Through this strategy, the combined safety impact of signal density and access density on the full arterial can be investigated. This strategy can also consider the safety impacts of road network patterns and road network density within each TAZ, whereas the traditional methodologies cannot. An illustration of the comparison between the different modeling strategies is shown in Table 5.

yi ∼ Poisson (λi )

where λi is the expectation of yi . A random effect term θi and a spatial correlation term ϕi were introduced into the basic Poisson model to explain separately the sitespecific heterogeneity and the spatial correlation between the neighboring TAZs. The model is defined as outlined in Eqs. (5) and (6):

The Bayesian inference has the advantage of mitigating the estimating error due to the randomness of each crash occurrence. All of the parameters are regarded as random variables that are characterized by a prior distribution, estimated after combining the prior distribution and the sample data. The theoretical framework for Bayesian inference can be expressed as outlined in Eq. (3) (Carlin and Louis, 2009):

(5)

θi ∼ Normal (0, σθ2)

(6)

ϕi ϕ(−i) ∼ N (∑ j

wi, j wi +

ϕj ,

1 ) τc wi +

(7)

where ϕ−i is collection of all ϕ except for ϕi , τc is the precision parameter which accounts for the variation of the spatial dependence, wi, j is the entry on the proximity matrix and generally reflects the spatial relationship between TAZs i and j, and wi + is the sum of wi, j in the TAZs that are adjacent to TAZi . As for the prior information, since there are no available historical data or results, both the non-informative priors and maximum likelihood priors were employed for the modeling process. The normal distribution of (0, 1E3) was employed as the non-informative priors for the coefficients of independent variables, as has been commonly used in previous research (Aguero-Valverde and Jovanis, 2006; Xu and Huang,

L (yθ) π (θ)

∫ L (yθ) π (θ) dθ

log (λi ) = ψi = X ′β + θi + ϕi

where X ‘ is the covariate matrix, β is the vector of regression coefficients, θi is the random effect term for TAZi , σθ2 is the variance of θi , and ϕi denotes the spatial correlation for TAZi , which is specified with a CAR prior. The conditional distribution of the CAR prior is defined as outlined in Eq. (7) (Besag, 1974):

4.2. Statistical modeling method

π (θy ) =

(4)

(3)

where y is the vector of the observed data, θ is the vector of parameters, L (yθ) is the likelihood function, π (θ) is the prior distribution of θ , ∫ L (yθ) π (θ) dθ is the marginal distribution of observed data, and π (θy ) is the posterior distribution of θ given y . At the beginning of the study, both the negative binomial (Poissongamma) and Poisson-lognormal models were employed. The model 143

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complexity (Spiegelhalter et al., 2002). DIC is defined as outlined in Eq. (10):

Table 6 Maximum likelihood prior distributions for Bayesian models. Independent Variables

Mean

Precision (1/variance)

DIC = D (θ) + pD

Ln_production Arterial length Access density Signal density Road network density

0.042 0.146 0.285 0.430 −0.077

273.205 1992.985 793.493 226.811 816.327

Road network patterns (Base: Grid) Irregular Grid Mixed Tree-like

0.503 0.871 0.872

29.218 23.680 23.474

where D (θ) is the Bayesian deviance of the estimated parameter, and D (θ) is the posterior mean of D (θ) . D (θ) can be viewed as a measure of model fitting, while pD denotes the effective number of parameters and indicates the complexity of a model. Models with a smaller DIC are preferred, and a greater than 10 difference in DIC value between models roughly indicates that the model with the greater DIC can be ruled out.

Land use types (Base: Industrial) Commercial Educational R&D Residential Greenspace Agricultural

0.651 −0.205 −0.376 0.459 −0.193 0.154

55.858 29.959 34.039 48.494 29.992 43.742

5. Modeling results 5.1. Bayesian model estimates The Bayesian method is usually implemented with a Markov Chain Monte Carlo (MCMC) algorithm. In this study, three Bayesian Poisson lognormal CAR models were developed using WinBUGS (Spiegelhalter et al., 2003). For each model, two chains of 20,000 iterations were set. After the convergence, evaluated using the built-in Brooks-GelmanRubin (BGR) diagnostic statistic (Brooks and Gelman, 1998), another 50,000 iterations were set to estimate the posterior distribution of the parameters. The model comparison results indicate that the maximum likelihood priors outperform the non-informative priors, which is consistent with a previous study (Yu and Abdel-Aty, 2013). Therefore, only the estimation results with informative priors are summarized in Table 7. The model comparison results based on the DICs show that all the CAR models perform better than the non-spatial model, which indicates that it is essential to take the spatial effects into consideration. The CAR models also provide smaller variance (0.004 (1/260), 0.06 (1/16.570), 0.107 (1/9.338)) in random effects than the non-spatial model (0.125 (1/8.011)), an expected result since the CAR models contain an extra CAR effect to accommodate the data over-dispersion. Among the CAR models, the 0–1 provides the lowest variance in random effect, which means that the 0–1 spatial proximity matrix outperforms the other spatial proximity matrices (common boundary length and total lane number) in accommodating the spatial correlation and heterogeneity. This conclusion can also be deduced based on the mean estimation result of alpha (0.800, 0.532, and 0.267). In terms of the DIC value, which considers model fitting and complexity simultaneously. The differences in DIC values are very significant among these CAR models, which indicate that the lane number model outperforms the other models. In terms of fitting performance (D (θ) ), all the three CAR models are nearly equivalent (Spiegelhalter et al., 2002). Nevertheless, the lane number model performs much better than the other two models in complexity ( pD ). The explanation might be that the spatial proximity structure of the total lane number of connecting arterials between adjacent TAZs is more suitable for this dataset, which may reduce the model complexity. Above all, the lane number model has the best overall performance among the three CAR models. Thus, all coefficients analyzed in the next section will be based on the lane number CAR model.

2015). To acquire the maximum likelihood priors, the maximum likelihood estimation was performed using SAS® with a negative binomial model to generate the informative priors for each independent variable, and then the means and variances of the independent variables were calculated and transformed into normally distributed prior distributions. The informative maximum likelihood priors are summarized in Table 6. The variance of random effect term follows the inverse-gamma distribution (1E-3, 1E-3), and the CAR precision parameter follows the gamma distribution (0.1, 0.1). The proportion of variability in error component due to spatial correlation (α) is defined as outlined in Eq. (8). It has been used to calculate the contribution of spatial correlation in the variability of random effect models (Aguero-Valverde and Jovanis, 2008, 2010; Huang et al., 2010):

α=

(10)

sd (ϕ) sd (θ) + sd (ϕ)

(8)

where sd is the empirical marginal standard deviation function. 4.3. Spatial proximity structures An important detail associated with the CAR model is the weight matrix of the neighboring structures. Common practice is to use the 0–1 first order neighboring structure between spatial units to act as the weight matrix of neighboring zones, hypothetically putting equal weight on the adjacent zones (Aguero-Valverde and Jovanis, 2008; Quddus, 2008). In this study, three types of spatial proximity structures were constructed, including 0–1 first order adjacency, common boundary length, and total lane number of those arterials connecting the adjacent TAZi and TAZj . The spatial correlation among TAZs can be expressed by a proximity matrix W with entry wi, j indicating the spatial relationship between TAZs i and j. For example, the 0–1 first order adjacency was used to complete this weight matrix W1, defined in Eq. (9):

5.2. Analysis of results

1, if TAZi and TAZj are adjacent wi, j = ⎧ ⎨ ⎩ 0, if TAZi and TAZj are not adjacent

5.2.1. Road network patterns All road network patterns variables were found to be significantly associated with crash occurrence on suburban arterials (i.e., they had higher crash occurrence than the base comparison pattern, the grid). According to the estimation coefficient, TAZs with irregular grid patterns tended to generate 74.7% (e 0.558−1) more crashes on their arterials than the grid TAZs. TAZs with mixed patterns generated about 88.1% (e 0.632−1) more crashes than the grid, and tree-like TAZs generated a 92.7% (e 0.656−1) increase in crash frequency when compared with the

(9)

wi, j is also equal to the other two types of spatial proximity, the common boundary length and total lane number of connecting arterials. 4.4. Model comparisons The Deviance Information Criterion (DIC) can be used to compare complicated models by offering a Bayesian measure of model fitting and 144

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Table 7 Model comparison and parameter estimation results. Variables

Poisson lognormal CAR models

Non-spatial Model

0–1 Mean (95% BCI)

Lane number Mean (95% BCI)

Boundary length Mean (95% BCI)

Poisson-lognormal Mean (95% BCI)

1.972 (1.311, 2.677) 0.052 (−0.02, 0.114) 0.132 (0.107, 0.158) 0.166 (0.124, 0.209) 0.336 (0.254, 0.417) −0.059 (−0.100, -0.017)

1.631 (0.862, 2.368) 0.078 (0.004, 0.161) 0.141 (0.116, 0.165) 0.159(0.118, 0.202) 0.334 (0.260, 0.411) −0.049(−0.088, -0.008)

1.615 (1.017, 2.180) 0.071 (0.014, 0.124) 0.153 (0.13, 0.177) 0.161 (0.123, 0.200) 0.343 (0.271, 0.417) −0.036 (−0.071, -0.002)

1.799 (1.197, 2.332) 0.051 (-0.001, 0.106)* 0.156 (0.132, 0.181) 0.169 (0.127, 0.210) 0.352 (0.273, 0.426) −0.038 (−0.073, −0.002)

Road network patterns (Base: Grid) Irregular Grid 0.529 (0.341, 0.720) Mixed 0.607 (0.407, 0.805) Tree-like 0.651 (0.443, 0.865)

0.558 (0.379, 0.737) 0.632 (0.444, 0.825) 0.656 (0.460, 0.854)

0.523 (0.351, 0.697) 0.615 (0.422, 0.813) 0.632 (0.437, 0.829)

0.498 (0.332, 0.680) 0.609 (0.418, 0.813) 0.618 (0.425, 0.818)

Land use types (Base: Industrial) Commercial 0.295 (0.149, 0.440) Educational −0.141 (−0.345, 0.066) R&D −0.110 (−0.307, 0.086) Residential 0.270 (0.113, 0.427) Greenspace −0.031 (−0.246, 0.181) Agricultural 0.114 (−0.042, 0.27)

0.268 (0.127, 0.413) −0.126 (−0.322, 0.070) −0.088 (−0.277, 0.097) 0.257 (0.109, 0.407) 0.002 (−0.198, 0.201) 0.142 (-0.013, 0.301)*

0.300 (0.165, 0.441) −0.143 (−0.333, 0.049) −0.122 (−0.302, 0.054) 0.249 (0.111, 0.393) −0.027(−0.214, 0.162) 0.106 (−0.044, 0.254)

0.314 (0.175, 0.456) −0.126 (−0.319, 0.066) −0.146 (−0.326, 0.035) 0.257 (0.111, 0.407) −0.058 (−0.251, 0.137) 0.082 (−0.069, 0.238)

Random effects and spatial correlation CAR effect (τc ) 1.890 (1.421, 2.486) 260 (24.200, 1390) Random effect ( 1 )

0.988 (0.587, 1.533) 16.570 (9.663, 30.460)

0.057 (0.009, 0.202) 9.338 (6.790, 12.810)

– 8.011 (6.091, 10.230)

0.376 (0.340, 0.413) 0.087 (0.026, 0.181) 0.800 (0.640, 0.934) 1263

0.303 (0.249, 0.359) 0.237 (0.158, 0.298) 0.532 (0.447, 0.639) 1265

0.146 (0.070, 0.230) 0.316 (0.275, 0.351) 0.267 (0.135, 0.409) 1266

– – – 1265

−257 1006

−554 711

27 1293

157 1422

Intercept Ln_Production Arterial length Access density Signal density Road network density

σθ2

sd(ϕ ) sd(θ ) α

D (θ) pD DIC

Note: Mean (95% BCI) values marked in bold are significant at the 0.05 level; mean (95% BCI) values marked in bold and noted by * are significant at the 0.1 level; “–” means there is no corresponding value for this parameter.

grid pattern. These results are quite different from previous studies based on zonal-level data. Previous studies found that the grid pattern (high street connectivity) road network experienced a higher crash rate than lower connectivity patterns such as loops and lollipops (Riffat et al., 2009; Riffat and Tay, 2009; Riffat et al., 2010) and the fused grid road network (Sun and Lovegrove, 2013; Wei and Lovegrove, 2012). The discrepancy in results can be explained in that the traffic pattern on suburban arterials is quite different from those in urban areas. In urban areas, the grid pattern road network usually indicates more intersections and more traffic conflicts, which tends to increase the overall crash frequency. As shown previously in Table 3, however, the grid pattern road network contains several collector roads parallel to the arterials. Around suburban arterials, the grid’s collector roads could distribute the local traffic more effectively than a lower connectivity road network pattern. The better distributed grid could reduce local traffic access to the arterials, which may improve the arterial safety. Conversely, the other patterns tended to increase the crash frequency on arterials in this study when compared with the regular grid. The irregular grid pattern is similar to the grid pattern but the collector roads are generally discontinuous, less able to distribute traffic. The mixed pattern combines tree and grid structure, also with discontinuous collector roads. The tree-like road network is nearly a whole tree-like structure that rarely includes collector roads parallel to arterials. Hence, this pattern shows even higher dependency on the arterials. The need for all traffic to be served by the arterials may result in mixed arterial traffic with high mobility vehicles and non-motorized vehicles sharing the same right of way. Together with the frequent access tree-like patterns provide along arterials, the increase in traffic conflict may significantly deteriorate the safety performance of these suburban arterials. The box-plot shown in Fig. 5 confirms the relationship between

Fig. 5. Relationship between road network patterns and crash rate for the analyzed TAZs.

arterial crash rate and road network patterns. TAZs with an absence of continuous collector roads and with road networks that most closely resemble the tree-like pattern tend to have an increased crash occurrence on their arterials. 5.2.2. Signal density The variable of signal density was found to have a positive effect on crash occurrence. Specifically, one additional signal in a kilometer along an arterial was associated with an increase in crash frequency of 39.7% (e 0.334−1). A likely explanation is that the traffic flow may be more confusing due to the higher density of signalized intersections, resulting in more lane-changing and overtaking behaviors that may increase the crash frequency. Additionally, vehicles may need to stop more frequently, which may, according to previous studies, result in 145

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local traffic may rely on the arterials, which may reduce traffic conflicts on arterials caused by the interaction between local and through traffic, therefore the arterial safety could be improved.

more rear-end crashes (Dinu and Veeraragavan, 2011; Gluck et al., 1999; Schultz et al., 2010; Wang et al., 2014). However, this study’s crash increase of 39.7% is much lower than that in a previous study on suburban arterials, in which Wang et al. (2014) found that the number of predicted crashes per kilometer would increase by about 172% with the installation of one additional signal per kilometer. The large difference may be explained by the sample size: only 8 samples were collected by Wang et al. (2014) at the arterial level to estimate the coefficient of signal density, which may result in a biased estimation.

6. Summary and discussion Applying a macro-level safety modeling method, this study attempted to identify the safety impacts of several factors on suburban arterials, especially road network patterns, which the study introduced into the safety analysis for these roads. Bayesian Poisson-lognormal CAR models were developed based on 173 TAZs, which were delineated from Jiading and Baoshan Districts (outside the Outer Ring) of Shanghai. The frequency of crashes that occurred on the suburban arterials within each TAZ was selected as the dependent variable. The model results show that all the CAR models performed better than the non-spatial model, which confirmed the existence of crosszonal spatial correlation in crash occurrence. The model comparison results demonstrate that the lane number model (i.e., the model considering the spatial proximity of the total number of lanes on the connecting arterials), is the best performing. This was expected because its proximity structure, being directly related to the dependent variable, makes it more appropriate for interpreting the spatial correlation of the dependent variable among adjacent TAZs. These results imply that future spatial modeling should give more attention to the spatial proximity structures which are directly related to the specific subject of the study, as they could significantly improve the model performance over the use of more general proximity structures. Several variables (i.e., trip production, arterial length, access density, signal density, roadway network patterns, road network density, and land use types) were shown to have statistically significant impacts on crash occurrence on suburban arterials. Higher trip production, higher access density and signal density, and commercial and residential land use all tended to increase crash occurrence. Contrary to studies of urban road networks, the tree-like pattern was shown to have the highest crash frequency, whereas the grid pattern outperformed the other road network patterns in suburban arterial safety. The modeling results showed that the tree-like road network pattern was associated with nearly twice the number of crashes on arterials than the grid pattern. Since the rapid development of suburban areas in China, road network construction is always lagging behind land use development. As tree-like patterns tend to be the immediate response to land use development, 17.9% of the road network patterns in Jiading and Baoshan Districts use the tree-like pattern. Due to the lack of a properly designed road network to distribute the local traffic, more accesses have to be opened along the arterials, which continues to decrease the efficiency and safety of arterials. Therefore, it is recommended that the government plan and construct more grid structure road networks in the busy suburban areas. At a minimum, collector roads should be constructed parallel to the arterials to distribute the local traffic and decrease the access density, which should improve the safety performance of suburban arterials. There are still several possible extensions to this study. First, using traffic volume data on suburban arterials might be better than zonal trip generation data in the context of arterial-level safety modeling. When the effect of traffic volume on suburban arterials could be controlled, the relationship between the road network variables and suburban arterial safety might be more straightforward. Specifically, as different road network patterns may result in different trip distribution, which might in turn result in multi-aspects of effects on arterial safety. For instance, compared to tree-like pattern, the grid pattern could distribute more local trips to the neighboring streets, which may result in two kinds of safety impacts on arterials: (1) the traffic volume on arterials could be reduced and less crashes will be produced; (2) the traffic conflicts between long-distance through traffic and local traffic on arterials would be significantly decreased as the grid pattern could better separate the two kinds of traffic. In this context, introducing arterial

5.2.3. Access density The coefficient of access density was significantly positive. The 0.159 coefficient in Table 7 indicates that an increase of one access point per kilometer would result in an increase of 17.2% (e 0.159−1) in crash frequency. The random access of vehicles through these points along the arterials would result in a greater number of conflict points that could deteriorate arterial safety. Several researchers who have analyzed the safety effect of access density have reached similar conclusions (Ackaah and Salifu, 2011; Schultz et al., 2010; Wang et al., 2014). Wang et al. (2014) investigated the safety impact of access density on the segment level and found that one more access point per kilometer was associated with an increase of 10.3% in crash frequency. This figure is a somewhat smaller than that of the current study, but is reasonable, as intersections as well as road segments were included simultaneously in this study. As shown in Fig. 6, the significant tendency toward increase confirms the estimated results. 5.2.4. Other variables The remaining variables of arterial length, land use types, trip production, and road network density were also found to be significantly correlated with crash occurrence on suburban arterials. Longer arterials tended to have a greater number of crashes than shorter arterials. A greater number crashes occurred on commercial and residential land than on industrial land, which is consistent with previous research (Rifaat and Tay, 2009; Rifaat et al., 2010). Total trip production showed a positive association with crash occurrences on arterials. As the number of trips increases, traffic exposure is understood to increase, and high exposure tends to increase the total number of crashes, as has been demonstrated in previous research (Abdel-Aty et al., 2011; Naderan and Shahi, 2010). Road network density was found to have a significant negative correlation with crash occurrence on suburban arterials, a result contrary to some previous studies (Rifaat et al., 2009, 2010; Wang et al., 2012; Wang and Huang, 2016). It can be reasoned that the higher crash occurrence in previous studies may be due to their main focus on the urban network safety performance, where higher road network density is correlated with increases in the number of vehicles turning and changing lanes, which may increase the probability of crash occurrence. In the suburban TAZ with high road network density, however, less

100

80

60

40

20

0 0

1

2

3

4

5

6

7

Fig. 6. Relationship of total arterial crash per kilometer and access density for each TAZ.

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traffic volume into the model would be better to control the safety benefits of volume reduction on arterials. Second, in terms of the crash migration issue, the proposed modeling strategy can only address the crash migration from arterial segments to intersections. However, for the crash migration from arterials to the neighboring local streets, this topic still needs further investigation. This future research would require several years of data for suburban arterials that might be better to investigate the crash migration. Third, at the time of this study, the geometric characteristics and road network features were only collected for the year of 2012. In future research, the sensitivity of the modeling results based on multipleyears of data should be conducted. Based on the results presented, the models developed for the suburban arterials appear to be useful with many applications, such as arterial-level hotspot identification, safety management of signal spacing and access density along suburban arterials, and road network planning for suburban areas. With the improvement of multi-source data (e.g., traffic count, travel speed, social-demographic) and sample size in future studies, research will contribute further toward suburban arterial safety.

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