the impact of congestion and traffic flow on …docs.trb.org/prp/17-01683.pdf · 11 luis...

THE IMPACT OF CONGESTION AND TRAFFIC FLOW ON CRASH FREQUENCY AND 1

SEVERITY: AN APPLICATION OF SMARTPHONE-COLLECTED GPS TRAVEL DATA 2 3

4

Joshua Stipancic, Corresponding Author, PhD Candidate 5

Department of Civil Engineering and Applied Mechanics, McGill University 6

Room 391, Macdonald Engineering Building, 817 Sherbrooke Street West 7

Montréal, Québec, Canada H3A 0C3 8

Email: [email protected] 9

10

Luis Miranda-Moreno, Associate Professor 11

Department of Civil Engineering and Applied Mechanics, McGill University 12

Room 268, Macdonald Engineering Building, 817 Sherbrooke Street West 13

Montréal, Québec, Canada H3A 0C3 14

Phone: (514) 398-6589 15

Fax: (514) 398-7361 16


18

Nicolas Saunier, Associate Professor 19

Department of Civil, Geological and Mining Engineering 20

Polytechnique Montréal, C.P. 6079, succ. Centre-Ville 21

Montréal, Québec, Canada H3C 3A7 22

Phone: (514) 340-4711 x. 4962 23


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Word count: 5507 words + 8 tables/figures x 250 words (each) = 7507 words 27

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November 15th, 2016 34

Stipancic, Miranda-Moreno, Saunier

2

ABSTRACT 1 Mobility and safety are the two greatest priorities within any transportation system. Ideally, traffic flow 2

enhancement and crash reduction could occur simultaneously, though their relationship is likely complex. 3

The impact of traffic congestion and flow on road safety requires more empirical evidence to determine the 4

direction and magnitude of the relationship. This study is an ideal application for instrumented vehicles and 5

surrogate safety measures (SSMs). The purpose of this paper is to correlate quantitative measures of 6

congestion and flow derived from GPS smartphone data to collision frequency and severity at the network 7

scale. GPS travel data was collected in Quebec City, Canada and the study sample contains over 4000 8

drivers and 20,000 trips. The extracted SSMs, congestion index (CI), average speed (V̄), and coefficient of 9

variation of speed (CVS), were compared to crash data over a five year period from 2006 to 2010 using 10

Spearman’s correlation coefficient and pairwise Kolmogorov-Smirnov tests. Correlations with crash 11

frequency were weak to moderate. CI was shown to be positively correlated with crash frequency, and the 12

relationship with crash severity was found to be non-monotonous. Higher congestion levels were related to 13

major injury crashes, while low congestion was related to minor and fatal crashes. Surprisingly, V̄ was 14

found to be negatively correlated with crash and had no conclusive statistical relationship with crash 15

frequency. CVS was observed to be positively correlated with crash frequency, and statistically related to 16

increased crash severity. Future work will focus on developing a network screening model that incorporates 17

these SSMs. 18

19 Keywords: surrogate safety, smartphone, GPS, urban, probe vehicles, congestion, traffic flow 20


3

INTRODUCTION 1 Mobility and safety are the two greatest priorities within any transportation system (1). Ideally, 2

improvements to traffic flow and reduction in crashes could occur simultaneously, as some have suggested 3

that traffic operations and road safety are “two sides of a coin” (1). Newer theories contradict earlier beliefs 4

that flow and collisions are positively linked. At low densities, traffic flow increases while speed remains 5

relatively stable. Increasing traffic volumes create more vehicle interactions and conflicts (2), which may 6

increase collision rates (1). As density increases to congestion, flow and speed both reduce significantly. 7

Decreased flow reduces crash frequency, while speed reduction results in reduced crash severity (1, 3). The 8

impact of safety on traffic flow is obvious: collisions create bottlenecks that can increase congestion levels 9

(1). The impact of traffic congestion and traffic flow on road safety is both less obvious (4) and less studied 10

(1), requiring more empirical evidence and quantitative measurements of congestion (5) to determine the 11

direction and magnitude of the relationship. Traffic congestion is worsening in many urban areas (6), where 12

traditional expectations of peak period congestion are being replaced by congestion lasting throughout the 13

day. Efforts to understand and reduce the “extent, duration, and intensity” of congestion (7) should be a 14

high priority (6). The relationship between traffic flow and collisions is likely non-monotonous (2), and a 15

thorough understanding is required to effectively control both (5). 16

Surrogate safety measures (SSMs) may bring an improved or complementary view on the 17

relationship and causal processes between congestion, flow, and safety. SSMs are any non-crash measures 18

that are physically and predictably related to crashes (8), and have the potential to reduce dependency on 19

crash data (9) and eliminate issues associated with crash-based methods including reactivity (10), long 20

collection periods (11), and errors and underreporting in collision databases (12). Popular methods for 21

surrogate safety analysis include event-based techniques, behavioural techniques, and techniques based on 22

measures of traffic flow. Event-based techniques consider traffic conflicts, interactions between road users, 23

or evasive manoeuvres, measured using human observation, video-based sensors, or other techniques (13). 24

Behavioural techniques aim to identify individual driver behaviours not related to conflict avoidance, 25

including yielding (7). Traffic flow techniques, which use measures of volume, speed, or density to estimate 26

risk (8), typically require roadside point sensors including loops, radar, or other sensors (16, 17, 18). Though 27

indicators based on traffic flow have been successful on freeways, it is impractical and costly to implement 28

roadside sensors across an urban network (19). 29

As traffic flow “is a dynamic phenomenon with elements of both space and time” (20), studies of 30

flow are an ideal application for instrumented vehicles. Instrumented vehicles act “as moving sensors, 31

continuously feeding information about traffic conditions” (21) and eliminate the need for roadside sensors. 32

Although several methods for instrumenting vehicles exist, GPS devices have been proven reliable (22) and 33

“there is increasing evidence that traffic conditions can be estimated accurately using only vehicular GPS 34

data” (23). Probe vehicle studies have traditionally been limited in driver sample size and spatio-temporal 35

coverage due to the labour cost associated with operating dedicated probe vehicles (24). New technologies, 36

including GPS-enabled smartphones, have made obtaining data easier over time. Smartphones are 37

inexpensive, simple, and user-friendly and eliminate the need for external sensors (25, 26). Although all 38

probe vehicles provide measurements for vehicles operating within normal traffic (27), collecting GPS data 39

from smartphones minimally impacts driver behaviour. The purpose of this paper is to correlate quantitative 40

measures of congestion, speed, and speed uniformity, derived from GPS smartphone data to historical 41

collision frequency and severity at the network scale. The objectives of this research are to describe the 42

extraction of data from GPS-enabled smartphones, and to explore the potential of congestion and traffic 43

flow measures as SSMs through correlation with collision data on a link and intersection basis at the 44

network level. 45

46

LITERATURE REVIEW 47 Many congestion measures have been proposed in research or implemented in practice. Aftabuzzaman (28) 48

provides a comprehensive review and proposes four categories. Basic measures are related to delay: they 49

are useful in econometric analysis, but may not accurately portray different levels of congestion. Ratios are 50

“usually developed by dividing one travel time or delay element by another” (28) and can be used to 51


4

estimate differences between expectation and actual performance. The traditional level of service (LOS) 1

classification is a popular measure of congestion and, although easily understood, it “cannot provide a 2

continuous range of values of congestion” (28). Of all the potential measures, ratio indicators are perhaps 3

the most promising. Although such indicators are limited to calculations on a particular link or route, they 4

“can be used for an urban area wide application” (28). Congestion indicators can combine several elements 5

of travel time or speed into a single measure (29). The Congestion Index (CI) is the difference between the 6

actual speed and free flow speed over the free flow speed (1). 7

Studies examining the relationship between congestion and safety have used various methods and 8

congestion metrics, ranging from simple to complex, applied mostly in freeway environments. Noland and 9

Quddus (3) used proxy variables for congestion, but found little effect on safety. Wang, Quddus, and Ison 10

(30) used delay as a measure of congestion, hypothesizing that high congestion levels would result in low 11

crash severity. They were unable to support their hypothesis. Martin (31) found that collision frequency 12

and severity were elevated during light traffic. Additionally, as traffic flow increased, single vehicle crashes 13

became less likely, and multi-vehicle crashes become prevalent. Zhou & Sisiopiku (2) found that the most 14

collisions occurred when the volume to capacity ratio (v/c) was either lowest or highest, demonstrating that 15

the relationship between congestion and safety is non-monotonous. The study also found that crash severity 16

was greatest at low flow, and decreased as v/c increased. Regarding studies specifically using CI, Dias et 17

al. (1) concluded that increasing CI could also increase the probability of a collision. Wang et al. (5) 18

calculated CI along a British motorway, finding a negative (though statistically insignificant) relationship 19

between CI and collision severity. Although the study reports that “the level of traffic congestion has no 20

impact on the frequency of road accidents” (5), as CI values were consistently less than 0.5, it is unclear 21

whether the data truly represented congested scenarios (1). Shi and Abdel-Aty (29) found that specific 22

scenarios (which included higher CI values), could indicate periods with a high probability for a crash on 23

the studied expressway (namely during the peak periods). 24

Other traffic flow SSMs have mainly focused on the use of traffic data collected by roadside sensors 25

along a single corridor. Oh et al. (16) considered average and variance of flow, occupancy, and speed as 26

potential indicators of traffic state. The standard deviation of speed was correlated with disruptive traffic 27

conditions and a higher likelihood of collisions (16). Lee et al. (18) used a log-linear statistical model to 28

show that variation in speed and density were significantly correlated with crash frequency (18). Abdel-29

Aty and Pande (32) applied a Bayesian classifying approach to categorize traffic conditions as either leading 30

to or not leading to a crash. Golob et al. (17) defined eight traffic flow regimes using speed and flow, 31

concluding “the key elements … affecting safety are not only mean volume and speed, but also variations 32

in volume and speed”. Despite the limited literature on traffic flow SSMs derived from GPS data, if the 33

volume of GPS data can be practically increased by leveraging the capabilities of GPS enabled 34

smartphones, traffic flow SSMs could be computed. Moreno and Garcia (33) present a methodology using 35

GPS trackers in which speed profiles are used to calculate measures of speed uniformity and over speeding. 36

Boonsiripant (34) utilized GPS data from the Commute Atlanta program to develop SSMs based on the 37

variation in vehicle speed profiles. 38

With this literature considered, several shortcomings remain. First, there has been no attempt to 39

derive SSMs from smartphone-collected GPS data of regular drivers alone. Instead, focus has been on 40

dedicated probe vehicles with low penetration rates. Second, there has been no comprehensive comparison 41

of GPS-based surrogate indicators to large quantities of crash data. Studies have compared indicators to 42

sample safety data, which often consists of self-reported near misses. Finally, there has been no application 43

of GPS data across an entire urban network. Studies to date have focussed on specific corridors (namely 44

freeways) despite that fact the GPS presents an opportunity for network-wide analysis. 45

46

METHODOLOGY 47 The details of collecting and processing GPS data from a smartphone application are covered in detail by 48

Stipancic, Miranda-Moreno, and Saunier (35). A brief description of the data structure, data filtering, and 49

network definition is provided below. 50


5

Data Structure 1 GPS data from the smartphones of regular drivers contains observations describing trips both across time 2

and space. For each logged trip, 𝑖, GPS travel data is returned as a series of observations from origin to 3

destination, 𝑂𝑖𝑗, such as 4

5

𝑡𝑟𝑖𝑝𝑖 =

{

𝑂𝑖0𝑂𝑖1⋮𝑂𝑖𝑗⋮𝑂𝑖𝑛}

=

{

𝑖, 𝑐𝑖0, 𝑡𝑖0, 𝑥𝑖0, 𝑦𝑖0 , 𝑧𝑖0, 𝑣𝑖0𝑖, 𝑐𝑖1, 𝑡𝑖1, 𝑥𝑖1, 𝑦𝑖1 , 𝑧𝑖1, 𝑣𝑖1

⋮𝑖, 𝑐𝑖𝑗 , 𝑡𝑖𝑗 , 𝑥𝑖𝑗 , 𝑦𝑖𝑗 , 𝑧𝑖𝑗 , 𝑣𝑖𝑗

⋮ 𝑖, 𝑐𝑖𝑛𝑖 , 𝑡𝑖𝑛𝑖 , 𝑥𝑖𝑛𝑖 , 𝑦𝑖𝑛𝑖 , 𝑧𝑖𝑛𝑖 , 𝑣𝑖𝑛𝑖}

6

7

where 𝑖 is a unique trip identifier, 𝑂𝑖𝑗 is the jth observation in trip 𝑖, 𝑐𝑖𝑗 is a unique coordinate identifier, 𝑡𝑖𝑗 8

is the datetime, 𝑥𝑖𝑗, 𝑦𝑖𝑗, and 𝑧𝑖𝑗 are the latitude, longitude, and altitude, and 𝑣𝑖𝑗 is the speed. The time 9

between consecutive observations is typically between 1 and 2 seconds. Once a trip has been collected and 10

reported by the user, initial pre-processing of the data using methods like Kalman filtering (36) to reduce 11

variability is typical. The data is stored in a remote database from which observations are exported for 12

analysis. 13

14

Map Matching 15 The data filtering procedure is illustrated in Figure 1. Raw GPS traces contain positional variability even 16

in cases where the data is pre-processed. Map matching can eliminate this variability by explicitly linking 17

GPS observations to the road network. For this reason, map matching is preferred to other filtering methods 18

that only smooth the data in terms of longitude and latitude. TrackMatching is a commercially available, 19

cloud-based web map matching software service (37) that matches GPS trip data to the OpenStreetMap 20

(OSM) road network (38). Individual trips are processed, and the software returns a new latitude and 21

longitude, 𝑥𝑖𝑗′ and 𝑦𝑖𝑗

′ , corresponding to a specific OSM link ID, 𝑙𝑖𝑗, and the source, 𝑠𝑖𝑗, and destination 22

nodes, 𝑑𝑖𝑗. 𝑥𝑖𝑗′ and 𝑦𝑖𝑗

′ are chosen based on the Euclidean distance from the unfiltered GPS points to the 23

road network and on network topology (39). 24

25

Speed Filtering 26 With the positions filtered using map matching, an additional filter is required to eliminate noise in the GPS 27

speeds. Although several different filters have been proposed and tested, both Zaki, Sayed, and Shaaban 28

(40) and Bagdadi and Varhelyi (41) found that the Savitzky-Golay filter was sufficient for this application, 29

noting that the filter is suitable for time series’ with fixed and uniform intervals and with limited 30

discontinuities in the data (40). This digital filter is “a weighted moving average–based filter, with 31

weighting described as a polynomial model of arbitrary degree” (40). In the Savitsky-Golay, both the degree 32

of the fitted polynomial and the window size (the number of points to which the polynomial is fitted) can 33

be varied to adjust the amount of filtering. Based on previous work (35), a polynomial of degree two and a 34

window length of five were shown to be accurate. The filter is applied to speeds 𝑣𝑖𝑗 and smoothed speeds 35

are denoted as 𝑣𝑖𝑗′ . The filtered data is merged with the original data set yielding the data structure below. 36

37

𝑡𝑟𝑖𝑝𝑖 =

{

𝑖, 𝑐𝑖0, 𝑡𝑖0, 𝑥𝑖1′ , 𝑦𝑖0

′ , 𝑧𝑖0, 𝑣𝑖0′ , 𝑎𝑖0, 𝑙𝑖0, 𝑠𝑖0, 𝑑𝑖0

𝑖, 𝑐𝑖1, 𝑡𝑖1, 𝑥𝑖1′ , 𝑦𝑖1

′ , 𝑧𝑖1, 𝑣𝑖1′ , 𝑎𝑖1, 𝑙𝑖1, 𝑠𝑖1, 𝑑𝑖1

⋮𝑖, 𝑐𝑖𝑗 , 𝑡𝑖𝑗 , 𝑥𝑖𝑗

′ , 𝑦𝑖𝑗′ , 𝑧𝑖𝑗 , 𝑣𝑖𝑗

′ , 𝑎𝑖𝑗 , 𝑙𝑖𝑗 , 𝑠𝑖𝑗 , 𝑑𝑖𝑗⋮

𝑖, 𝑐𝑖𝑛𝑖 , 𝑡𝑖𝑛𝑖 , 𝑥𝑖𝑛𝑖′ , 𝑦𝑖𝑛𝑖

′ , 𝑧𝑖𝑛𝑖 , 𝑣𝑖𝑛𝑖′ , 𝑎𝑖𝑛𝑖 , 𝑙𝑖𝑛𝑖 , 𝑠𝑖𝑛𝑖 , 𝑑𝑖𝑛𝑖}

38

39

40


6

1

FIGURE 1 Collection and map matching of smartphone-collected GPS data 2

Network Definition 3 The use of the OSM road network in the TrackMatching algorithm presents a challenge. Ideally, road links 4

would never be divided by an intersection (7) (each link should connect adjacent intersections). The OSM 5

road network is generated non-systematically by users, and OSM links do not always meet this definition. 6

It is desired to redefine the network such that each link is properly defined between adjacent intersections. 7

Redefining the network requires the following steps, which can be completed in any GIS software 8

environment, to yield links as illustrated in Figure 2: 9

10

1. Identify all nodes that represent an intersection in the road network. 11

2. Split the road network at the identified nodes. 12

3. Rename each link according to its original ID and the nodes on either end of the link. 13

4. Remap the GPS observations to the new network. 14

15

16

FIGURE 2 Redefinition of OSM Links 17


7

Extracting Surrogate Safety Measures 1 Similar to Boonsiripant (34), each proposed SSM was calculated across several time periods throughout 2

the day. For this study, values of each SSM were calculated for the AM peak (6:00 to 10:00 AM), PM peak 3

(3:00 to 7:00 PM), the peak periods combined, and the off-peak trips. These start and end times of the peak 4

periods were determined previously (42). A single time period was chosen for each SSM based on which 5

time period was shown to be most strongly associated with collision frequency and severity during analysis. 6

7

Congestion Index 8

Estimating congestion from GPS travel data is covered in detail in a previous study by Stipancic, Miranda-9

Moreno, and Labbe (42). Aftabuzzaman (28) suggested that measures of congestion meet several criteria 10

including clarity, simplicity, comparability, and continuity. Though several measures based on travel time 11

have been proposed, because link travel time is dependent on position, and because the true latitude and 12

longitude are unknown because of map matching, a congestion measure based on speed (which is directly 13

available from the GPS data) is preferred. Dias et al. (1) proposed CI calculated as; 14

15

𝐶𝐼 =

free flow speed − actual speed

free flow speed if 𝐶𝐼 > 0

= 0 if 𝐶𝐼 ≤ 0 (1)

16

This formulation yields CI values ranging from 0 (speed is equal to the free flow speed) and 1 (speed is 17

zero), and meets several of the suggested criteria. Free flow speed has been defined in numerous ways. As 18

congestion is generally constrained to the AM and PM peak periods, speeds observed outside of these times 19

can be used as estimates. For each link, 𝐿𝑖𝑗, the free flow speed, 𝐹𝐹𝑆𝐿𝑖𝑗, is simply the average of all observed 20

speeds falling on link 𝐿𝑖𝑗 outside of the defined peak periods. Next, CI for every observation can be 21

computed according to 22

23

𝐶𝐼𝑖𝑗 =

𝐹𝐹𝑆𝐿𝑖𝑗 − 𝑣′𝑖𝑗

𝐹𝐹𝑆𝐿𝑖𝑗 if 𝐹𝐹𝑆𝐿 > 𝑣′𝑖𝑗

= 0 otherwise

(2)

24

where 𝐶𝐼𝑖𝑗 is the congestion index for observation 𝑂𝑖𝑗, 𝐹𝐹𝑆𝐿𝑖𝑗 is the free flow speed on link, 𝐿𝑖𝑗, and 𝑣′𝑖𝑗 is 25

the observed speed. Finally, CI was calculated for each link, 𝐿𝑖𝑗, by averaging each observed 𝐶𝐼𝑖𝑗; 26

27

𝐶𝐼𝐿𝑖𝑗 =∑ ∑ 𝐶𝐼𝑖𝑗𝑗𝑖

𝑁 (3)

28

where 𝑁 is the count of all observations on link 𝐿𝑖𝑗. As in previous work (42) filters were used to eliminate 29

links with too few observations for a valid calculation (less than two trips with two observations per trip). 30

Preliminary results indicated that CI during the PM peak had the strongest relationship with crash frequency 31

and severity in this study. 32

33

Average Speed 34

Travel speed has long been believed to be an indicator of crash risk at the link level. Over speeding is 35

regarded as a dangerous behaviour, and efforts to increase adherence to the speed limit have been 36

implemented across North America. Locating facilities where high speeds contribute to collision frequency 37

and severity would be beneficial to law enforcement agencies, who could increase the effectiveness of 38

enforcement operations by targeting the highest risk sites. Average speed is calculated for each link, by 39

considering every observation falling on that link. The average speed is computed as 40

41


8

�̅�𝐿𝑖𝑗 =∑ ∑ 𝑣′𝑖𝑗𝑗𝑖

𝑁 (4)

1

where 𝑁 is the count of those observations on link 𝐿𝑖𝑗. The off-peak period was chosen for calculation to 2

avoid collinearity with CI (in this case, �̅�𝐿𝑖𝑗 is exactly equal to 𝐹𝐹𝑆𝐿𝑖𝑗 defined above). 3

4

Speed Uniformity 5

Although the magnitude of speed is widely believed to contribute to crash occurrence, much of the existing 6

literature supports that variation in speed may be a better predictor of risk. Although several measures of 7

speed uniformity have been suggested, including standard deviation, coefficient of variation, and 8

acceleration noise, Ko et al. (43) demonstrated that these measures are highly correlated. Although initial 9

tests were done on several possible SSMs, the coefficient of variation of speed (CVS) was determined to 10

have the strongest relationship with safety. CVS is defined as the standard deviation of speed over the mean 11

speed. For each link, CVS is computed as 12

13

𝐶𝑉𝑆𝐿𝑖𝑗 =𝜎(𝑣′𝑖𝑗)

�̅�𝐿𝑖𝑗 (5)

14

where 𝜎(𝑣′𝑖𝑗) is the standard deviation of all speeds on link 𝐿 during the considered time period. CVS was 15

found to be most strongly related to crash frequency and severity during the off-peak period for this study. 16

17

Data Analysis 18 Surrogate safety measures must be predictably related to crashes (8), and any proposed measure must 19

demonstrate correlation with actual risk. Although the measures above have been proposed as SSMs, the 20

objective of this analysis is to demonstrate the statistical relationship between congestion, speed, and speed 21

uniformity, and collision frequency and severity, by comparing the proposed indicators with historical 22

collision data at the link and intersection level. It is necessary to consider both frequency and severity, as 23

the relationships of these independent dimensions of safety are likely complex. Previous studies have 24

identified the need of separating facilities according to functional classification (34). Therefore, the analysis 25

was completed separately considering five distinct functional road classes: freeway, primary, secondary, 26

tertiary, and residential (where primary, secondary, and tertiary are arterials and collectors classified by 27

importance to the road network, with primary being most important). 28

29

Collision Frequency 30

Spearman’s Rank Correlation Coefficient, or Spearman’s rho, indicates how strongly the dependency 31

between two variables is described by a monotonic function, and is recommended for the evaluation of 32

SSMs in an FHWA report (44). Locations with high collision frequency should also have extreme values 33

of an SSM. A rho of 1.0 indicates perfect positive correlation, 0.0 indicates no correlation, and -1.0 indicates 34

perfect negative correlation. Spearman’s rho, 𝜌, is calculated using 35

36

𝜌 = 1 −6∑(𝑤𝐿 − 𝑣𝐿)

2

𝑁(𝑁2 − 1) (6)

37

where 𝑤𝐿 is the rank of link 𝐿 in the collision data set (determined by the number of collisions per unit 38

length of roadway), 𝑣𝐿 is the rank of link 𝐿 in the surrogate data set (determined by each SSM), and 𝑁 is 39

the total number of links. Link collision rates were determined by counting the number of collisions within 40

a 50 m buffer surrounding the link. Although traffic flow SSMs are inherently geared towards analysis at 41

the link level, an attempt was made to quantify correlation at the intersection level. Collision ranks were 42

determined by counting the number of collisions within a 200 m buffer around the intersection, and the 43

surrogate ranks were determined by averaging the value of the SSM on any intersecting links with data. 44


9

Collision Severity 1

A Kolmogorov-Smirnov test (K-S test) can be used to test equality between two continuous probability 2

distributions. The K-S test is preferred over other statistical techniques because it is nonparametric, 3

requiring no assumption to be made about the shape of the probability distributions. The two-sample K-S 4

test is used to compare the empirical cumulative distribution functions, and return the K-S statistic 𝐷, which 5

represents the maximum difference between the two distribution functions, computed as 6

7

𝐷 = 𝑚𝑎𝑥1<𝑖<𝑁|𝐸1(𝑖) − 𝐸2(𝑖)| (7) 8

where 𝐸1 and 𝐸2 are the empirical cumulative distribution functions of the two samples. 9

In order to evaluate if the extracted surrogate measures are statistically linked to collision severity, 10

links and intersections were divided into three groups each; 1) links or intersections with at least one fatal 11

collision; 2) links or intersections with at least one major injury collision, but no fatal collisions, and; 3) 12

links or intersections with only minor injury collisions. A series of pairwise K-S tests were then performed 13

between each combination of the above groups for each functional classification, to determine if any 14

statistical differences exist in the distributions of the SSMs at different levels of collision severity. 15

16

RESULTS 17 18

Data Description 19 This project made use of GPS data collected using the Mon Trajet application (45), originally developed 20

for the City of Quebec, Canada by Brisk Synergies (46). Screenshots from the application are shown in 21

Figure 3. The application, which is available for Apple and Android devices, was installed voluntarily by 22

drivers and allowed them to anonymously log trips into the application. In total, nearly 5000 driver 23

participants have logged nearly 40,000 trips using the application. The sample for this study contained over 24

4000 drivers and 21,939 individual trips during the period between April 28 and May 18, 2014. Over the 25

21 days sampled, 19.7 million individual data points were logged. Crash data for the City of Quebec was 26

obtained from the Ministry of Transportation Quebec for a five year period from 2006 to 2010. 9248 27

collisions identified across the 5-year period involved at least one vehicle. Geometric map data was 28

obtained from OpenStreetMaps in order to ensure consistency with the map matching results. 29

30

31

FIGURE 3 Smartphone application interfaces 32


10

Extraction of Surrogate Measures 1 At the link level, there was sufficient data to compute each of the three SSMs on 4912 links. The fact that 2

the number of links was equal for all three measures is merely a coincidence, and it is not required that a 3

single link be represented in all three data sets (CI requires both peak and off peak data to be available, but 4

accepts 0 as a legitimate value, whereas the others do not). Figure 4 illustrates the network coverage for the 5

three considered SSMs. Although many residential links are missing data (they experienced few, if any, 6

trips), the coverage is sufficient to include most of the main highways, arterials, and collectors, as well as 7

fair coverage in downtown Quebec City. When aggregating data to the intersection level, CI was evaluated 8

at 4540 intersections, while for V̄ and CVS, data was available at 4818 intersections. Correlations between 9

the measures are provided in Table 1. 10

TABLE 1 Correlation between Traffic Flow SSMs at the Link and Intersection Level 11

Link Level Intersection Level

CI V̄ CVS CI V̄ CVS

CI 1.00 0.28 -0.17 CI 1.00 0.27 -0.16

V̄ - 1.00 -0.57 V̄ - 1.00 -0.59

CVS - - 1.00 CVS - - 1.00

12

Collision Frequency 13 The average values and correlation strength with collision frequency for the three SSMs is provided in 14

Table 2. CI was positively correlated with crash frequency at both the link and intersection levels for all of 15

the functional classifications. This result (that increased congestion leads to more crashes) supports the 16

results found in several past studies (1, 17, 29). The indicator performed best on primary streets at the link 17

level (ρ = 0.21), and performed better at the link level in general. However, compared to the other indicators, 18

CI had the lowest correlation strength, and performed very poorly on motorways. One possible explanation 19

is that motorways, on average, are the most congested facilities. At high congestion levels, changes in 20

density have relatively little effect on flow and speed. Therefore, large changes in CI have relatively little 21

impact on traffic conditions and collisions. 22

In contrast, V̄ showed the strongest correlation with crash frequency, although the direction of the 23

correlation was consistently negative across functional classes. This result implies that, within a given 24

roadway class, links and intersections with higher off-peak speeds have fewer crashes than those with lower 25

speeds. The indicator performed well on primary, secondary, and tertiary facilities (-0.50 ≤ ρ ≤ -0.30), but 26

performed poorest on residential streets (ρ ≤ -0.20). Although the negative correlation opposes most 27

existing literature (47), two things should be noted: besides functional class, there is no controlling for other 28

factors which may themselves influence speed (geometry, distance from the city centre, etc.), and this study 29

considers the network scale, while many previous studies considered individual corridors or links. CVS 30

was consistently positively correlated with crash frequency, and generally performed well on all facility 31

types (0.20 ≤ ρ ≤ 0.40), except for residential facilities (ρ < 0.20). This result supports the specific findings 32

by Lee et al. (11) that increased CVS is associated with more collisions, and the general findings by other 33

authors that speed variation and crash frequency are positively linked (17, 32, 33). In general, the strength 34

of these correlations is weak to moderate, which means that traffic flow measures may not be great 35

predictors of crash frequency. However, their relationship with crash severity must also be considered. 36


11

1 (a) 2

3

4 (b) 5

6

7 (c) 8

FIGURE 4 Maps of congestion index (a), average speed (b), and coefficient of variation of speed (c) 9


12

TABLE 2 Averages and Spearman’s rho For Traffic Flow SSMs at the Link and Intersection Level 1

Average Values for CI, V̄ (km/h), and CVS 2 3


Classification CI V̄ CVS Classification CI V̄ CVS

Motorway 0.116 75.52 0.199 Motorway 0.118 75.39 0.195

Primary 0.104 45.74 0.326 Primary 0.103 43.50 0.338

Secondary 0.102 43.94 0.305 Secondary 0.102 42.97 0.308

Tertiary 0.087 38.84 0.314 Tertiary 0.086 38.42 0.320

Residential 0.065 30.74 0.347 Residential 0.083 34.14 0.334

4 Spearman’s rho for CI, V̄ (km/h), and CVS 5

6


Classification CI V̄ CVS Classification CI V̄ CVS

Motorway 0.05 -0.27 0.17 Motorway 0.02 -0.14 0.20

Primary 0.21 -0.35 0.16 Primary 0.18 -0.45 0.38

Secondary 0.11 -0.41 0.10 Secondary 0.11 -0.37 0.36

Tertiary 0.12 -0.22 0.16 Tertiary 0.15 -0.18 0.20

Residential 0.08 0.05 0.15 Residential 0.09 0.00 0.13

7

Collision Severity 8 The results of the collision severity testing are summarized in Figure 5. Aggregate results for all links are 9

provided in the left column, and an example for one functional class is provided in the right. All plots are 10

at the link level, as the results for intersections were substantially similar. The full results of all K-S tests 11

are provided in Table 3. With regards to CI, the distributions for links (shown in Figure 5a) and intersections 12

with minor injury and fatal collisions was shifted to significantly lower values than links with major injury 13

collision (by K-S test at 90% confidence). This pattern was verified for several different functional 14

classifications such as motorways, as illustrated in Figure 5b. In fact, this was the most common pattern for 15

CI, being observed to be statistically significant (at 90% confidence) in 4 out of 10 test cases (5 classes at 16

both the link and intersection levels), and non-significant in 4 additional cases (see Table 3). This result 17

suggests that congestion could be used to define two categories: high congestion, which have more major 18

crashes, and low congestion which can have either minor or fatal crashes, as decided by other factors. 19

Importantly, this result highlights the complex relationship between congestion and crash severity. 20

For V̄, no statistically significant difference was found in the distributions for all links (Figure 5c) 21

or all intersections. When dividing the data by functional classifications, no consistent patterns were 22

observed. For example, on secondary links (shown in Figure 5d), the distribution of speed for links with 23

major injuries was shifted to lower values compared to distributions for those with minor and fatal collisions 24

(by K-S test at 90% confidence). Decreasing severity with increasing speed was observed to be significant 25

in only two cases. Off-peak speed shares, at best, a weak relationship with crash severity at the network 26

level in this data set. CVS had the strongest relationship with crash severity. The cumulative distributions 27

of all links is provided in Figure 5e. For all links and intersections, the distribution of links with major 28

injuries was shifted towards higher values compared to the distribution for links with major injuries (by K-29

S test at 90% confidence). Furthermore, the distribution for links and intersections with fatal crashes was 30

shifted to higher values compared to both other distributions (at 90% confidence). This pattern was 31

observed to be statistically significant in 5 out of 10 test cases, and insignificant in an additional 4 (see 32

Table 3). One of the clearest examples of this pattern was for tertiary links, provided in Figure 5f. In general, 33

higher values of CVS were related to increased crash severity for a majority of the functional classes. 34


13

1 (a) (b) 2

3 (c) (d) 4

5 (e) (f) 6

7

FIGURE 5 Cumulative distributions for CI, all links (a) and motorways (b), V̄, all links (c) and 8

secondaries (d), and CVS, all links (e) and tertiaries (f)9

0.0

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Congestion Index

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Coefficient of Variation of Speed

0.0

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Coefficient of Variation of Speed

mean = 0.086

mean = 0.101

mean = 0.075

mean = 0.115

mean = 0.196

mean = 0.103

mean = 0.326

mean = 0.352

mean = 0.371

mean = 0.310

mean = 0.344

mean = 0.400

mean = 39.06

mean = 38.63

mean = 41.72

mean = 43.42

mean = 41.36

mean = 45.07


14

1 TABLE 3 Results of the Pairwise K-S Tests for Crash Severity 2

LINKS All Motorway Primary Secondary Tertiary Residential

D P-value D P-value D P-value D P-value D P-value D P-value

CI

Mi/Ma 0.086 0.000 0.244 0.010 0.183 0.023 -0.060 0.289 0.054 0.413 0.049 0.417

Ma/F -0.136 0.006 -0.406 0.015 -0.297 0.021 -0.068 0.720 -0.108 0.521 -0.231 0.040

Mi/F -0.071 0.219 -0.247 0.152 -0.229 0.102 -0.101 0.464 -0.082 0.670 -0.199 0.070

V

Mi/Ma -0.031 0.288 -0.167 0.116 -0.250 0.001 -0.111 0.015 -0.127 0.007 -0.078 0.109

Ma/F 0.090 0.108 0.253 0.197 0.215 0.132 0.119 0.365 -0.254 0.027 0.124 0.393

Mi/F 0.073 0.201 0.206 0.270 -0.125 0.507 -0.139 0.237 -0.282 0.008 -0.129 0.325

CVS

Mi/Ma 0.107 0.000 0.124 0.308 0.215 0.006 0.175 0.000 0.105 0.034 0.137 0.001

Ma/F 0.093 0.095 -0.273 0.151 -0.147 0.388 -0.147 0.212 0.295 0.008 0.238 0.032

Mi/F 0.144 0.002 -0.235 0.181 0.152 0.366 0.181 0.087 0.349 0.001 0.237 0.023

3

INTERSECTIONS All Motorway Primary Secondary Tertiary Residential

D P-value D P-value D P-value D P-value D P-value D P-value

CI

Mi/Ma 0.109 0.000 0.119 0.082 0.262 0.001 0.116 0.006 0.155 0.000 0.090 0.000

Ma/F -0.070 0.094 -0.156 0.218 -0.227 0.065 -0.139 0.096 0.154 0.136 -0.056 0.460

Mi/F 0.092 0.013 0.113 0.389 0.177 0.225 0.124 0.164 0.274 0.001 0.092 0.111

V

Mi/Ma -0.065 0.000 -0.106 0.133 -0.268 0.000 -0.143 0.000 -0.142 0.001 -0.094 0.000

Ma/F -0.056 0.212 -0.114 0.436 -0.141 0.320 -0.110 0.227 -0.213 0.022 -0.093 0.108

Mi/F -0.109 0.002 -0.194 0.058 -0.279 0.018 -0.217 0.004 -0.313 0.000 -0.150 0.002

CVS

Mi/Ma 0.102 0.000 0.193 0.001 0.228 0.003 0.126 0.002 0.092 0.050 0.091 0.000

Ma/F 0.106 0.004 0.115 0.427 -0.114 0.479 0.155 0.054 0.208 0.026 0.186 0.000

Mi/F 0.170 0.000 0.231 0.017 0.313 0.006 0.233 0.002 0.269 0.002 0.215 0.000

4 Notes: Statistically significant values are in red. Crash severity levels have been abbreviated as Mi (minor), Ma (major), and F (fatal). A positive D statistic means the distribution of the first 5 member of the pair is shifted to lower values, while a negative D statistic means the second of the pair is shifted to lower values. 6 7


15

CONCLUSIONS 1 The purpose of this paper is to correlate quantitative traffic flow measures, namely congestion, speed, and 2

speed uniformity, to historical collision frequency and severity at the network scale. Methods for collecting, 3

processing, and extracting the SSMs from the GPS smartphone data of regular drivers is presented. 4

Spearman’s correlation coefficient and pairwise K-S tests were used to determine statistical relationships 5

between crash frequency and severity, respectively. 6

Congestion, measured using CI during the PM peak period, was shown to be positively correlated 7

with crash frequency. According to the data in this study, links and intersections having higher levels of 8

PM congestion also tend to have a greater number of collisions. This result supports findings in existing 9

literature. However, CI had the poorest correlation strength of the three considered SSMs. When 10

considering collision severity, the relationship with CI was found to be non-monotonous. The distributions 11

of links with, at worst, major injury crashes were found to be shifted towards higher values compared to 12

links with minor or fatal collisions. This complex relationship can be potentially explained considering the 13

relationship between flow, density, and speed. In general, fatal crashes are rare. Although scenarios with 14

the lowest CI levels have the high speeds required to increase crash severity, the low vehicle densities make 15

the occurrence of a fatal crash exceedingly rare. Therefore, injury crashes are much more likely. As density 16

initially increases, the number of vehicular interactions increase (probability of crash) and speeds remain 17

high (severity of crash). This increase in density at the beginning of the fundamental diagram creates the 18

environment necessary to produce fatal crashes, where high severity (due to speed) and high probability 19

(due to density) coexist. This could explain why uncongested facilities are split into two groups: minor 20

injury only and fatal. As congestion continues to increase, conflicts and crashes also increase, but speed 21

decreases rapidly. Although the high number of interactions increases the likelihood of a crash, speed 22

reduction reduces the probability of fatal crashes. 23

Speed, measured as the average speed during the off-peak period, was found to be negatively 24

correlated with crash frequency (in fact, the strongest correlations of all proposed SSMs), and had no 25

conclusive statistical relationship with crash frequency. There are two possible explanations for these 26

results. First, the only factor controlled for in the analysis was functional class of the roadway. Additional 27

features which themselves are related to speed, such as geometry, were not considered. If the speed measure 28

is correlated with another factor with a causal relationship to lower crash frequency, this would mask the 29

true effect of speed on safety. A second possible explanation is the scale of the analysis. To date, most 30

studies considering speed as an indicator of risk have done so using a single link or corridor. As has been 31

shown in existing literature, it is clear that for a single link, increasing speed should increase crash severity. 32

However, at the network scale, little if any work has been done, and it is possible that the relationship 33

between speed and crash frequency and severity is different. 34

Speed uniformity, measured using CVS during the off-peak period, was observed to be positively 35

correlated with crash frequency, and statistically related to increased crash severity. According to the data 36

utilized in this study, links and intersections with more speed variation experience, not only a greater 37

number of crashes, but also more severe crashes. High CVS implies speed variation across both space 38

(vehicles of different speeds interacting) and time (changing traffic conditions). This could mean that traffic 39

flow is more complex, with more maneuvering, creating more opportunities for conflicts and crashes. High 40

relative speed differences between conflicting vehicles could also lead to more major and fatal crashes, 41

compared to facilities with less variation in speed. This result supports several past studies, which identified 42

variation in speed as an important predictor of risk. In general, the strength of the correlations with respect 43

to crash frequency is weak to moderate. Traffic flow SSMs may be stronger indicators of crash severity 44

than crash frequency. 45

Perhaps the greatest limitation of this work, and in fact most surrogate safety studies, is the fact the 46

temporal coverage of the surrogate data and the crash data do not overlap. However, the assumption 47

underlying the validity of surrogate safety methods is that the relationship between SSMs and safety should 48

remain fairly stable, though more research is needed in this area. Future work will focus on developing a 49

network screening model that incorporates these and other potential SSMs. Not only will a network 50

screening model demonstrate the practical application of SSMs derived from smartphone GPS data, but it 51


16

will also control for factors ignored in this study (geometry, exposure, etc.). This will contribute to a better 1

understanding of the complex relationship between congestion, flow, and crash frequency and severity. 2

3

ACKNOWLEDGEMENT 4 Funding for this project was provided in part by the Natural Sciences and Engineering Research Council 5

of Canada. 6


17

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