Abstract

Despite similar population densities, levels of urbanization, climates, and levels of economic development, traffic accidents across the province of Québec (and the rest of Canada) are twice as high as in Sweden, as measured by traffic accident frequency and severity. Some of this disparity may be explained by differences in road design, but some of this disparity is hypothesized to also be attributed to latent behavioural factors present in the general population.

The objective of this research is to investigate these latent differences in road user behaviour and experience that may explain differences in accident history beyond any road safety effects derived from road design and traffic composition. To that aim, a number of roundabouts in Québec and Sweden are selected on the basis of similarity in design, for cross-sectional comparison. Analysis of behaviour and resulting safety is performed proactively using video data, automated video analysis for road user trajectory extraction and surrogate measures of safety. Surrogate measures of safety of interest for this study include speed and time-to-collision, based on motion prediction with empirical motion patterns.

Accident records available at the sample of roundabouts studied are found to be consistent with national averages of each country respectively (twice as high and severe in Québec as in Sweden). After controlling for various geometric design features, land use, construction year, traffic exposure, and traffic patterns, an overall tendency of lower speeds and fewer serious conflicts (as measured by time-to-collision) are found at the Swedish roundabouts. These results would suggest that some important latent regional factors—possibly related to driver education, culture or traffic safety enforcement—are at play at the microscopic level.

# Introduction

Design differences are especially striking regarding traffic control at intersections without traffic lights. While European design tends to favour a limited use of stop signs in favour of yield signs or no signalization at all (other than the right-hand rule), North American design favours two- and four-way stop signs almost exclusively. In fact, yield signs in North America are used almost exclusively for slip lanes or merges, and never to control square intersections directly. Given the yielding nature of the roundabout design, it is unsurprising to learn that roundabout adoption has been very slow in North America. While roundabouts are a relatively new phenomenon in North America, they have existed in the United Kingdom since 1966 where the modern design of the roundabout was first conceived (at the Transport Research Laboratory).

The choice of using surrogate safety methods for this analysis solves several issues related to inconsistencies in historical accident data collected in different jurisdictions (Turner et al., 2011), and provides fine-grained control over the quality of the data; unlike historical accident data which is typically administered by transportation authorities and devised ahead of independent road safety studies, surrogate safety data can be planned and administered directly by independent researchers in a timely manner. Furthermore, because surrogate safety analysis models and examines microscopic movement data, it intrinsically provides great insight into potential collision mechanisms (Tarko et al., 2009). Finally, it should be noted that traffic video data collection provides some unique benefits as well as tradeoffs. The primary benefit of video-based traffic data collection is that it is possible to collect high-resolution motion data of all road users without exception. This is made possible because this form of data collection is non-intrusive and is administered anonymously. The consequence of this, however, is that individual-specific human factors cannot be collected simultaneously. Nevertheless human factors aggregated at a region level (such as country) can be included.

While many international studies of road safety and design have been conducted, to date, only a limited number of international behavioural comparison studies have been attempted, and none have been conducted at the level of detail, and scale as in this study. This paper briefly reviews the literature and methodology to be used before presenting an exploratory analysis and regression analysis of speed, time-to-collision, and yielding post-encroachment time between 19 Québec and Swedish merging zones (over 23,000 road users) carefully selected to be similar in geometric design and environment.

# Literature Review

## Regional Effects

As highly-developed countries, Canada, and Sweden especially, are among some of the safest countries in the world for motorists, cyclists, and pedestrians. Despite this, annual traffic fatality rates in Canada are nearly twice as high than in Sweden, as measured per 100,000 inhabitants (World Health Organization, 2013; OECD et al., 2015)), per 10,000 registered motor vehicles (OECD et al., 2015), and per billion veh-km travelled (OECD et al., 2015), and this despite a relatively comparable car occupancy and mode share (OECD et al., 2015). Figures of reported accidents per 100,000 inhabitants share a similar trend (OECD, 2015). These numbers are summarized in Table \ref{tab:se_accident_stats_summary}. While all of these rates have been observed to be decreasing consistently over the last 40 years, the proportion between the two countries has been fairly constant (OECD, 2015). Furthermore, fatality and accident rates in Québec are consistent with, and thus representative of the Canadian national average (Transport Canada, 2015).

\label{tab:se_accident_stats_summary}

Comparison of Historical Accident Statistics
Statistic Canada Sweden Ratio Year Source
Fatalities per 100,000 inhabitants 6.8 3.0 2.26 2010 (World Health Organization, 2013)
Fatalities per 100,000 inhabitants 5.5 2.7 2.03 2013 (OECD et al., 2015)
Fatalities per 10,000 registered motor vehicles 0.85 0.45 1.88 2013 (OECD et al., 2015)
Fatalities per billion veh-km travelled 5.6 3.4 1.65 2013 (OECD et al., 2015)
Accidents per 100,000 inhabitants 501 210 2.39 2013 (OECD, 2015)

The disparity in road safety between Sweden and Québec is unexplained given that both share similar population sizes and density, levels of urbanization (81 % in Québec versus 86 % in Sweden), climate, and economic development factors. The disparity might instead be explained by one of two sets of microscopic factors: road design and road user behaviour. To this end, a comparative study of road user behaviour between the two regions is warranted by first isolating geometric factors as these are the most straightforward to control. One important difference is that cycling prevalence is significantly higher in Sweden than in Canada or Québec. On the other hand, grade-separated cycle crossings tend to be favoured in Sweden for most busy roundabouts(Sakshaug et al., 2010).

Roundabouts might arguably be one of the best candidates of road design for direct comparison of road user behaviour and driving culture between North America and Europe. Although a relatively new phenomenon in North America (the first roundabout in Quebec dates back to 1998), roundabouts are one of the few types of road designs with highly similar geometric and aesthetic design elements in both regions. This is in large part due to the European influenced on design of the roundabout in North American, e.g. roundabout design guides (NHCRP, 2010) including Québec’s very own guide (Ministère des Transports du Québec, 2002).

Key differences between the roundabout designs are mostly-pedestrian and cyclist related, as Swedish sidewalks tend to incorporate cycle paths, even at intersections and roundabouts, but that these often bypass the roundabout entirely via grade-separation (Sakshaug et al., 2010). Roundabout cycle lanes should be avoided given the higher collision rates and a general lack of the safety-in-numbers effect (Daniels et al., 2010).

## Road User Behaviour Comparison Studies

A couple of recent and relevant works stand out, including a comparison of road safety records between Sweden and Finland (Peltola et al., 2016) and a study of general cyclist perceptions between Brisbane and Copenhagen based on stated preference surveys (Chataway et al., 2014). However, while these and a small number of other studies exist comparing measurable difference in driving behaviour and driving culture between regions, few if any exist that do so using microscopically-collected road-user data and tightly controlling for geometric and land use factors, i.e. a level of analysis comparable to the study of gap acceptance of a saturated multi-lane roundabout in Lund performed by Irvenå and Randahl using some manually-annotated video data to calibrate microsimulation software (Irvenå et al., 2010).

This lack of research is in part due to the challenge of coordinating such a study, and also in part due to the lack of a robust framework and technology for collecting and processing large amounts of driver behaviour. The bulk of international road safety comparison research seems to be concentrated on historical accident data (Morris et al., 2011). The level of detail of the analysis presented here is made possible with improvements of large-scale automated surrogate safety analysis tools and frameworks (St-Aubin et al., 2015).

# Methodology

## Site Selection

Existing roundabout data for Québec was taken from a related road safety project at roundabouts (St-Aubin et al., 2013). This pool of data includes traffic video data for roughly 20 % of Québec’s 110 roundabouts (at the time of study) with uniform representation of various land use, geometric design, and regional characteristics. From this data, six roundabouts were retained for this study. In Sweden, four roundabouts were selected to complement the existing Québec data. These roundabouts were selected on the basis of similar geometric design and land use. This typical design is characterized by a single lane (on the approach, exit, and ring, each), an approach speed limit of 50 km/h, an outside radius of 15-25 m, very-low to medium urban density, suburban or light commercial land use, moderate visibility over the center island, and pedestrian crosswalks. Québec roundabout vertical signalization design is functionally identical to Swedish design, though differs slightly in terms of aesthetics (using an MUTCD-influenced style). The Swedish roundabouts chosen were all located in the Skåne province, near the city of Lund.

Despite a longer history of roundabout construction in Europe and Sweden, the Swedish roundabouts selected for this study are relatively new compared to other areas of Europe and are incidentally comparable in age to Québec roundabouts: these samples are both, on average at least ten years old, to control for the short term effects of recent construction.

It should be noted that while the approach speed limits were all set to 50 km/h, the city center of Lund (a distance greater than 500 m from any included roundabout) has a speed limit set to 30 km/h and features significant traffic calming measures. On the other hand, a 2008 study of blanket speed limit reductions across Sweden found that these had little effect in reducing speed (Hydén et al., 2008). Similar blanket speed limit reductions can be found at the municipal level of some, but not all, of the included Québec roundabouts, and all of them feature 30 km/h reduced speed limits in relative close proximity given the built environment.

## Traffic Data Collection

Video data is collected at a number of sites using purpose-built video data collection systems (Jackson et al., 2013; St-Aubin, 2016). As mentioned earlier, video data at Québec roundabouts from a video database prepared in a related road safety project (Saunier et al., 2015). Complementary video data was taken at the selected Swedish sites, deploying a similar video data collection system employing two cameras to cover the entire view of the roundabout. Data collection at the Swedish sites was performed under similar weather conditions (mild, partially overcast), periods (weekdays in late spring), and at times when no significant events could disrupt normal driving conditions.

The video data is then processed with state-of-the-art computer vision software developed specifically for surrogate safety analysis applications. The feature-based tracker from the open-source Traffic Intelligence project1 extracts all road user trajectories from image space (Saunier et al., 2006), providing Cartesian coordinates of all moving objects within the field of view at the camera frame rate, typically thirty times a second. This high-resolution data of all road users within a traffic scene is needed for the road user behaviour analysis to follow. Given the large volume of data to be processed, additional software2 is used to partially calibrate and automate the analysis and to annotate the traffic scene with contextual metadata (St-Aubin et al., 2015).

Example trajectory data extracted from two cameras at one Swedish site is shown in Figure \ref{fig:Trajectory_data}. In this case two cameras are placed in the north-west corner to provide full and overlapping coverage of the roundabout.

\label{fig:Trajectory_data} Trajectory data in blue and pink, image-space masks, and corresponding meta data coverage at a Swedish roundabout using two cameras.

## Merging Zone

While the sites are selected in such a manner so as to control for as many factors as possible, inevitably, some variation between sites still exists, especially regarding traffic volumes and patterns; these differences are identified such that they may be controlled during analysis. Table \ref{tab:analysis_zones} lists a summary of the merging zones selected at each roundabout studied along with the most important geometric and land use variations, as well as a summary of historical accident data recorded at each roundabout.

It should be noted that the study includes multi-level data. There are 19 merging zones among 11 roundabouts split between two countries. Ultimately, the behaviour of over 23,000 individual road users are observed.

Quality of the available historical accident data, summarized in Table \ref{tab:analysis_zones}, is relatively poor, with sampling periods ranging from 2 to 15 years (with an average of 7) and data missing entirely at one roundabout. Furthermore, this historical accident data is collected for the entire roundabout instead of the merging zone exclusively since geolocation of the historical accident data is not precise or reliable enough to determine corresponding roundabout merging zones (this is especially true for the Québec data). Nevertheless, the general trend observed in this data is consistent with the regional trends in accidents cited earlier: accidents seem to be twice as likely to occur in Québec than in Sweden, consistent with national averages between countries.

\label{tab:analysis_zones}

Merging Zone Inventory
Site (Sweden) Land Use Urban Density Outside Radius (m) Hourly Flow (veh/h/ln) Flow Ratio Con-struction year Accidents per year
Fasanvägen/ Trollebergsvägen-1 Mixed Medium 25.0 408.4 -0.432 1965 4.1
Fasanvägen/ Trollebergsvägen-2 Mixed Medium 25.0 394.7 0.283 1965 4.1
R103/Företagsvägen-1 Mixed Very low 22.0 281.8 0.293 2003 1.0
R103/Företagsvägen-2 Mixed Very low 22.0 289.0 0.517 2003 1.0
R103/Företagsvägen-3 Mixed Very low 22.0 226.8 0.252 2003 1.0
R103/Företagsvägen-4 Mixed Very low 22.0 218.4 0.934 2003 1.0
Ruben Rausings gata/ Borgs väg-1 Mixed Low 22.0 123.9 0.646 2010 1.5
Ruben Rausings gata/ Borgs väg-2 Mixed Low 22.0 121.4 0.568 2010 1.5
Svenshögs/Norra Gränsvägen-1 Residential Low 16.5 191.0 -0.417 1995 1.4
Svenshögs/Norra Gränsvägen-2 Residential Low 16.5 142.9 0.054 1995 1.4
MEAN (Sweden) 21.5 239.9 0.270 1995 1.8
Site (Québec) Land Use Urban Density Outside Radius (m) Hourly Flow (veh/h/ln) Flow Ratio Con-struction year Accidents per year
des Soeurs/du Golf Residential Medium 25.0 315.1 -0.327 2004 7.0
des Soeurs/Rene-Levesque Residential Low 22.5 178.8 0.421 2003 1.4
Fréchette/Anne-Le-Seigneur Mixed Low 24.5 51.5 0.600 2003 7.0
des Sources/Riverdale Residential Low 18.5 236.9 -0.361 2003 0.7
Mouettes/Alouettes-1 Residential Low 15.5 64.6 -0.518 2004* -
Mouettes/Alouettes-2 Residential Low 15.5 93.4 0.607 2004* -
St-Emilie/St-Denis Residential Low 18.5 46.6 0.112 2005 1.0
Talbot/Jacques-Cartier-1 Mixed Medium 18.0 150.8 0.608 2004 7.7
Talbot/Jacques-Cartier-2 Mixed Medium 18.0 238.6 0.534 2004 7.7
MEAN (Québec) 19.5 152.3 0.186 2004 4.19

* No construction date available. Date is estimated from historical aerial footage and carries an uncertainty of $$\pm~2$$ years.

Traffic data is prepared from the video data including basic hourly traffic flow rates for the approach lanes, $$Q_{app}$$, and conflicting lanes, $$Q_{conf}$$. The relationship between these two observed measures is summarized as the flow ratio, i.e. expressed as

$\label{eqn:flow_ratio} Flow ratio=\frac{Q_{app}-Q_{conf}}{Q_{app}+Q_{conf}}$

The flow ratio measures which of the approach lanes or the conflicting lanes has a greater proportion of arrivals. This is important because the expected behaviour of road users is different depending on which lane their arrival is made on. This flow ratio is further normalized between 0 and 1 for easier interpretation using

$\label{eqn:approach_dominance} Approach dominance=\frac{\frac{Q_{app}-Q_{conf}}{Q_{app}+Q_{conf}}+1}{2}$

It follows that an approach dominance value closer to 0 indicates that the merge zone serves a greater share of road users who have right of way, where as an approach dominance value closer to 1 indicates that the merge zone serves a greater share of road users who do not have right of way and must yield to other road users.

Mixed land use designates urban areas with non-distinct land use; this typically includes small, local commercial services integrated immediately next door to residences, and can include small institutional facilities (e.g. fire station, local clinic, etc.). All sites had a posted approach speed limit of 50 km/h. Some of the Québec roundabouts had a 35 km/h speed advisory posted as well. Swedish roundabouts do not have posted speed advisory signs (Isebrands, 2011).

## Behaviour and Safety Indicators

The parameters of interest for this particular study are the most notable surrogate measures of safety: two measures obtained directly from the observed road user trajectories, speed and post-encroachment time (PET) (Allen et al., 1978), and time-to-collision (TTC) (Hayward, 1971), a measure derived from position and speed based on assumptions of the road users’ expected motion.

Speed is widely regarded in the literature as a useful predictor of collision severity given the relationship between speed and kinetic energy carried by a road user in motion (Fildes et al., 1993; Elvik et al., 2004).

Provided that road user trajectories overlap, PET is measured in units of time and describes “near-miss” situations. In this study, the PET is measured specifically at the merging zone yield line, where encroachment is prohibited by way of mandated yielding on the part of the approaching road user only, and is denoted yPET. yPET is of interest as a model of yielding behaviour and merging aggressivity as it is associated with gap time and gap acceptance. Note that yPET values can be of any size: if demand is low, some arrivals may be minutes apart and would thus obviously hold no value in interpreting interaction safety. To counter this, a conservative maximum threshold of consideration of 5 s on yPET is used. This value is arbitrarily selected to reject those interactions where it is very clear that road users are not coexisting in time and space (the dwell time across each merging zone rarely surpasses 5 seconds). TTC is one of the most popular surrogate measures of safety. Like PET, it is defined for pairs of road users and measured in units of time. It can be computed only if the road users are in a situation of collision course, where the road uses would collide if “their movements remain unchanged” (Amundsen et al., 1977). Identifying a collision course at a given instant thus depends on a method to predict the road users’ motion after that instant. TTC is most easily understood as the remaining time before a potential collision ensues unless a road user initiates evasive action (if at all). In its most basic form, motion prediction at constant velocity (Amundsen et al., 1977), TTC is the distance between any two road users, at any time, divided by the differential speed between the two.

In addition to the surrogate measures of safety outlined above, additional measures of behaviour describing instantaneous collision-course situations are stored alongside each pair of road user and TTC measure. These include 15-s exposure, a micro-measure of exposure, which counts the number of road users present within the merging zone 7.5 s before and after the collision course is modeled, as well as intersection angle, which measures the angle of approach of the road users at the instant of the collision course in degrees. This angle is $$0^{\circ}$$ when the road users are following each other and $$180^{\circ}$$ when approaching others head on.

### Advanced Motion Prediction Methods for TTC

As stated previously, computing the TTC requires motion prediction methods to identify collision course situations. The most common motion prediction method is constant velocity. Given the non-linear driving required to navigate the deflection induced by roundabout central islands and approaches, a more sophisticated motion prediction model is used in this work instead: the motion prediction model based on discretized motion pattern developed specifically to address the issues of modeling movement in complex environments like roundabouts (St-Aubin et al., 2014). Another advantage of advanced motion prediction methods, e.g. using discretized motion patterns, is that they are probabilistic: that is, they intrinsically take into account the uncertainty about future road user positions by incorporating a basic model of collision probably. These models therefore also predict multiple potential collision points simultanesouly and probabilistically, returning TTC for any single instant of interaction between two road users. These multiple measures are simply aggregated into the expected TTC denoted $$TTC_{cmp}$$ (Saunier et al., 2010; St-Aubin et al., 2014).

Furthermore, TTC is measured continuously for two road users, unlike yPET which results in a single measure. The TTC time series is usually aggregated into a signel value, typically the minimum (i.e. most severe) value at any instant in the timeseries (Laureshyn et al., 2010). This however is somewhat sensitive to noisy data and outliers, and as such a 15$$^{th}$$-centile value, $$TTC_{15^{th}cmp}$$, may be used instead (St-Aubin, 2016).

### Data Analysis and Aggregation

While surrogate measures of safety such as speed are easily summarized over time at the site level using descriptive statistics (given the consistency of normal-like unimodal distributions of speed observations at the sites), TTC is less well summarized as it is measured continuously and, because multiple competing definitions (to be more precise, hypotheses of prediction and aggregation) exist, very few robust collision conversion models have been developed for it. While more sophisticated models are developed, TTC can be used in a comparative manner under the condition that error remains identical in either comparison case (same prediction models, same data sources, same lighting conditions, etc.). There are generally two approaches used in the literature to making TTC comparisons:

• serious event comparison (SEC), which defines events based on an assumed (or calibrated) target threshold or set of rules defining interaction “seriousness”. For example, TTC values below 1.5 s are problematic because of driver reaction times, commonly cited as 1.5 s (Hydén, 1987; Green, 2000). This approach thus evaluates the rate of serious events per unit of traffic exposure, or converts them into predicted collisions using conversion factors (Hydén, 1987). This approach is simple to implement and is the most analogous to current approaches to road safety study, but has two main disadvantages: i) it is a coarse measure, and ii) it makes simplistic assumptions about the underlying mechanisms governing the safety indicator, e.g. in this case, assuming a strong relationship between $$TTC_{15^{th}cmp}$$ and a strict reaction time of 1.5 s. If probabilistic motion prediction methods are used, as in the case of discretized motion patterns, the number of serious events can be further weighed by their collision probability (St-Aubin, 2016).

• safety continuum comparison (SCC), which evaluates the effects of all safety indicators in proportion to their seriousness. It is more complex to implement and interpret, but makes fewer assumptions about the underlying mechanisms of safety. This approach is disaggregated by nature, typically comparing one distribution versus another.

# Results

Speed, TTC, and yPET are measured from the trajectory data collected at all 19 roundabout merging zones (over 23,000 individual road users) and presented in this section. All dependent variables are measured at the individual road user level.

## Exploratory Analysis

Overall, speed is found to be normally distributed at each site for each movement. Comparing hourly flows versus speed, it is clear that increased traffic is associated with lower speeds, as illustrated in Figure \ref{fig:hourly_speed}. It can also be seen that the Swedish sites have significantly reduced speed, even after controlling for effects of congestion, as measured by traffic volume. Figure \ref{fig:hourly_speed} also demonstrates that the selected sites have, from one hour to the next, roughly comparable traffic demand patterns, although variation is present from hour to hour at the same site (as is expected). Given that the recorded speeds seem to vary based on movement types, speed measures are plotted continuously as a function of space for all four movements in a merging zone, as proposed and first demonstrated in (St-Aubin et al., 2013):

1. vehicles travelling through the merging zone on the roundabout ring exclusively,

2. vehicles leaving the roundabout via an exit lane,

3. vehicles entering the roundabout via an approach lane, and

4. vehicles entering the roundabout via an approach lane and exiting via the next exit lane.

For example, a road user wishing to turn right at a roundabout only needs to travel across a single merging zone i.e. following a single movement type (4) through this merging zone. However, a road user wishing to make a through movement at the same roundabout must cross two successive merging zones following one movement type (3) through the first merging zone followed by a second movement type (2) through the second merging zone. In the same way, a left turn at a roundabout corresponds to movement (3) followed by one movement (1), and finally one movement (2). Finally, a U-turn or a turn at a roundabout with more than four approaches will follow movement (3) followed by multiple movements (1), and finally one movement (2).

The observed speed profiles of road users travelling along these movements are illustrated in Figures \ref{fig:speed_profile_qc} and \ref{fig:speed_profile_se}. A similar overall reduction in speed is noted at the Swedish sites, although this discrepancy is found to be most pronounced for movement type (4). Furthermore, the average approach speed just ahead of each approach yield line also appears to be lower at the Swedish sites.

\label{fig:hourly_speed} Hourly average speed across roundabout merge zone for all movement types.

\label{fig:speed_profile_qc} Mean speed for each movement profile across Québec merging zones along with $$\pm~1~\sigma$$ standard deviation.

\label{fig:speed_profile_se} Mean speed for each movement profile across Swedish merging zones along with $$\pm~1$$ standard deviation.

## Regression Results

### Speed

A linear regression is performed on mean road user merging zone speed measured (in km/h) at each merging zone individually, testing all explainable differences between sites, shown in Table \ref{tab:analysis_zones}, with the exception of collision statistics, given that this dataset isn’t as reliable. The coefficients of regression, adjusted $$R^2$$, Wald test score, and number of observations are provided in Table \ref{tab:se_regression_mean_speed}. Note that roundabout outside radius, flow ratio, land use, urban density, and construction year were not significant in predicting mean speed. Instead, a relatively good model (with an adjusted $$R^2 = 0.658$$) with only two factors remains:

• A significant reduction in mean speed of 4.5 km/h is observed at the Swedish sites.

• Increases in hourly traffic volume are correlated with reductions in mean speed as well. This is not surprising, given standard traffic flow theory (e.g. Greenshield’s Model).

The conclusions of the regression analysis support what was suggested in the exploratory analysis, concluding that, given that all sites in this study have identical posted speed limits, regional effects such as education, enforcement, or culture might be in play instead.

\label{tab:se_regression_mean_speed}

 Coefficient $$P>|t|$$ Coefficient $$P>|t|$$ constant 35.108 0.000 1.310 0.023 Swedish site -4.576 0.004 -0.194 0.276 Approach crosswalk -2.921 0.053 0.0239 0.895 Outside radius (m) - - 0.085 0.016 Hourly flow per lane -0.0197 0.010 -0.00431 0.002 Approach dominance 3.556 0.243 -0.091 0.822 Years since construction - - 0.014 0.121 Adjusted $$R^2$$ Wald prob. $$> F$$ Groups

### Yielding Post-Encroachment Time

A linear regression is performed on median $$yPET$$ at each site (including only yPET below 5 s), to test all explainable differences between sites, as shown in Table \ref{tab:analysis_zones}. $$yPET$$ observations are separated into lead $$yPET$$—between the road user already in the roundabout preceding the road user entering from the approach—and lag $$yPET$$—between the road user entering from the approach and the following road user already in the roundabout. The coefficients of regression, adjusted $$R^2$$, Wald test score, and number of observations are provided in Table \ref{tab:se_regression_mean_speed}.

No suitable regression model is found for lead $$yPET$$. Meanwhile, while Outside Radius and Flow are found to be associated with lag $$yPET$$ with intuitive signs, having a moderately powerful relationship, region is not found to be significantly correlated with median lag $$yPET$$ either.

### Time-to-Collision

Given the hierarchical nature of the data, a random effects regression of motion pattern-based serious $$TTC_{15}$$ (shorthand for $$TTC_{15^{th}cmp}$$) SCC events is performed, using the log of $$TTC_{15}$$:

$ln(TTC_{15_{ij}}) = \alpha + {\sum}_{k} ( \beta_k X_{kij} + u_{ik}) + u_{i} + \epsilon_{ij} \label{eq:se_ttc_regress_random_effects}$

for $$j=1,...,m$$ pairs of road users and for sites $$i=1,...,n$$ (merging zones), where $$\alpha$$ is the model intercept, $$\beta_k$$ is the coefficient of factor $$X_{kij}$$ for $$k=1,...,o$$ factors, $$u_{i}$$ is the approach-specific random error, and $$\epsilon_{ij}$$ is the “ordinary” regression error.

Results of the regression are shown in Table \ref{tab:se_regression_ttc_continuum}. The regression yields a moderately predictive model with a $$R^2 = 0.425$$ (which accounts for differences between merging zones). The difference in safety between sites seems to be in large part accounted for by the Swedish Site variable, as it is associated with an increase in expected $$TTC_{15}$$ of 0.293 seconds, thus suggesting that sites located in Sweden benefit from a non-trivial reduction in collision probability. Construction year (or elapsed time since roundabout construction) is not found to be correlated significantly suggesting that, at this time scale at least, acclimatization to roundabouts is not a significant effect.

A very minor within-effect is also noted: fifteen-second-traffic-exposure being associated with an increase in $$TTC_{15}$$ at a rate of 0.017 seconds per road user present within 15 seconds. This appears to be somewhat counterintuitive, but it might suggest that increasing driving complexity really does have a positive effect on increasing driver alertness. Furthermore, as evidenced with the angle of incidence parameter, interactions with a small angle of incidence, i.e. rear end conflicts, seem to be associated with lower $$TTC_{15}$$ values than with a larger angle of incidence, i.e. side swipe conflicts.

\label{tab:se_regression_ttc_continuum}

SCC Random Effects Regression Model for $$TTC_{15^{th}cmp}$$
Coefficient $$P>|t|$$
constant -0.414 0.166
Swedish site 0.196 0.023
Approach crosswalk 0.458 0.000
Hourly flow per lane 0.000039 0.150
Approach dominance 0.425 0.029
Fifteen Second Exposure (s) 0.016 0.000
Interaction Angle (deg) 0.003279 0.000
Wald prob. $$> F$$
Observations
Groups

# Conclusion

In this paper, an international comparison of driver behaviour at roundabout merging zones is performed aiming to explain regional discrepancies in road safety using highly detailed trajectory data and surrogate measures of safety. Conclusions derived from the surrogate measures of safety of speed, yielding PET, and TTC are found to be consistent among each other as well as with observed discrepancies in national historical records of road safety after controlling for a number of road geometry, land use, traffic composition, weather and climate conditions, temporal effects, and traffic exposure factors. This leaves a latent, unobserved component of road user behaviour that might be affected by local road use norms. This discrepancy might in particular be explained by systematic lack of exposure to roundabouts (or yield signs) within an entire region. It remains to be seen, whether the rest of this behaviour is shaped by collective trends in education, enforcement, or design policy, i.e. “culture”, but it seems clear that road user behaviour is shaped by more than site-specific effects.

Additional research is warranted for investigating how systematic overuse or underuse of certain design elements, such as stop signs and yield signs, shapes driver behaviour towards other elements of the system. Future research is also warranted examining other, complementary types of individual specific human factors between these countries, such as distracted driving habits, traffic violations, or demographics.

Limited historical accident data was also available at individual sites and would seem to suggest that the effects present at the selected sites are generally consistent with national historical records of road safety as well as the conclusions drawn from the studied surrogate measures of safety. However, given the issues with this accident data set, this last observation remains, for the time being, inconclusive, prompting further investigation. In general, a more thorough statistical analysis using larger sets of accident data may be beneficial in further understanding the predictive power of surrogate measures of safety.

One other limitation of this study is that, while the sample of Québec roundabouts can be considered to be regionally representative of most of the province of Québec, the roundabouts sampled in Sweden were all located in or nearby the city of Lund. Comparison between North American sites and a greater variety of European sites will be needed in a future study to determine if the regional effects demonstrated in this paper apply evenly across entire continents, or if these regional effects vary at a smaller scale (e.g. from city to city), even after controlling for environment and geometry.

# Acknowledgements

The authors would like to acknowledge the funding of the Québec road safety research program supported by the Fonds de recherche du Québec – Nature et technologies, the Ministère des Transports du Québec and the Fonds de recherche du Québec – Santé (proposal number 2012-SO-163493), as well as the various municipalities for their logistical support during data collection.

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