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\subsection{Roundabout Safety Studies in Europe}  A number of roundabout safety studies have been performed throughout Europe. In the Netherlands, for example, one study found a decrease in casualty rate across 46 roundabout conversions of up to 74\% \cite{Schoon_1994} (though admittedly the rates were small to begin with). A more recent example in Denmarkimportant  shows important  reductions in accident rates and accident severity across a large data set, though it also suggests that roundabouts have the least effect on mitigating property-damage-only (PDO) collisions \cite{Jensen_2013}. This study also looked at contributing factors and recommends tapered central islands above installations with islands which are not elevated or that have elevations with cylindrical shape (obstruction of visibility). Finally, it notes that cyclist collisions increased over the same period. Similar results have been shown in Sweden \cite{Bergh_1997, Hyd_n_2000} and in 28 other studies \cite{Elvik_2003}. Overall, there is clear evidence of roundabouts reducingat the very least accident severity in  accident severity. \subsection{Roundabout Safety Studies in North America}  Experience and research in North America is are  still lacking, though some efforts have nevertheless been undertaken. made.  One study found a decreases decrease  in collision severity, particularly for fatal collisions collisions,  using an empirical Bayes model on 24 stop-controlled intersection conversions into roundabout roundabouts  \cite{Persaud_2001, Rodegerdts_2007}. A more recent, but similar similar,  study found essentially the same result across 28 sites in the same region \cite{Gross_2013}. Meanwhile, closer to Québec, Burns found that large passenger vehicles, multiple vehicles, and night time was were  associated with increased accident severity \cite{Burns_2013}. \subsection{Behavioural and Surrogate Safety Studies}  Surrogate safety analysis is a pro-active road safety diagnosis methodology which aims to improve road safety analysis methods by complementing historical accident data (or supplanting it altogether when it is not available) with cheap and short observations of ordinary traffic behaviour \cite{Tarko_2009}. Speed is a classic surrogate safety measure, though this designation is rather new: many studies in the literature infer from or target speed directly for purposes of road safety directly. safety.  Its effects on collision severity are well known, though its effects on collision probability are less sure \cite{Hauer_2009}. Roundabout speed is consistently measured around 30 km/h in the literature \cite{Chen_2013}. In fact, it has been observed that, while high-speed areas typically have their speed decreased decrease  to 30 km/h after implementation of a roundabout, areas with lower speeds (e.g. 20 km/h) can have their speed increase increased  to 30 km/h as well \cite{Hyd_n_2000}. This effect has been also observed at the microscopic level in Québec \cite{St_Aubin_2013}. There are many other surrogate safety measures, but time-to-collision (TTC) is the surrogate measure of safety of choice for its relative maturity, simplicity, and transferability properties. TTC measures the time remaining, at any instant in time time,  before two road users on a potential collision course collide: higher values are better for safety. It does not have the same level of validation in the literature as speed, but while speed is a good predictor of collision severity, TTC promises to be a good predictor of collision probability, a property which is arguably lacking with speed \cite{Hauer_2009}. Therefore, modelling one ant the other both speed and time-to-collision  should give a good overall representation ofof  collision risk associated with road user behaviour. Several collision course collision-course  modelling techniques are used in the literature, chief amongst them in terms of ubiquity is constant velocity \cite{Laureshyn_2010}. The However, the  constant velocity motion prediction motion-prediction  model is deemed inadequate for TTC measurement in roundabouts however, roundabouts,  as road users in roundabouts rarely follow straight trajectories, both inside the roundabout and on a significant portion of the approach. Fortunately, some more sophisticated naturalistic motion prediction motion-prediction  models have been developed to overcome this shortcoming: motion patterns are used for their ability to learn normal movement within a traffic scene. A discretised motion pattern discretized motion-pattern  matrix method was has been  developed specifically for roundabouts \cite{St_Aubin_2014}.