deletions | additions       diff --git a/subsection_Merging_Zone_The_merging__.tex b/subsection_Merging_Zone_The_merging__.tex  index 5609179..45e6abb 100644  --- a/subsection_Merging_Zone_The_merging__.tex  +++ b/subsection_Merging_Zone_The_merging__.tex 
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\subsection{Merging Zone}  The merging zone is defined as in \cite{St_Aubin_2013b}. It encapsulates any region of the roundabout where an approach and an exit lane physically overlap with the ring, as well as any sufficient portions before and after this region to capture road users entering and exiting this region (circa 10 meters of approach and exit). Given that all roundabout roundabouts  have multiple approaches and an  exits and that in the vast majority of cases these alternate in order around the ring, multiple merging zones exist within the roundabout. The rationale for using merging zones as the unit of study, instead of roundabouts as a whole, is that, while many factors such as land use are shared between merging zones of the same roundabout, many more are not. This includes flows and flow ratios especially, but may also include a host of geometric factors such as lane configuration, signage, presence of a crosswalk, approach angle, etc. which can vary from one merging zone to the next even within the same roundabout \cite{St_Aubin_2013b}. Studying merging zones individually also better encapsulates the microscopic nature of the data being collected and analysed: roundabouts are often large enough for road user interactions on different sides of the roundabout to occur more or less independently \citep[this is especially true if center island obstructs view][]{Jensen_2014}. 
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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 (no two intersections are perfectly identical); 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 and along with the most important geometric and land use variations, as well as a summary of historical accident data at each roundabout. Quality of the available historical accident data 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 accident geolocation was not precise enough to associate with individual roundabout merging zones (this is especially true for the Québec data). These problems justify using surrogate safety measures for this study, and more generally. However, the pattern 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, suggesting that from a safety point of view, the selected roundabouts are comparable with respective national trends.    \begin{table}    \caption{Merging Zone Inventory}  \label{tab:analysis_zones}  \begin{tabular}{p{1.5in}lp{0.5in}p{0.5in}p{0.5in}p{0.5in}p{0.5in}p{0.5in}p{0.5in}} \begin{tabular}{llllllllll}  \hline  \textbf{Site (Sweden)} \textbf{Site}  & \textbf{Land Use} & \textbf{Urban Density} & \textbf{Outside Radius (m)} & \textbf{Hourly Flow (veh/h/ln)} & \textbf{Flow Ratio} & \textbf{Construction year} & \textbf{Accidents per year} \\ \hline  Fasanvägen/ Trollebergsvägen-1 Fasanvägen/Trollebergsvägen-1  & Mixed & Medium & 25.0 & 408.4 & -0.432 & 1965 & 4.1 \\ %Sweden accident data is over a 2-15 year period Fasanvägen/ Trollebergsvägen-2 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 gata/Borgs  väg-1 & Mixed & Low & 22.0 & 123.9 & 0.646 & 2010 & 1.5 \\ Ruben Rausings gata/ Borgs 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 \\ \textbf{MEAN} \textbf{MEAN (Sweden)}  & & & \textbf{21.5} & \textbf{239.9} & \textbf{0.270} & \textbf{1995} & \textbf{1.8} \\ \hline\textbf{Site (Québec)} & \textbf{Land Use} & \textbf{Urban Density} & \textbf{Outside Radius (m)} & \textbf{Hourly Flow (veh/h/ln)} & \textbf{Flow Ratio} & \textbf{Construction year} & \textbf{Accidents per year} \\  des Soeurs/du Golf & Residential & Medium & 25.0 & 315.1 & -0.327 & 2004 & 7.0 \\ %Québec Accident data is over a 4-7 year period  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 \\  
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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 \\   \textbf{MEAN} \textbf{MEAN (Québec)}  & & & \textbf{19.5} & \textbf{152.3} & \textbf{0.186} & \textbf{2004} & \textbf{4.19} \\ \hline                            \end{tabular}  * No construction date available. Date is estimated from historical aerial footage and carries an uncertainty of $\pm~2$~years. \end{table} %flows last updated Sept-10 
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While surrogate safety measures such as speed are easily summarised at the site level using descriptive statistics (given the consistency of normal-like distribution of speed observations at any given site), TTC is less well summarised as it tends to have a distribution shape that varies from one site to the next. There are generally two approaches used in the literature to making TTC comparisons between sites:  \begin{itemize}  \item serious event comparison (SEC), which sets an assumed target threshold or set of rules of ``seriousness'', “seriousness”,  e.g. $\zeta < 1.5$~seconds corresponding to the commonly cited driver reaction times of 1.5~seconds \citep[][]{Hyden_1987, Green_2000}, and counts the number of events (pairs of road users), where the representative safety indicator, e.g. $TTC_{15^{th}}$, meets this criterion. This approach thus evaluates the rate of serious events per unit of traffic exposure, or converts them into predicted collisions accidents  using conversion factors \citep{Hyden_1987}. This approach is simple to implement and is the most analogous to current approaches to road safety study, but has the two main disadvantages being that it is a very coarse measure, and it makes the most assumptions about the significance of the safety indicator, e.g. in this case, a strict relationship between $TTC_{15^{th}}$ and a reaction time of 1.5~seconds is assumed. If collision-course probabilities are modeled, as in the case of discretised motion patterns, serious events can be further weighed by their modeled probability: weighted SEC \cite{St_Aubin_2016_thesis}. \item safety continuum comparison (SCC), which attempts instead to evaluate the effects of each safety indicator individually without explicitly attributing collision probability or "seriousness" to safety indicators besides the value of the safety indicator itself. Stated differently, the objective of this approach is to decrease TTC overall, without directly investigating equivalent collisions accidents  or events. This approach is disaggregated by nature: all safety indicators impact safety in proportion to their value. This results in a data set that is hierarchical: each site having multiple road user interactions, each having different $TTC_{15^{th}}$. \end{itemize}