deletions | additions       diff --git a/subsection_Merging_Zone_The_reasoning__.tex b/subsection_Merging_Zone_The_reasoning__.tex  index 28cd46b..09f290c 100644  --- a/subsection_Merging_Zone_The_reasoning__.tex  +++ b/subsection_Merging_Zone_The_reasoning__.tex 
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\subsection{Merging Zone}  Thereasoning for using  merging zones zone is defined  as the unit of study---instead in \cite{St_Aubin_2013b}. It encapsulates any region  of roundabouts the roundabout where an approach and an exit lane physically overlap with the ring,  as a whole---is that, while many factors such well  as land use are shared, many more are not. This includes flows any sufficient portions before  and flow ratios especially, but may also include a host of geometric factors such as lane configuration, signalisation, presence after this region to capture road users entering and exiting this region (circa 10 meters  ofa crosswalk,  approach angle, etc. which can vary from one merging zone to the next even within the same and exit). Given that all  roundabout \cite{St_Aubin_2013b}. Studying merging zones individually also better encapsulates have multiple approaches and an exits and that in  the microscopic nature vast majority  of cases these alternate in order around  the data being collected and analysed: roundabouts are often large enough for road user interactions on different sides of ring, multiple merging zones exist within  the roundabout to occur independently \citep[this is especially true if center islands obstruct view][]{Jensen_2014}. roundabout.  The rationale for using  merging zone zones as the unit of study, instead of roundabouts as a whole,  is defined and constructed that, while many factors such  as in \cite{St_Aubin_2013b}. It encapsulates land use are shared between merging zones of  the region 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, signalisation, presence  of a crosswalk, approach angle, etc. which can vary from one merging zone to  the next even within the same  roundabout where \cite{St_Aubin_2013b}. Studying merging zones individually also better encapsulates  the approach and exit lanes physically overlap with microscopic nature of  the ring, as well as sufficient portions before data being collected  and after this region to capture analysed: roundabouts are often large enough for  road users entering and exiting this region (circa 10 meters user interactions on different sides  of approach and exit). the roundabout to occur more or less independently \citep[this is especially true if center island obstructs view][]{Jensen_2014}.  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; 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 any remaining variable along with the most important  geometric and land use characteristics, 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 between from  2 and to  15 years (average (with an average  of 7) and data missing entirely at one roundabout. Furthermore, this historical accident data is representative of collected for  the entire roundabout instead of the merging zone exclusively since accident geolocation is often was  not fine precise  enough to distinguish 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. In any case, However,  the pattern in this data is consistent with the  regional trends in accidents cited earlier: accidents are seem to be  twice as likely to occur in Québec than in Sweden,even at comparable sites,  suggesting that unexplained effects can be found between from a safety point of view,  the sites selected. selected roundabouts are comparable with respective national trends.    \begin{table}  \caption{Merging Zone Inventory} 
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\end{table} %flows last updated Sept-10  Traffic data is prepared from the video data.  In addition tothe  flow rate, the flow ratio governs tends to govern  how many interactions occur across the any single  merging zone, and of what nature they these interactions  tend to be since expected behaviour be. This  is asymmetric between approaching self-evident: when more  road users are present simltaneously within the merging zone  and conflicting (within when  the roundabout) road users. presence involves more mixing from independant sources of arrivals (the effect of the flow ratio), more interctions must necessaily take place. This is especially important for low-demand sites where simultaneous arrivals may be rare events.  The flow ratio is defined as \begin{equation} \label{eqn:flow_ratio} Flow ratio=\frac{Q_{app}-Q_{conf}}{Q_{app}+Q_{conf}} \end{equation}  where $Q_{app}$ is the total flow rate at the approach and $Q_{conf}$ is the total conflicting flow (in the roundabout lanes at the beginning of the merging zone). It follows that a negative flow ratio would indicate that the conflicting flow is greater than the approach flow, and vice versa for a positive flow ratio. Mixed land use involved mostly residential and commercial land use, and occasionally institutional land use. 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 advisories \cite{Isebrands_2011}.      \subsection{Behavioural Measures}  The parameters of interest for this particular study are the most notable surrogate safety measures: speed (and speed profiles), time-to-collision (TTC) \citep{Hayward_1971}, and post-encroachment time (yPET). Note that yPET is an ordinary PET measure \citep{allen1978analysis} but is designated yPET as it 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. Other than this selection criterion, it is comparable to any other standard PET measure. Speed and yPET are measured directly from the observed road user trajectories as they occur.