# Road Safety Management of Uncontrolled Access Points:
## 2 Materials and Methods
### Identification and Selection of Traffic Accidents Attributable to an Access Point  
The difficulty in defining the relationship between accidents and access features lies in the exact allocation of a collision to the access point with which it could be associated. A more correct correlation between these two variables should select accidents based on the circumstances by including in the analysis only crashes whose causes are explicitly related to the presence of an access point. At this level of analysis, a high degree of accuracy of the accident data is required, but it is rare to obtain such an order of detail. For the intersections, \"intersection accidents\" are defined as collisions that occurred within the intersection's physical area [35]; regarding private access points, some studies refer to the concept of \"functional area\" [36]. According to the definition given by AASHTO in the Highway Safety Manual, the intersection functional area is the \"area extending upstream and downstream from the physical intersection area including any auxiliary lanes and their associated channelization\" [35]. This definition can be extended to uncontrolled access by identifying the space in which there is a speed differential due to manoeuvres to enter or exit the roadway [2]. Some previous studies addressed the extension of the functional area to access points: [PERSON] et al. [36] use a fixed distance of 250 feet whereas in the research of [PERSON] et al. [11] and [PERSON] et al. [14] the functional area varies as a function of the speed.  
In light of the above, a method for evaluating the functional area of an uncontrolled access point is proposed in this study. The schematic representation of the elements of an access point is shown in Figure 4.  
Figure 4: Schematic representation of the geometric elements of an access point and the distances identifying the Functional Area (top view). R\({}_{\text{i}}\) = entry radius, R\({}_{\text{u}}\) = exit radius, \(\alpha\) = angle, L\({}_{\text{a}}\) = access width, L\({}_{\text{ss}}\) = downstream functional area (distance), L\({}_{\text{dxTOT}}\) = upstream functional area (distance), L\({}_{\text{dx}}\) = distance related to the deceleration manoeuvre; L\({}_{\text{pr}}\) = distance traveled during the perception-reaction time.  
Figure 3: Access Management measures (top view); (**a**) right-turn deceleration lane, (**b**) right-turn acceleration lane, (**c**) frontage or service roads (a parallel road to the main roadway which is used to provide connection to lateral facilities and private developments), (**d**) shared access (the access is shared by more than two adjacent access points). The red line identifies the roadway modification linked to each specific access management measure.  
The total distance identifying the functional area for the i-th access point (L(AF)) is defined by:  
\[\mathrm{L(AF)_{i}}\ =\ \mathrm{(L_{\mathrm{dxTOT}})_{i}}\ +\mathrm{(L_{\mathrm{xx}})_{i} }+\mathrm{(L_{\mathrm{a}})_{i}} \tag{1}\]  
where \(\mathrm{(L_{\mathrm{dxTOT}})_{i}}\) and \(\mathrm{(L_{\mathrm{xx}})_{i}}\) are the distances identifying the upstream and the downstream functional areas, respectively; \(\mathrm{(L_{\mathrm{a}})_{i}}\) is the width of the i-th access. The area is obtained by multiplying the total distance L(AF)i by the width of the main roadway.