## 4 Methodology of Research
### Determining the Empirical Values of Relevant Traffic Flow Parameters  
Before reviewing the aerial video recordings, it was necessary to define the positions of entrance and exit reference lines separately for each observed road segment on ZC5210 regional road. These lines were used for detection of vehicle entrance and exit times on each observed road segment, based on which, it was possible to calculate the empirical values of all relevant traffic flow parameters, including vehicle time headways, vehicle speeds, traffic density and traffic flow values. Vehicle time headways at defined entry/exit reference lines on each observed road section of ZC5210 regional road were computed by subtracting the times at which two successive vehicles in a traffic stream have passed through each entry/exit reference line. Mathematically, this can be expressed using the following formulae:  
\[\mathrm{th_{Ui}}=\mathrm{t_{Ui+1}}-\mathrm{t_{Ui}}[\mathrm{s}], \tag{1}\]  
\[\mathrm{th_{Hi}}=\mathrm{t_{i+1}}-\mathrm{t_{Hi}}[\mathrm{s}], \tag{2}\]  
where \(\mathrm{th_{Ui}}\) and \(\mathrm{th_{Hi}}\) represent vehicle time headways between two successive vehicles in a traffic stream determined on the entry and exit reference lines in seconds, respectively; \(\mathrm{t_{Ui}}\) and \(\mathrm{t_{Hi}}\) represent the arrival time of the i-th vehicle (leading vehicle) on the entry and exit reference line in seconds, respectively; \(\mathrm{t_{Ui+1}}\) and \(\mathrm{t_{Hi+1}}\) represent the arrival time of the first successive vehicle behind the i-th vehicle (following vehicle) on the entry and exit reference line in seconds, respectively. The velocity of each vehicle in the traffic stream was calculated by dividing the distance between the defined entry and exit reference lines, which represents the length of the observed road segment, by the difference between the exit times and the entry times recorded for each vehicle in the database, which represents the travel time of each vehicle through the observed road segment. This can be expressed using the following formula:  
\[\mathrm{V_{i}}=3.6\cdot\mathrm{v_{i}}=3.6\cdot\frac{\mathrm{L_{o}}}{\Delta \mathrm{t_{i}}}=3.6\cdot\frac{\mathrm{L_{o}}}{(\mathrm{t_{Ui}}-\mathrm{t_{Hi}} )}[\mathrm{km/h}], \tag{3}\]  
where \(\mathrm{V_{i}}\) represents the velocity of the i-th vehicle in the traffic stream, expressed in kilometers per hour; \(\mathrm{v_{i}}\) represents the velocity of the i-th vehicle in the traffic stream, expressed in meters per second; \(\mathrm{L_{o}}\) represents the length of the observed road segment in meters; and all other variables are as previously defined. In order to determine the empirical values of traffic density, the aerial videos were stopped at frames on which individual vehicles were present on the entry reference detection lines defined for each observed road segment. The current number of vehicles, which were present between the entry and exit reference lines at those times, was recorded in the database. The recorded number of vehicles between the entry and exit detection lines at discrete time intervals was then used to calculate traffic density using the following formula:  
\[\mathrm{g_{i}}=1000\cdot\frac{\mathrm{N_{i}}}{\mathrm{L_{0}}}[\mathrm{veh/km }], \tag{4}\]  
where \(\mathrm{g_{i}}\) represents traffic density at discrete time interval i, expressed in the number of vehicles per kilometer, and \(\mathrm{N_{i}}\) represents the number of vehicles on the observed road segment at discrete time interval i. All other variables are as previously defined.