## 4 Methodology of Research
### Determining the Empirical Values of Relevant Traffic Flow Parameters
The traffic flow values were computed based on the previously determined empirical values of relevant macroscopic and microscopic traffic flow parameters, according to the following expressions:  
\[\mathrm{q_{i}}=\mathrm{V_{i}}\cdot\mathrm{g_{i}}=\frac{3600\cdot\mathrm{Ni}}{( \mathrm{t_{Ui}}-\mathrm{t_{ti}})}=\frac{3600\cdot\mathrm{Ni}}{\Delta\mathrm{t}}= \frac{3600}{\mathrm{t_{h}}}[\mathrm{veh}/\mathrm{h}], \tag{5}\]  
where \(\mathrm{q_{i}}\) represents the traffic flow at discrete time interval i, expressed in vehicles per hour; \(\Delta\mathrm{t}\) represents the travel time of the i-th vehicle in a traffic stream through the observed road segment, expressed in seconds; \(\mathrm{t_{h}}\) represents the time headway in seconds; and all other parameters are as previously defined. All empirical traffic flow parameter values were stored in a database set up within the MS Excel platform. The traffic flow parameter values, computed based on data collected on two observed road sections of ZC5210 regional road, were stored in two distinct data tables named \"ZC5210_Road_Section_A\" (Table S1) and \"ZC5210_Road_Section_B\" (Table S2). Following a data filtering process, the values stored in relevant data columns were then extracted separately for each observed traffic stream and recorded in a comparative output table named \"ZC5210_Comparative_Models\" (Table S3). The comparative output table comprises the computed empirical values of relevant traffic flow parameters for a total of 1581 vehicles, i.e., a total of 4743 observations, including 1581 vehicle speed values, 1581 traffic density values and 1581 time headway values. Comparative Analysis, Calibration and Fitting the Deterministic \"Speed-Density\" and \"Flow-Density\" Fundamental Traffic Flow Diagrams to Collected Empirical Data  
The empirical values of traffic flow parameters were visualized on \"speed-density\" and \"flow-density\" scatterplots and then analyzed using the least-squares method to identify the best fitting regression functions, which could be effectively used for deterministic modeling of traffic flow characteristics under continuous and interrupted traffic stream conditions on the two observed road segments of ZC5210 regional road. In order to determine specific \"speed-density\" and \"flow-density\" fundamental traffic flow diagrams suitable for modeling traffic flow characteristics under continuous and interrupted traffic stream conditions, in the scope of this research, we comparatively analyzed, calibrated and fitted mathematical formulations of twelve selected traffic flow models. Based on the regression fitting procedure conducted using Python script created in the PyCharm integrated development environment [68], three distinct \"speed-density\" and three \"flow-density\" regression functions were established for each of the traffic flow models considered:  
* \"Speed-Density\" and \"Flow-Density\" regression functions obtained using the overall statistical sample collected containing all empirical values of traffic flow parameters determined both under continuous and interrupted traffic stream conditions;
* \"Speed-Density\" and \"Flow-Density\" regression functions developed based on the partial empirical sample collected under continuous traffic stream conditions on the open road segment (road segment A); and
* \"Speed-Density\" and \"Flow-Density\" regression functions developed based on the partial empirical sample collected under interrupted traffic stream conditions on the road segment with signalized intersection (road segment B). The obtained regression functions of proposed deterministic models were compared to highlight the differences among the deterministic fundamental traffic flow diagrams suitable for describing the continuous and interrupted traffic stream conditions on the selected undivided bi-directional two-lane road in the Republic of Croatia.