## 3 Research Methodology
### Modeling Minimum Travel Time  
Minimum travel time considers ideal traffic conditions:  
* Trams do not wait at signalized intersections;
* Unsignalized crossings are not occupied by the pedestrians;
* There are no other vehicles (private cars or transit vehicles) causing a reduction in vehicle speed. So, to achieve these conditions, the data collected were obtained during workdays in the evening. Since a significant problem in this kind of modeling arises from heterogeneity of vehicle and driver performance, the idea was to represent usual driver and vehicle performance. For this, the segments were split into smaller units named sections characterized by constant acceleration, speed or deceleration, and constant section type. To determine constant speed categories, the smallest speed was determined as basic, and the other ones as multiples. The basic speed of 3 m/s (10.8 km/h) was determined by observing driving through active track switches and driving through curves with the smallest radius. Other multiples up to 15 m/s (54.0 km/h) were determined, considering limitations in the following:  
* Route geometry: curves reduce speed depending on the radius;
* Track intersections: vehicles must slow down to cross safely;
* Unsignalized pedestrian crossings: drivers anticipate pedestrians to appear at crossings;
* Parking spots: drivers reduce speed, anticipating parked vehicles to enter traffic recklessly;
* Overpasses: drivers reduce speed for pantographs to contract smoothly;
* Segregation: fully segregated tram tracks allow for the highest speeds, and lanes segregated by legislation or mixed lanes allow for lower speeds because of more possible interactions with other traffic. Regarding stop time (when the speed was zero at stops), in ideal conditions, there are low levels of passenger alighting and boarding, and these are evenly distributed between the doors. The observations showed that in these cases, drivers have the usual behavior of waiting longer at stops with high passenger demand (stops adjacent to tram track intersections and stops at terminals) and fewer at stops with low passenger demand (every other stop), and that the stop time is as follows:  
* Approximately 12 s if the stop has low passenger demand;  
Figure 4: Line 4 segments determined by the constant frequency criterion. Segment borders are marked as yellow dots, and segments are numbered in cyan (01 to 15 to Dubec terminal and 16 to 30 to the Savski most terminal). The geographic coordinates of the area borders are shown in white. Approximately 18 s if the stop has high passenger demand. The constant acceleration of transit vehicles was determined so that it produces a whole number of meters for simpler measurements. In ideal conditions, the vehicles will decelerate to zero or accelerate from zero only at stops, and we assume that acceleration and deceleration will always be surrounded by constant speed sections at least one second in duration (drivers do not decelerate just after finishing accelerating or vice versa). Again, for the purposes of simplification, acceleration and deceleration were adjusted to the five speed categories, and measurements in ideal conditions at night included measuring the time vehicles need to accelerate from zero to 36 km/h and decelerate from 36 km/h to zero, assuming constant acceleration and deceleration. The measurements showed that the most suitable values for terms in Zagreb to produce a whole number of meters and to adjust to speed categories were as follows:  
* For acceleration, 3/4 m/s\({}^{2}\);
* For deceleration, 9/8 m/s\({}^{2}\). Besides constant acceleration, speed and deceleration, sections were also determined by segment borders and lane type, resulting in six categories:  
* Unsignalized pedestrian crossing--PRIJ;
* Physically segregated tram lane--ZELE;
* Signalized intersections--RASK;
* Stop area--STAJ;
* Unsignalized intersection with tram tracks--TRAM;
* Mixed traffic lane (white lane in Zagreb)--BIJE;
* Lane segregated by legislation (yellow lane in Zagreb)--ZUTI.