## 2 Methodology
### Public Transport Priority  
The microsimulation model of the current and future state was created using the VISIM software tool, and the simulation of public transport vehicle priorities was performed using the EPICS software module, as part of VISSIM. To address the problem of increasing transport demand at signalized intersections, an increasing number of intersections are subject to traffic-dependent signal plan management. The traditional variant of these systems is based on the principle of impulse (detector) reaction, i.e., control algorithms consist of highly complex elements (if-then queries), especially regarding prioritizing public transport vehicles. A more modern approach to adaptive optimization, such as EPICS, is based on an iterative approach. EPICS was first intended to replace existing priority measures of public transport vehicles [31]. Initially, it focused only on public transport vehicles, but with further developments it became a control method providing real-time optimization of traffic control parameters for all users [29]. EPICS allows special attention to be paid to the time of arrival of public transport vehicles from the moment of the first announcement on the sensor (check-in detector) to the passage of the stop line (check-out detector). Unlike private transport flows, PT vehicles usually appear discretely at intersections. Therefore, due to the desired possibility of prioritization, the vehicles must be considered as single events. Differences in the arrival time of vehicles that occur due to occasional disturbances are respected by considering them to have a trapezoidal probability distribution, rather than treating them as a point (Figure 3) [27]. To obtain the probability density function, it was necessary to determine the ranges of PT vehicle time arrivals to the stop line for each intersection. That was accomplished by measuring arrivals in the field and entering the time values P1, P2, P3 and P4 in the EPICS program, where P1 represents fastest, P2 typical, P3 typical slow and P4 slowest travel times to the stop line. If the public transport vehicle uses a common lane with private transport, EPICS gives priority to the PT vehicle by extending the duration of the green light or switching on the signal group to clear the queue and allow unobstructed passage of the public transport vehicle. The relevant quantities entering the target function of the optimization of EPICS are the total delay and the number of stops of vehicles, which are calculated by summing up all detected traffic flows, each with a configurable weight. Additionally, there is the possibility to compare with a reference signal plan to guarantee coordination of the local  
Figure 3: Trapezoidal probability density function of the travel time of a public transport vehicle from the first announcement to the stop line [27]. control with the surrounding network as good as possible. It can be provided offline by a traffic engineer or generated online by means of a suitable network control such as BALANCE [27]. Based on the input data, the efficiency models calculate different variant process optimization scenarios using the Performance Index (PI) shown in Formula (1) [27]. \[PI\left(\wp\right)=\sum_{sg\in SG}\alpha_{sg}D_{sg}(sp)+\beta\Delta(\mathit{ ref},sp) \tag{1}\]  
where: \begin{tabular}{l l} \(SG\) & = set of signal groups \\ \(sp\) & = signal plan to be evaluated \\ \(\mathit{ref}\) & = reference signal plan \\ \(\alpha_{sg}\) & = weighting of the signal group sg \\ \(D_{sg}\) & = sum of delay at signal group sg over time horizon considered \\ \(\Delta\) & = deviation of control alternative sp from ref \\ \(\beta\) & = weighting of deviation from ref \\ \end{tabular}   
From this formula, the waiting times of each vehicle are calculated depending on the management scenario, and the scenario with the lowest total waiting time of all vehicles is selected as the optimal one. The only element in the EPICS module that can influence the priority of individual signal groups is the weight factor \(\alpha_{\text{sg}}\).